Revision as of 16:33, 24 March 2011

PDE and Geometric Analysis Seminar

The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

Seminar Schedule Spring 2011

date	speaker	title	host(s)
Jan 24	Bing Wang (Princeton)	The Kaehler Ricci flow on Fano manifold	Viaclovsky
Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)	Francois Hamel (Marseille)	Optimization of eigenvalues of non-symmetric elliptic operators	Zlatos
Mar 28	Juraj Foldes (Vanderbilt)	Symmetry properties of parabolic problems and their applications	Zlatos
Date TBA	Mikhail Feldman (UW Madison)	TBA	Local speaker
Date TBA	Sigurd Angenent (UW Madison)	TBA	Local speaker

Seminar Schedule Fall 2010

date	speaker	title	host(s)
Sept 13	Fausto Ferrari (Bologna)	Semilinear PDEs and some symmetry properties of stable solutions	Feldman
Sept 27	Arshak Petrosyan (Purdue)	Nonuniqueness in a free boundary problem from combustion	Feldman
Oct 7, Thursday, 4:30 pm, Room: 901 Van Vleck. Special day, time & room.	Changyou Wang (U. of Kentucky)	Phase transition for higher dimensional wells	Feldman
Oct 11	Philippe LeFloch (Paris VI)	Kinetic relations for undercompressive shock waves and propagating phase boundaries	Feldman
Oct 29 Friday 2:30pm, Room: B115 Van Vleck. Special day, time & room.	Irina Mitrea (IMA)	Boundary Value Problems for Higher Order Differential Operators	WiMaW
Nov 1	Panagiota Daskalopoulos (Columbia U)	Ancient solutions to geometric flows	Feldman
Nov 8	Maria Gualdani (UT Austin)	A nonlinear diffusion model in mean-field games	Feldman
Nov 18 Thursday 1:20pm Room: 901 Van Vleck Special day & time.	Hiroshi Matano (Tokyo University)	Traveling waves in a sawtoothed cylinder and their homogenization limit	Angenent & Rabinowitz
Nov 29	Ian Tice (Brown University)	Global well-posedness and decay for the viscous surface wave problem without surface tension	Feldman
Dec. 8 Wed 2:25pm, Room: 901 Van Vleck. Special day, time & room.	Hoai Minh Nguyen (NYU-Courant Institute)	Cloaking via change of variables for the Helmholtz equation	Feldman

Abstracts

Fausto Ferrari (Bologna)

Semilinear PDEs and some symmetry properties of stable solutions

I will deal with stable solutions of semilinear elliptic PDE's and some of their symmetry's properties. Moreover, I will introduce some weighted Poincaré inequalities obtained by combining the notion of stable solution with the definition of weak solution.

Arshak Petrosyan (Purdue)

Nonuniqueness in a free boundary problem from combustion

We consider a parabolic free boundary problem with a fixed gradient condition which serves as a simplified model for the propagation of premixed equidiffusional flames. We give a rigorous justification of an example due to J.L. V ́azquez that the initial data in the form of two circular humps leads to the nonuniqueness of limit solutions if the supports of the humps touch at the time of their maximal expansion.

This is a joint work with Aaron Yip.

Changyou Wang (U. of Kentucky)

Phase transition for higher dimensional wells

For a potential function [math]\displaystyle{ F }[/math] that has two global minimum sets consisting of two compact connected Riemannian submanifolds in [math]\displaystyle{ \mathbb{R}^k }[/math], we consider the singular perturbation problem:

Minimizing [math]\displaystyle{ \int \left(|\nabla u|^2+\frac{1}{\epsilon^2} F(u)\right) }[/math] under given Dirichlet boundary data.

I will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as the parameter [math]\displaystyle{ \epsilon }[/math] tends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and the energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary data. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem.

Philippe LeFloch (Paris VI)

Kinetic relations for undercompressive shock waves and propagating phase boundaries

I will discuss the existence and properties of shock wave solutions to nonlinear hyperbolic systems that are small-scale dependent and, especially, contain undercompressive shock waves or propagating phase boundaries. Regularization-sensitive patterns often arise in continuum physics, especially in complex fluid flows. The so-called kinetic relation is introduced to characterize the correct dynamics of these nonclassical waves, and is tied to a higher-order regularization induced by a more complete model that takes into account additional small-scale physics. In the present lecture, I will especially explain the techniques of Riemann problems, Glimm-type scheme, and total variation functionals adapted to nonclassical shock waves.

Irina Mitrea

Boundary Value Problems for Higher Order Differential Operators

As is well known, many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator L in a domain D.

When L is a differential operator of second order a variety of tools are available for dealing with such problems including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. The situation when the differential operator has higher order (as is the case for instance with anisotropic plate bending when one deals with fourth order) stands in sharp contrast with this as only fewer options could be successfully implemented. Alberto Calderon, one of the founders of the modern theory of Singular Integral Operators, has advocated in the seventies the use of layer potentials for the treatment of higher order elliptic boundary value problems. While the layer potential method has proved to be tremendously successful in the treatment of second order problems, this approach is insufficiently developed to deal with the intricacies of the theory of higher order operators. In fact, it is largely absent from the literature dealing with such problems.

In this talk I will discuss recent progress in developing a multiple layer potential approach for the treatment of boundary value problems associated with higher order elliptic differential operators. This is done in a very general class of domains which is in the nature of best possible from the point of view of geometric measure theory.

Panagiota Daskalopoulos (Columbia U)

Ancient solutions to geometric flows

We will discuss the clasification of ancient solutions to nonlinear geometric flows. It is well known that ancient solutions appear as blow up limits at a finite time singularity of the flow. Special emphasis will be given to the 2-dimensional Ricci flow. In this case we will show that ancient compact solution is either the Einstein (trivial) or one of the King-Rosenau solutions.

Maria Gualdani (UT Austin)

A nonlinear diffusion model in mean-field games

We present an overview of mean-field games theory and show recent results on a free boundary value problem, which models price formation dynamics. In such model, the price is formed through a game among infinite number of agents. Existence and regularity results, as well as linear stability, will be shown.

Hiroshi Matano (Tokyo University)

Traveling waves in a sawtoothed cylinder and their homogenization limit

My talk is concerned with a curvature-dependent motion of plane curves in a two-dimensional cylinder with spatially undulating boundary. In other words, the boundary has many bumps and we assume that the bumps are aligned in a spatially recurrent manner.

The goal is to study how the average speed of the traveling wave depends on the geometry of the domain boundary. More specifically, we consider the homogenization problem as the boundary undulation becomes finer and finer, and determine the homogenization limit of the average speed and the limit profile of the traveling waves. Quite surprisingly, this homogenized speed depends only on the maximal opening angles of the domain boundary and no other geometrical features are relevant.

Next we consider the special case where the boundary undulation is quasi-periodic with m independent frequencies. We show that the rate of convergence to the homogenization limit depends on this number m.

This is joint work with Bendong Lou and Ken-Ichi Nakamura.

Ian Tice (Brown University)

Global well-posedness and decay for the viscous surface wave problem without surface tension

We study the incompressible, gravity-driven Navier-Stokes equations in three dimensional domains with free upper boundaries and fixed lower boundaries, in both the horizontally periodic and non-periodic settings. The effect of surface tension is not included. We employ a novel two-tier nonlinear energy method that couples the boundedness of certain high-regularity norms to the algebraic decay of lower-regularity norms. The algebraic decay allows us to balance the growth of the highest order derivatives of the free surface function, which then allows us to derive a priori estimates for solutions. We then prove local well-posedness in our energy space, which yields global well-posedness and decay. The novel LWP theory is established through the study of the linear Stokes problem in moving domains. This is joint work with Yan Guo.

Hoai Minh Nguyen (NYU-Courant Institute)

Cloaking via change of variables for the Helmholtz equation

A region of space is cloaked for a class of measurements if observers are not only unaware of its contents, but also unaware of the presence of the cloak using such measurements. One approach to cloaking is the change of variables scheme introduced by Greenleaf, Lassas, and Uhlmann for electrical impedance tomography and by Pendry, Schurig, and Smith for the Maxwell equation. They used a singular change of variables which blows up a point into the cloaked region. To avoid this singularity, various regularized schemes have been proposed. In this talk I present results related to cloaking via change of variables for the Helmholtz equation using the natural regularized scheme introduced by Kohn, Shen, Vogelius, and Weintein, where the authors used a transformation which blows up a small ball instead of a point into the cloaked region. I will discuss the degree of invisibility for a finite range or the full range of frequencies, and the possibility of achieving perfect cloaking. If time permits, I will mention some results related to the wave equation.

Bing Wang (Princeton)

The Kaehler Ricci flow on Fano manifold

We show the convergence of the Kaehler Ricci flow on every 2-dimensional Fano manifold which admits big [math]\displaystyle{ \alpha_{\nu, 1} }[/math] or [math]\displaystyle{ \alpha_{\nu, 2} }[/math] (Tian's invariants). Our method also works for 2-dimensional Fano orbifolds. Since Tian's invariants can be calculated by algebraic geometry method, our convergence theorem implies that one can find new Kaehler Einstein metrics on orbifolds by calculating Tian's invariants. An essential part of the proof is to confirm the Hamilton-Tian conjecture in complex dimension 2.

Francois Hamel (Marseille)

Optimization of eigenvalues of non-symmetric elliptic operators

The talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of [math]\displaystyle{ R^n }[/math]. To each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new symmetrization technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.

Juraj Foldes (Vanderbilt)

Symmetry properties of parabolic problems and their applications

Positive solutions of nonlinear parabolic problems can have a very complex behavior. However, assuming certain symmetry conditions, it is possible to prove that the solutions converge to the space of symmetric functions. We show that this property is 'stable'; more specifically if the symmetry conditions are replaced by asymptotically symmetric ones, the solutions still approach the space of symmetric functions. As an application, we show new results on convergence of solutions to a single equilibrium.

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14	0.1575	2454992	MediaWiki\Page\ParserOutputAccess->getParserOutput( $page = class WikiPage { protected $mTitle = class Title { private $mTextform = 'PDE Geometric Analysis seminar'; private $mUrlform = 'PDE_Geometric_Analysis_seminar'; private $mDbkeyform = 'PDE_Geometric_Analysis_seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 82; protected $mLatestID = 25605; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'PDE Geometric Analysis seminar'; protected $mLength = 62882; public $mRedirect = FALSE; private $mHasSubpages = NULL; private $mPageLanguage = [...]; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; 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protected $mLanguage = NULL; protected $mLinksUpdated = '20231117212331'; private $derivedDataUpdater = NULL }, $parserOptions = class ParserOptions { private $options = ['dateformat' => 'default', 'speculativeRevId' => NULL, 'speculativePageId' => NULL, 'interfaceMessage' => FALSE, 'targetLanguage' => NULL, 'removeComments' => TRUE, 'suppressTOC' => FALSE, 'enableLimitReport' => FALSE, 'preSaveTransform' => TRUE, 'isPreview' => FALSE, 'isSectionPreview' => FALSE, 'printable' => FALSE, 'allowUnsafeRawHtml' => TRUE, 'wrapclass' => 'mw-parser-output', 'currentRevisionRecordCallback' => class Closure { ... }, 'templateCallback' => [...], 'speculativeRevIdCallback' => class Closure { ... }, 'speculativePageIdCallback' => class Closure { ... }, 'interwikiMagic' => TRUE, 'allowExternalImages' => FALSE, 'allowExternalImagesFrom' => '', 'enableImageWhitelist' => FALSE, 'allowSpecialInclusion' => TRUE, 'maxIncludeSize' => 2097152, 'maxPPNodeCount' => 1000000, 'maxPPExpandDepth' => 100, 'maxTemplateDepth' => 100, 'expensiveParserFunctionLimit' => 100, 'externalLinkTarget' => FALSE, 'cleanSignatures' => TRUE, 'disableContentConversion' => FALSE, 'disableTitleConversion' => FALSE, 'magicISBNLinks' => FALSE, 'magicPMIDLinks' => FALSE, 'magicRFCLinks' => FALSE, 'thumbsize' => 5, 'userlang' => class LanguageEn { ... }]; private $mTimestamp = NULL; private $mUser = class User { public $mId = 0; public $mName = '18.206.13.203'; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20231129054140'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = 'default'; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $onAccessCallback = [0 => class ParserOutput { ... }, 1 => 'recordOption']; private $redirectTarget = NULL; private $mExtraKey = '' }, $revision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 1880; protected $mPageId = 82; protected $mUser = class MediaWiki\User\UserIdentityValue { private $id = 52; private $name = 'Zlatos'; private $wikiId = FALSE }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20110324163310'; protected $mDeleted = 0; protected $mSize = 13566; protected $mSha1 = NULL; protected $mParentId = 1840; protected $mComment = class CommentStoreComment { public $id = '1'; public $text = ''; public $message = class RawMessage { ... }; public $data = NULL }; protected $mPage = class Title { private $mTextform = 'PDE Geometric Analysis seminar'; private $mUrlform = 'PDE_Geometric_Analysis_seminar'; private $mDbkeyform = 'PDE_Geometric_Analysis_seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 82; protected $mLatestID = 25605; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'PDE Geometric Analysis seminar'; protected $mLength = 62882; public $mRedirect = FALSE; private $mHasSubpages = NULL; private $mPageLanguage = [...]; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; protected $mSlots = class MediaWiki\Revision\RevisionSlots { protected $slots = [...] }; protected $mCurrent = FALSE }, $options = 0 )	.../WikiPage.php:1290
15	0.1585	2456832	PoolCounterWork->execute( $skipcache = ??? )	.../ParserOutputAccess.php:299
16	0.1585	2457024	PoolWorkArticleViewOld->doWork( )	.../PoolCounterWork.php:162
17	0.1585	2457280	PoolWorkArticleView->renderRevision( )	.../PoolWorkArticleViewOld.php:66
18	0.1586	2460288	MediaWiki\Revision\RenderedRevision->getRevisionParserOutput( $hints = ??? )	.../PoolWorkArticleView.php:91
19	0.1587	2460288	call_user_func:{/var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php:199}( $callback = class Closure { public $this = class MediaWiki\Revision\RevisionRenderer { private $saveParseLogger = class MediaWiki\Logger\LegacyLogger { ... }; private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $roleRegistery = class MediaWiki\Revision\SlotRoleRegistry { ... }; private $contentRenderer = class MediaWiki\Content\Renderer\ContentRenderer { ... }; private $dbDomain = FALSE }; public $parameter = ['$rrev' => '<required>', '$hints' => '<required>'] }, $args = class MediaWiki\Revision\RenderedRevision { private $revision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 1880; protected $mPageId = 82; protected $mUser = class MediaWiki\User\UserIdentityValue { ... }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20110324163310'; protected $mDeleted = 0; protected $mSize = 13566; protected $mSha1 = NULL; protected $mParentId = 1840; protected $mComment = class CommentStoreComment { ... }; protected $mPage = class Title { ... }; protected $mSlots = class MediaWiki\Revision\RevisionSlots { ... }; protected $mCurrent = FALSE }; private $options = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $audience = 3; private $performer = NULL; private $revisionOutput = NULL; private $slotsOutput = []; private $combineOutput = class Closure { public $this = class MediaWiki\Revision\RevisionRenderer { ... }; public $parameter = [...] }; private $saveParseLogger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'SaveParse'; private $minimumLevel = 999; private $isDB = FALSE }; private $contentRenderer = class MediaWiki\Content\Renderer\ContentRenderer { private $contentHandlerFactory = class MediaWiki\Content\ContentHandlerFactory { ... } } }, [] )	.../RenderedRevision.php:199
20	0.1587	2460360	MediaWiki\Revision\RevisionRenderer->MediaWiki\Revision\{closure:/var/www/wiki_mediawiki-1.39.3/includes/Revision/RevisionRenderer.php:157-159}( $rrev = class MediaWiki\Revision\RenderedRevision { private $revision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 1880; protected $mPageId = 82; protected $mUser = class MediaWiki\User\UserIdentityValue { ... }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20110324163310'; protected $mDeleted = 0; protected $mSize = 13566; protected $mSha1 = NULL; protected $mParentId = 1840; protected $mComment = class CommentStoreComment { ... }; protected $mPage = class Title { ... }; protected $mSlots = class MediaWiki\Revision\RevisionSlots { ... }; protected $mCurrent = FALSE }; private $options = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $audience = 3; private $performer = NULL; private $revisionOutput = NULL; private $slotsOutput = []; private $combineOutput = class Closure { public $this = class MediaWiki\Revision\RevisionRenderer { ... }; public $parameter = [...] }; private $saveParseLogger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'SaveParse'; private $minimumLevel = 999; private $isDB = FALSE }; private $contentRenderer = class MediaWiki\Content\Renderer\ContentRenderer { private $contentHandlerFactory = class MediaWiki\Content\ContentHandlerFactory { ... } } }, $hints = [] )	.../RenderedRevision.php:199
21	0.1587	2460360	MediaWiki\Revision\RevisionRenderer->combineSlotOutput( $rrev = class MediaWiki\Revision\RenderedRevision { private $revision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 1880; protected $mPageId = 82; protected $mUser = class MediaWiki\User\UserIdentityValue { ... }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20110324163310'; protected $mDeleted = 0; protected $mSize = 13566; protected $mSha1 = NULL; protected $mParentId = 1840; protected $mComment = class CommentStoreComment { ... }; protected $mPage = class Title { ... }; protected $mSlots = class MediaWiki\Revision\RevisionSlots { ... }; protected $mCurrent = FALSE }; private $options = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $audience = 3; private $performer = NULL; private $revisionOutput = NULL; private $slotsOutput = []; private $combineOutput = class Closure { public $this = class MediaWiki\Revision\RevisionRenderer { ... }; public $parameter = [...] }; private $saveParseLogger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'SaveParse'; private $minimumLevel = 999; private $isDB = FALSE }; private $contentRenderer = class MediaWiki\Content\Renderer\ContentRenderer { private $contentHandlerFactory = class MediaWiki\Content\ContentHandlerFactory { ... } } }, $hints = [] )	.../RevisionRenderer.php:158
22	0.1594	2461064	MediaWiki\Revision\RenderedRevision->getSlotParserOutput( $role = 'main', $hints = [] )	.../RevisionRenderer.php:221
23	0.1595	2460416	MediaWiki\Revision\RenderedRevision->getSlotParserOutputUncached( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = '= PDE and Geometric Analysis Seminar =\n\nThe seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.\n\n== Seminar Schedule Spring 2011 ==\n{\| cellpadding="8"\n!align="left" \| date \n!align="left" \| speaker\n!align="left" \| title\n!align="left" \| host(s)\n\|-\n\|Jan 24\n\|Bing Wang (Princeton)\n\|[[#Bing Wang (Princeton)\|\n \'\'The Kaehler Ricci flow on Fano manifold \'\']]\n\|Viaclovsky\n\|-\n\|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)\n\|Francois Hamel (Marseille)'...; private $redirectTargetAndText = [0 => NULL, 1 => '= PDE and Geometric Analysis Seminar =\n\nThe seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.\n\n== Seminar Schedule Spring 2011 ==\n{\| cellpadding="8"\n!align="left" \| date \n!align="left" \| speaker\n!align="left" \| title\n!align="left" \| host(s)\n\|-\n\|Jan 24\n\|Bing Wang (Princeton)\n\|[[#Bing Wang (Princeton)\|\n \'\'The Kaehler Ricci flow on Fano manifold \'\']]\n\|Viaclovsky\n\|-\n\|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)\n\|Francois Hamel (Marseille)'...]; private $preSaveTransformFlags = [] }, $withHtml = TRUE )	.../RenderedRevision.php:237
24	0.1595	2460416	MediaWiki\Content\Renderer\ContentRenderer->getParserOutput( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = '= PDE and Geometric Analysis Seminar =\n\nThe seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.\n\n== Seminar Schedule Spring 2011 ==\n{\| cellpadding="8"\n!align="left" \| date \n!align="left" \| speaker\n!align="left" \| title\n!align="left" \| host(s)\n\|-\n\|Jan 24\n\|Bing Wang (Princeton)\n\|[[#Bing Wang (Princeton)\|\n \'\'The Kaehler Ricci flow on Fano manifold \'\']]\n\|Viaclovsky\n\|-\n\|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)\n\|Francois Hamel (Marseille)'...; private $redirectTargetAndText = [0 => NULL, 1 => '= PDE and Geometric Analysis Seminar =\n\nThe seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.\n\n== Seminar Schedule Spring 2011 ==\n{\| cellpadding="8"\n!align="left" \| date \n!align="left" \| speaker\n!align="left" \| title\n!align="left" \| host(s)\n\|-\n\|Jan 24\n\|Bing Wang (Princeton)\n\|[[#Bing Wang (Princeton)\|\n \'\'The Kaehler Ricci flow on Fano manifold \'\']]\n\|Viaclovsky\n\|-\n\|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)\n\|Francois Hamel (Marseille)'...]; private $preSaveTransformFlags = [] }, $page = class Title { private $mTextform = 'PDE Geometric Analysis seminar'; private $mUrlform = 'PDE_Geometric_Analysis_seminar'; private $mDbkeyform = 'PDE_Geometric_Analysis_seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 82; protected $mLatestID = 25605; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'PDE Geometric Analysis seminar'; protected $mLength = 62882; public $mRedirect = FALSE; private $mHasSubpages = NULL; private $mPageLanguage = [0 => 'en', 1 => 'en']; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = ['mTextform' => [...], 'mUrlform' => [...], 'mDbkeyform' => [...], 'mNamespace' => [...], 'mInterwiki' => [...], 'mFragment' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE }, $revId = 1880, $parserOptions = class ParserOptions { private $options = ['dateformat' => 'default', 'speculativeRevId' => NULL, 'speculativePageId' => NULL, 'interfaceMessage' => FALSE, 'targetLanguage' => NULL, 'removeComments' => TRUE, 'suppressTOC' => FALSE, 'enableLimitReport' => FALSE, 'preSaveTransform' => TRUE, 'isPreview' => FALSE, 'isSectionPreview' => FALSE, 'printable' => FALSE, 'allowUnsafeRawHtml' => TRUE, 'wrapclass' => 'mw-parser-output', 'currentRevisionRecordCallback' => class Closure { ... }, 'templateCallback' => [...], 'speculativeRevIdCallback' => class Closure { ... }, 'speculativePageIdCallback' => class Closure { ... }, 'interwikiMagic' => TRUE, 'allowExternalImages' => FALSE, 'allowExternalImagesFrom' => '', 'enableImageWhitelist' => FALSE, 'allowSpecialInclusion' => TRUE, 'maxIncludeSize' => 2097152, 'maxPPNodeCount' => 1000000, 'maxPPExpandDepth' => 100, 'maxTemplateDepth' => 100, 'expensiveParserFunctionLimit' => 100, 'externalLinkTarget' => FALSE, 'cleanSignatures' => TRUE, 'disableContentConversion' => FALSE, 'disableTitleConversion' => FALSE, 'magicISBNLinks' => FALSE, 'magicPMIDLinks' => FALSE, 'magicRFCLinks' => FALSE, 'thumbsize' => 5, 'userlang' => class LanguageEn { ... }]; private $mTimestamp = NULL; private $mUser = class User { public $mId = 0; public $mName = '18.206.13.203'; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20231129054140'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = 'default'; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $onAccessCallback = [0 => class ParserOutput { ... }, 1 => 'recordOption']; private $redirectTarget = NULL; private $mExtraKey = '' }, $generateHtml = TRUE )	.../RenderedRevision.php:265
25	0.1596	2460528	ContentHandler->getParserOutput( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = '= PDE and Geometric Analysis Seminar =\n\nThe seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.\n\n== Seminar Schedule Spring 2011 ==\n{\| cellpadding="8"\n!align="left" \| date \n!align="left" \| speaker\n!align="left" \| title\n!align="left" \| host(s)\n\|-\n\|Jan 24\n\|Bing Wang (Princeton)\n\|[[#Bing Wang (Princeton)\|\n \'\'The Kaehler Ricci flow on Fano manifold \'\']]\n\|Viaclovsky\n\|-\n\|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)\n\|Francois Hamel (Marseille)'...; private $redirectTargetAndText = [0 => NULL, 1 => '= PDE and Geometric Analysis Seminar =\n\nThe seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.\n\n== Seminar Schedule Spring 2011 ==\n{\| cellpadding="8"\n!align="left" \| date \n!align="left" \| speaker\n!align="left" \| title\n!align="left" \| host(s)\n\|-\n\|Jan 24\n\|Bing Wang (Princeton)\n\|[[#Bing Wang (Princeton)\|\n \'\'The Kaehler Ricci flow on Fano manifold \'\']]\n\|Viaclovsky\n\|-\n\|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)\n\|Francois Hamel (Marseille)'...]; private $preSaveTransformFlags = [] }, $cpoParams = class MediaWiki\Content\Renderer\ContentParseParams { private $page = class Title { private $mTextform = 'PDE Geometric Analysis seminar'; private $mUrlform = 'PDE_Geometric_Analysis_seminar'; private $mDbkeyform = 'PDE_Geometric_Analysis_seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 82; protected $mLatestID = 25605; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'PDE Geometric Analysis seminar'; protected $mLength = 62882; public $mRedirect = FALSE; private $mHasSubpages = NULL; private $mPageLanguage = [...]; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $revId = 1880; private $parserOptions = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $generateHtml = TRUE } )	.../ContentRenderer.php:47
26	0.1597	2462624	WikitextContentHandler->fillParserOutput( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = '= PDE and Geometric Analysis Seminar =\n\nThe seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.\n\n== Seminar Schedule Spring 2011 ==\n{\| cellpadding="8"\n!align="left" \| date \n!align="left" \| speaker\n!align="left" \| title\n!align="left" \| host(s)\n\|-\n\|Jan 24\n\|Bing Wang (Princeton)\n\|[[#Bing Wang (Princeton)\|\n \'\'The Kaehler Ricci flow on Fano manifold \'\']]\n\|Viaclovsky\n\|-\n\|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)\n\|Francois Hamel (Marseille)'...; private $redirectTargetAndText = [0 => NULL, 1 => '= PDE and Geometric Analysis Seminar =\n\nThe seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.\n\n== Seminar Schedule Spring 2011 ==\n{\| cellpadding="8"\n!align="left" \| date \n!align="left" \| speaker\n!align="left" \| title\n!align="left" \| host(s)\n\|-\n\|Jan 24\n\|Bing Wang (Princeton)\n\|[[#Bing Wang (Princeton)\|\n \'\'The Kaehler Ricci flow on Fano manifold \'\']]\n\|Viaclovsky\n\|-\n\|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)\n\|Francois Hamel (Marseille)'...]; private $preSaveTransformFlags = [] }, $cpoParams = class MediaWiki\Content\Renderer\ContentParseParams { private $page = class Title { private $mTextform = 'PDE Geometric Analysis seminar'; private $mUrlform = 'PDE_Geometric_Analysis_seminar'; private $mDbkeyform = 'PDE_Geometric_Analysis_seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 82; protected $mLatestID = 25605; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'PDE Geometric Analysis seminar'; protected $mLength = 62882; public $mRedirect = FALSE; private $mHasSubpages = NULL; private $mPageLanguage = [...]; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $revId = 1880; private $parserOptions = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; private $generateHtml = TRUE }, $parserOutput = class ParserOutput { protected $mParseUsedOptions = []; protected $mCacheTime = ''; protected $mCacheExpiry = NULL; protected $mCacheRevisionId = NULL; private $mText = NULL; private $mLanguageLinks = []; private $mCategories = []; private $mIndicators = []; private $mTitleText = ''; private $mLinks = []; private $mLinksSpecial = []; private $mTemplates = []; private $mTemplateIds = []; private $mImages = []; private $mFileSearchOptions = []; private $mExternalLinks = []; private $mInterwikiLinks = []; private $mNewSection = FALSE; private $mHideNewSection = FALSE; private $mNoGallery = FALSE; private $mHeadItems = []; private $mModules = []; private $mModuleStyles = []; private $mJsConfigVars = []; private $mOutputHooks = []; private $mWarnings = []; private $mWarningMsgs = []; private $mSections = []; private $mProperties = []; private $mTOCHTML = ''; private $mTimestamp = NULL; private $mEnableOOUI = FALSE; private $mIndexSet = FALSE; private $mNoIndexSet = FALSE; private $mExtensionData = []; private $mLimitReportData = []; private $mLimitReportJSData = []; private $mCacheMessage = ''; private $mParseStartTime = []; private $mPreventClickjacking = FALSE; private $mExtraScriptSrcs = []; private $mExtraDefaultSrcs = []; private $mExtraStyleSrcs = []; private $mFlags = []; private $mSpeculativeRevId = NULL; private $speculativePageIdUsed = NULL; private $revisionTimestampUsed = NULL; private $revisionUsedSha1Base36 = NULL; private $mWrapperDivClasses = []; private $mMaxAdaptiveExpiry = INF } )	.../ContentHandler.php:1720
27	0.1597	2462624	Parser->parse( $text = '= PDE and Geometric Analysis Seminar =\n\nThe seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.\n\n== Seminar Schedule Spring 2011 ==\n{\| cellpadding="8"\n!align="left" \| date \n!align="left" \| speaker\n!align="left" \| title\n!align="left" \| host(s)\n\|-\n\|Jan 24\n\|Bing Wang (Princeton)\n\|[[#Bing Wang (Princeton)\|\n \'\'The Kaehler Ricci flow on Fano manifold \'\']]\n\|Viaclovsky\n\|-\n\|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)\n\|Francois Hamel (Marseille)'..., $page = class Title { private $mTextform = 'PDE Geometric Analysis seminar'; private $mUrlform = 'PDE_Geometric_Analysis_seminar'; private $mDbkeyform = 'PDE_Geometric_Analysis_seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 82; protected $mLatestID = 25605; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'PDE Geometric Analysis seminar'; protected $mLength = 62882; public $mRedirect = FALSE; private $mHasSubpages = NULL; private $mPageLanguage = [0 => 'en', 1 => 'en']; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = ['mTextform' => [...], 'mUrlform' => [...], 'mDbkeyform' => [...], 'mNamespace' => [...], 'mInterwiki' => [...], 'mFragment' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE }, $options = class ParserOptions { private $options = ['dateformat' => 'default', 'speculativeRevId' => NULL, 'speculativePageId' => NULL, 'interfaceMessage' => FALSE, 'targetLanguage' => NULL, 'removeComments' => TRUE, 'suppressTOC' => FALSE, 'enableLimitReport' => FALSE, 'preSaveTransform' => TRUE, 'isPreview' => FALSE, 'isSectionPreview' => FALSE, 'printable' => FALSE, 'allowUnsafeRawHtml' => TRUE, 'wrapclass' => 'mw-parser-output', 'currentRevisionRecordCallback' => class Closure { ... }, 'templateCallback' => [...], 'speculativeRevIdCallback' => class Closure { ... }, 'speculativePageIdCallback' => class Closure { ... }, 'interwikiMagic' => TRUE, 'allowExternalImages' => FALSE, 'allowExternalImagesFrom' => '', 'enableImageWhitelist' => FALSE, 'allowSpecialInclusion' => TRUE, 'maxIncludeSize' => 2097152, 'maxPPNodeCount' => 1000000, 'maxPPExpandDepth' => 100, 'maxTemplateDepth' => 100, 'expensiveParserFunctionLimit' => 100, 'externalLinkTarget' => FALSE, 'cleanSignatures' => TRUE, 'disableContentConversion' => FALSE, 'disableTitleConversion' => FALSE, 'magicISBNLinks' => FALSE, 'magicPMIDLinks' => FALSE, 'magicRFCLinks' => FALSE, 'thumbsize' => 5, 'userlang' => class LanguageEn { ... }]; private $mTimestamp = NULL; private $mUser = class User { public $mId = 0; public $mName = '18.206.13.203'; public $mActorId = NULL; public $mRealName = ''; public $mEmail = ''; public $mTouched = '1'; protected $mQuickTouched = NULL; protected $mToken = NULL; public $mEmailAuthenticated = NULL; protected $mEmailToken = ''; protected $mEmailTokenExpires = NULL; protected $mRegistration = '20231129054140'; protected $mLoadedItems = TRUE; public $mFrom = 'session'; protected $mDatePreference = 'default'; private $mBlockedby = -1; protected $mHash = FALSE; protected $mBlockreason = NULL; protected $mGlobalBlock = NULL; protected $mLocked = NULL; private $mHideName = NULL; private $mRequest = class WebRequest { ... }; private $mBlock = NULL; private $mBlockedFromCreateAccount = FALSE; protected $queryFlagsUsed = 0; private $mThisAsAuthority = class MediaWiki\Permissions\UserAuthority { ... }; private $isTemp = NULL }; private $onAccessCallback = [0 => class ParserOutput { ... }, 1 => 'recordOption']; private $redirectTarget = NULL; private $mExtraKey = '' }, $linestart = TRUE, $clearState = TRUE, $revid = 1880 )	.../WikitextContentHandler.php:301
28	0.1598	2469896	Parser->internalParse( $text = '= PDE and Geometric Analysis Seminar =\n\nThe seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.\n\n== Seminar Schedule Spring 2011 ==\n{\| cellpadding="8"\n!align="left" \| date \n!align="left" \| speaker\n!align="left" \| title\n!align="left" \| host(s)\n\|-\n\|Jan 24\n\|Bing Wang (Princeton)\n\|[[#Bing Wang (Princeton)\|\n \'\'The Kaehler Ricci flow on Fano manifold \'\']]\n\|Viaclovsky\n\|-\n\|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)\n\|Francois Hamel (Marseille)'..., $isMain = ???, $frame = ??? )	.../Parser.php:724
29	0.1599	2469928	Parser->replaceVariables( $text = '= PDE and Geometric Analysis Seminar =\n\nThe seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.\n\n== Seminar Schedule Spring 2011 ==\n{\| cellpadding="8"\n!align="left" \| date \n!align="left" \| speaker\n!align="left" \| title\n!align="left" \| host(s)\n\|-\n\|Jan 24\n\|Bing Wang (Princeton)\n\|[[#Bing Wang (Princeton)\|\n \'\'The Kaehler Ricci flow on Fano manifold \'\']]\n\|Viaclovsky\n\|-\n\|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)\n\|Francois Hamel (Marseille)'..., $frame = ???, $argsOnly = ??? )	.../Parser.php:1610
30	0.1630	2529776	PPFrame_Hash->expand( $root = class PPNode_Hash_Tree { public $name = 'root'; private $rawChildren = [0 => [...], 1 => '\n\nThe seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.\n\n', 2 => [...], 3 => '\n{\| cellpadding="8"\n!align="left" \| date \n!align="left" \| speaker\n!align="left" \| title\n!align="left" \| host(s)\n\|-\n\|Jan 24\n\|Bing Wang (Princeton)\n\|', 4 => '[[#Bing Wang (Princeton)\|\n \'\'The Kaehler Ricci flow on Fano manifold \'\']]\n\|Viaclovsky\n\|-\n\|Mar 15 (TUESDAY) at 4pm in B139 (joint wit Analysis)\n\|Francois Hamel (Marseille)\n\|', 5 => '[[#Francois Hamel (Marseille)\|\n \'\'Optimization of eigenvalues of non-symmetric elliptic operators\'\']]\n\|Zlatos\n\|-\n\|Mar 28\n\|Juraj Foldes (Vanderbilt)\n\|', 6 => '[[#Juraj Foldes (Vanderbilt)\|\n \'\'Symmetry properties of parabolic problems and their applications\'\']]\n\|Zlatos\n\|-\n\|Date TBA\n\|Mikhail Feldman (UW Madison)\n\|\'\'TBA\'\'\n\|Local speaker\n\|-\n\|Date TBA\n\|Sigurd Angenent (UW Madison)\n\|\'\'TBA\'\'\n\|Local speaker\n\|-\n\|}\n', 7 => [...], 8 => '\n{\| cellpadding="8"\n!align="left" \| date \n!align="left" \| speaker\n!align="left" \| title\n!align="left" \| host(s)\n\|-\n\|Sept 13\n\|Fausto Ferrari (Bologna)\n\|', 9 => '[[#Fausto Ferrari (Bologna)\|\n\'\'Semilinear PDEs and some symmetry properties of stable solutions\'\']]\n\|Feldman\n\|-\n\|Sept 27\n\|Arshak Petrosyan (Purdue)\n\|', 10 => '[[#Arshak Petrosyan (Purdue)\|\n\'\'Nonuniqueness in a free boundary problem from combustion\'\']]\n\|Feldman\n\|-\n\|Oct 7, Thursday, 4:30 pm, Room: 901 Van Vleck. \'\'\'Special day, time & room.\'\'\'\n\|Changyou Wang (U. of Kentucky)\n\|', 11 => '[[#Changyou Wang (U. of Kentucky)\|\n\'\'Phase transition for higher dimensional wells\'\']]\n\|Feldman\n\|-\n\|Oct 11\n\|Philippe LeFloch (Paris VI)\n\|', 12 => '[[#Philippe LeFloch (Paris VI)\|\n\'\'Kinetic relations for undercompressive shock waves and propagating phase boundaries\'\']]\n\|Feldman\n\|-\n\|Oct 29 Friday 2:30pm, Room: B115 Van Vleck. \'\'\'Special day, time & room.\'\'\'\n\|[http://www.ima.umn.edu/~imitrea/ Irina Mitrea] (IMA)\n\|', 13 => '[[#Irina Mitrea \|\n\'\'Boundary Value Problems for Higher Order Differential Operators\'\']]\n\|[https://www.math.wisc.edu/~wimaw/ WiMaW]\n\|-\n\|-\n\|Nov 1\n\|Panagiota Daskalopoulos (Columbia U)\n\|', 14 => '[[#Panagiota Daskalopoulos (Columbia U)\|\n\'\'Ancient solutions to geometric flows\'\']]\n\|Feldman\n\|-\n\|Nov 8\n\|Maria Gualdani (UT Austin)\n\|', 15 => '[[#Maria Gualdani (UT Austin)\|\n\'\'A nonlinear diffusion model in mean-field games\'\']]\n\|Feldman\n\|-\n\|Nov 18 Thursday 1:20pm Room: 901 Van Vleck \'\'\'Special day & time.\'\'\'\n\|Hiroshi Matano (Tokyo University) \n\|', 16 => '[[#Hiroshi Matano (Tokyo University)\|\n\'\'Traveling waves in a sawtoothed cylinder and their homogenization limit\'\']]\n\|Angenent & Rabinowitz\n\|-\n\|Nov 29\n\|Ian Tice (Brown University)\n\|', 17 => '[[#Ian Tice (Brown University)\|\n\'\'Global well-posedness and decay for the viscous surface wave\nproblem without surface tension\'\']]\n\|Feldman\n\|-\n\|Dec. 8 Wed 2:25pm, Room: 901 Van Vleck. \'\'\'Special day, time & room.\'\'\'\n\|Hoai Minh Nguyen (NYU-Courant Institute)\n\|', 18 => '[[#Hoai Minh Nguyen (NYU-Courant Institute)\|\n\'\'Cloaking via change of variables for the Helmholtz equation\'\']]\n\|Feldman\n\|-\n\|}\n\n', 19 => [...], 20 => '\n', 21 => [...], 22 => '\n\'\'Semilinear PDEs and some symmetry properties of stable solutions\'\'\n\nI will deal with stable solutions of semilinear elliptic PDE\'s \nand some of their symmetry\'s properties. Moreover, I will introduce some weighted Poincaré inequalities obtained by combining the notion of stable solution with the definition of weak solution.\n\n', 23 => [...], 24 => '\n\'\'Nonuniqueness in a free boundary problem from combustion\'\'\n\nWe consider a parabolic free boundary problem with a fixed gradient condition\nwhich serves as a simplified model for the propagation of premixed equidiffusional\nflames. We give a rigorous justification of an example due to J.L. V ́azquez that \nthe initial data in the form of two circular humps leads to the nonuniqueness of limit \nsolutions if the supports of the humps touch at the time of their maximal expansion.\n\nThis is a joint work with Aaro'..., 25 => [...], 26 => '\n\'\'Phase transition for higher dimensional wells\'\'\n\nFor a potential function ', 27 => [...], 28 => ' that has two global minimum sets consisting of two compact connected\nRiemannian submanifolds in ', 29 => [...], 30 => ', we consider the singular perturbation problem:\n\nMinimizing ', 31 => [...], 32 => ' under given Dirichlet boundary data.\n\nI will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as the parameter ', 33 => [...], 34 => '\ntends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and\nthe energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary\ndata. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem.\n\n', 35 => [...], 36 => '\n\'\'Kinetic relations for undercompressive shock waves and propagating phase boundaries\'\'\n\nI will discuss the existence and properties of shock wave solutions to nonlinear hyperbolic systems that are small-scale dependent and, especially, contain undercompressive shock waves or propagating phase boundaries. Regularization-sensitive patterns often arise in continuum physics, especially in complex fluid flows. The so-called kinetic relation is introduced to characterize the correct dynamics of these nonclassic'..., 37 => [...], 38 => '\n\'\'Boundary Value Problems for Higher Order Differential Operators\'\'\n\nAs is well known, many phenomena in engineering and mathematical physics\ncan be modeled by means of boundary value problems for a certain elliptic\ndifferential operator L in a domain D.\n\nWhen L is a differential operator of second order a variety of tools\nare available for dealing with such problems including boundary integral\nmethods,\nvariational methods, harmonic measure techniques, and methods based on\nclassical\nharmonic analysis. The '..., 39 => [...], 40 => '\n\'\'Ancient solutions to geometric flows\'\'\n\nWe will discuss the clasification of ancient solutions to nonlinear geometric flows. \nIt is well known that ancient solutions appear as blow up limits at a finite time \nsingularity of the flow.\nSpecial emphasis will be given to the 2-dimensional Ricci flow.\nIn this case we will show that ancient compact solution\nis either the Einstein (trivial) or one of the King-Rosenau solutions. \n\n', 41 => [...], 42 => '\n\'\'A nonlinear diffusion model in mean-field games\'\'\n\nWe present an overview of mean-field games theory and show \nrecent results on a free boundary value problem, which models \nprice formation dynamics. \nIn such model, the price is formed through a game among infinite number \nof agents. \nExistence and regularity results, as well as linear stability, will be shown.\n\n', 43 => [...], 44 => '\n\'\'Traveling waves in a sawtoothed cylinder and their homogenization limit\'\'\n\nMy talk is concerned with a curvature-dependent motion of plane \ncurves in a two-dimensional cylinder with spatially undulating\nboundary. In other words, the boundary has many bumps and we \nassume that the bumps are aligned in a spatially recurrent manner.\n\nThe goal is to study how the average speed of the traveling wave \ndepends on the geometry of the domain boundary. More specifically, \nwe consider the homogenization problem a'..., 45 => [...], 46 => '\n\'\'Global well-posedness and decay for the viscous surface wave\nproblem without surface tension\'\'\n\nWe study the incompressible, gravity-driven Navier-Stokes\nequations in three dimensional domains with free upper boundaries and\nfixed lower boundaries, in both the horizontally periodic and\nnon-periodic settings. The effect of surface tension is not included.\nWe employ a novel two-tier nonlinear energy method that couples the\nboundedness of certain high-regularity norms to the algebraic decay of\nlower-regular'..., 47 => [...], 48 => '\n\'\'Cloaking via change of variables for the Helmholtz equation\'\'\n\nA region of space is cloaked for a class of measurements if observers\nare not only unaware of its contents, but also unaware of the presence\nof the cloak using such measurements. One approach to cloaking is the\nchange of variables scheme introduced by Greenleaf, Lassas, and\nUhlmann for electrical impedance tomography and by Pendry, Schurig,\nand Smith for the Maxwell equation. They used a singular change of\nvariables which blows up a point in'..., 49 => [...], 50 => '\n\'\'The Kaehler Ricci flow on Fano manifold \'\'\n\nWe show the convergence of the Kaehler Ricci flow on every 2-dimensional Fano manifold which admits big ', 51 => [...], 52 => '\nor ', 53 => [...], 54 => ' (Tian\'s invariants). Our method also works for 2-dimensional Fano orbifolds.\nSince Tian\'s invariants can be calculated by algebraic geometry method, our convergence theorem implies that one can find new Kaehler Einstein metrics\non orbifolds by calculating Tian\'s invariants.\nAn essential part of the proof is to confirm the Hamilton-Tian conjecture in complex dimension 2.\n\n', 55 => [...], 56 => '\n\'\'Optimization of eigenvalues of non-symmetric elliptic operators\'\'\n\nThe talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of ', 57 => [...], 58 => '. To each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new symmetrization technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirash'..., 59 => [...], 60 => '\n\'\'Symmetry properties of parabolic problems and their applications\'\'\n\nPositive solutions of nonlinear parabolic problems can have a very complex behavior. However, assuming certain symmetry conditions, it is possible to prove that the solutions converge to the space of symmetric functions. We show that this property is \'stable\'; more specifically if the symmetry conditions are replaced by asymptotically symmetric ones, the solutions still approach the space of symmetric functions. As an application, we sh'...]; private $store = [0 => [...]]; private $index = 0 }, $flags = 0 )	.../Parser.php:2955
31	0.1632	2542480	Parser->extensionSubstitution( $params = ['name' => class PPNode_Hash_Tree { public $name = 'name'; private $rawChildren = [...]; private $store = [...]; private $index = 0 }, 'attr' => class PPNode_Hash_Tree { public $name = 'attr'; private $rawChildren = [...]; private $store = [...]; private $index = 1 }, 'inner' => class PPNode_Hash_Tree { public $name = 'inner'; private $rawChildren = [...]; private $store = [...]; private $index = 2 }, 'close' => class PPNode_Hash_Tree { public $name = 'close'; private $rawChildren = [...]; private $store = [...]; private $index = 3 }], $frame = class PPFrame_Hash { public $parser = class Parser { private $mTagHooks = [...]; private $mFunctionHooks = [...]; private $mFunctionSynonyms = [...]; private $mStripList = [...]; private $mVarCache = [...]; private $mImageParams = [...]; private $mImageParamsMagicArray = [...]; public $mMarkerIndex = 1; private $mVariables = class MagicWordArray { ... }; private $mSubstWords = class MagicWordArray { ... }; private $mExtLinkBracketedRegex = '/\\[(((?i)bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/)(?:[0-9.]+\|\\[(?i:[0-9a-f:.]+)\\]\|[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])\\p{Zs}([^\\]\\x00-\\x08\\x0a-\\x1F\\x{FFFD}]*?)\\]/Su'; private $urlUtils = class MediaWiki\Utils\UrlUtils { ... }; private $mPreprocessor = class Preprocessor_Hash { ... }; private $mOutput = class ParserOutput { ... }; private $mAutonumber = 0; private $mStripState = class StripState { ... }; private $mLinkHolders = class LinkHolderArray { ... }; private $mLinkID = 0; private $mIncludeSizes = [...]; public $mPPNodeCount = 11; public $mHighestExpansionDepth = 2; private $mTplRedirCache = [...]; public $mHeadings = [...]; private $mDoubleUnderscores = [...]; public $mExpensiveFunctionCount = 0; private $mShowToc = TRUE; private $mForceTocPosition = FALSE; private $mTplDomCache = [...]; private $mUser = NULL; public $mOptions = class ParserOptions { ... }; public $mTitle = class Title { ... }; private $mOutputType = 1; public $ot = [...]; private $mRevisionId = 1880; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 13566; private $mRevisionRecordObject = NULL; private $mLangLinkLanguages = [...]; private $currentRevisionCache = NULL; private $mInParse = '#0 /var/www/wiki_mediawiki-1.39.3/includes/parser/Parser.php(699): Parser->lock()\n#1 /var/www/wiki_mediawiki-1.39.3/includes/content/WikitextContentHandler.php(301): Parser->parse()\n#2 /var/www/wiki_mediawiki-1.39.3/includes/content/ContentHandler.php(1720): WikitextContentHandler->fillParserOutput()\n#3 /var/www/wiki_mediawiki-1.39.3/includes/content/Renderer/ContentRenderer.php(47): ContentHandler->getParserOutput()\n#4 /var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php(265): MediaWiki\\Co'...; private $mProfiler = class SectionProfiler { ... }; private $mLinkRenderer = NULL; private $magicWordFactory = class MagicWordFactory { ... }; private $contLang = class LanguageEn { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $factory = class ParserFactory { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $titleFormatter = class MediaWikiTitleCodec { ... }; private $svcOptions = class MediaWiki\Config\ServiceOptions { ... }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { ... }; private $nsInfo = class NamespaceInfo { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $badFileLookup = class MediaWiki\BadFileLookup { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $tidy = class MediaWiki\Tidy\RemexDriver { ... }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { ... }; private $trackingCategories = class TrackingCategories { ... }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; public $preprocessor = class Preprocessor_Hash { public $parser = class Parser { ... }; protected $wanCache = class WANObjectCache { ... }; protected $disableLangConversion = FALSE; protected $rules = [...]; protected $cacheThreshold = 1000 }; public $title = class Title { private $mTextform = 'PDE Geometric Analysis seminar'; private $mUrlform = 'PDE_Geometric_Analysis_seminar'; private $mDbkeyform = 'PDE_Geometric_Analysis_seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 82; protected $mLatestID = 25605; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'PDE Geometric Analysis seminar'; protected $mLength = 62882; public $mRedirect = FALSE; private $mHasSubpages = NULL; private $mPageLanguage = [...]; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; public $titleCache = [0 => 'PDE_Geometric_Analysis_seminar']; public $loopCheckHash = []; public $depth = 0; private $volatile = FALSE; private $ttl = NULL; protected $childExpansionCache = []; private $maxPPNodeCount = 1000000; private $maxPPExpandDepth = 100 }, $processNowiki = FALSE )	.../PPFrame_Hash.php:353
32	0.1633	2542984	SimpleMathJaxHooks::renderMath( $tex = 'F', $args = [], $parser = class Parser { private $mTagHooks = ['pre' => [...], 'nowiki' => [...], 'gallery' => [...], 'indicator' => [...], 'langconvert' => [...], 'math' => 'SimpleMathJaxHooks::renderMath', 'chem' => 'SimpleMathJaxHooks::renderChem', 'source' => [...], 'syntaxhighlight' => [...], 'ref' => [...], 'references' => [...]]; private $mFunctionHooks = ['ns' => [...], 'nse' => [...], 'urlencode' => [...], 'lcfirst' => [...], 'ucfirst' => [...], 'lc' => [...], 'uc' => [...], 'localurl' => [...], 'localurle' => [...], 'fullurl' => [...], 'fullurle' => [...], 'canonicalurl' => [...], 'canonicalurle' => [...], 'formatnum' => [...], 'grammar' => [...], 'gender' => [...], 'plural' => [...], 'bidi' => [...], 'numberofpages' => [...], 'numberofusers' => [...], 'numberofactiveusers' => [...], 'numberofarticles' => [...], 'numberoffiles' => [...], 'numberofadmins' => [...], 'numberingroup' => [...], 'numberofedits' => [...], 'language' => [...], 'padleft' => [...], 'padright' => [...], 'anchorencode' => [...], 'defaultsort' => [...], 'filepath' => [...], 'pagesincategory' => [...], 'pagesize' => [...], 'protectionlevel' => [...], 'protectionexpiry' => [...], 'namespace' => [...], 'namespacee' => [...], 'namespacenumber' => [...], 'talkspace' => [...], 'talkspacee' => [...], 'subjectspace' => [...], 'subjectspacee' => [...], 'pagename' => [...], 'pagenamee' => [...], 'fullpagename' => [...], 'fullpagenamee' => [...], 'rootpagename' => [...], 'rootpagenamee' => [...], 'basepagename' => [...], 'basepagenamee' => [...], 'subpagename' => [...], 'subpagenamee' => [...], 'talkpagename' => [...], 'talkpagenamee' => [...], 'subjectpagename' => [...], 'subjectpagenamee' => [...], 'pageid' => [...], 'revisionid' => [...], 'revisionday' => [...], 'revisionday2' => [...], 'revisionmonth' => [...], 'revisionmonth1' => [...], 'revisionyear' => [...], 'revisiontimestamp' => [...], 'revisionuser' => [...], 'cascadingsources' => [...], 'int' => [...], 'special' => [...], 'speciale' => [...], 'tag' => [...], 'formatdate' => [...], 'displaytitle' => [...]]; private $mFunctionSynonyms = [0 => [...], 1 => [...]]; private $mStripList = [0 => 'pre', 1 => 'nowiki', 2 => 'gallery', 3 => 'indicator', 4 => 'langconvert', 5 => 'math', 6 => 'chem', 7 => 'source', 8 => 'syntaxhighlight', 9 => 'ref', 10 => 'references']; private $mVarCache = []; private $mImageParams = []; private $mImageParamsMagicArray = []; public $mMarkerIndex = 1; private $mVariables = class MagicWordArray { public $names = [...]; private $factory = class MagicWordFactory { ... }; private $hash = [...]; private $baseRegex = NULL; private $regex = NULL }; private $mSubstWords = class MagicWordArray { public $names = [...]; private $factory = class MagicWordFactory { ... }; private $hash = NULL; private $baseRegex = [...]; private $regex = NULL }; private $mExtLinkBracketedRegex = '/\\[(((?i)bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/)(?:[0-9.]+\|\\[(?i:[0-9a-f:.]+)\\]\|[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])\\p{Zs}([^\\]\\x00-\\x08\\x0a-\\x1F\\x{FFFD}]?)\\]/Su'; private $urlUtils = class MediaWiki\Utils\UrlUtils { private $server = 'https://wiki.math.wisc.edu'; private $canonicalServer = 'https://wiki.math.wisc.edu'; private $internalServer = 'https://wiki.math.wisc.edu'; private $fallbackProtocol = 'http'; private $httpsPort = 443; private $validProtocols = [...]; private $validProtocolsCache = 'bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/'; private $validAbsoluteProtocolsCache = NULL }; private $mPreprocessor = class Preprocessor_Hash { public $parser = ...; protected $wanCache = class WANObjectCache { ... }; protected $disableLangConversion = FALSE; protected $rules = [...]; protected $cacheThreshold = 1000 }; private $mOutput = class ParserOutput { protected $mParseUsedOptions = [...]; protected $mCacheTime = ''; protected $mCacheExpiry = NULL; protected $mCacheRevisionId = NULL; private $mText = NULL; private $mLanguageLinks = [...]; private $mCategories = [...]; private $mIndicators = [...]; private $mTitleText = ''; private $mLinks = [...]; private $mLinksSpecial = [...]; private $mTemplates = [...]; private $mTemplateIds = [...]; private $mImages = [...]; private $mFileSearchOptions = [...]; private $mExternalLinks = [...]; private $mInterwikiLinks = [...]; private $mNewSection = FALSE; private $mHideNewSection = FALSE; private $mNoGallery = FALSE; private $mHeadItems = [...]; private $mModules = [...]; private $mModuleStyles = [...]; private $mJsConfigVars = [...]; private $mOutputHooks = [...]; private $mWarnings = [...]; private $mWarningMsgs = [...]; private $mSections = [...]; private $mProperties = [...]; private $mTOCHTML = ''; private $mTimestamp = NULL; private $mEnableOOUI = FALSE; private $mIndexSet = FALSE; private $mNoIndexSet = FALSE; private $mExtensionData = [...]; private $mLimitReportData = [...]; private $mLimitReportJSData = [...]; private $mCacheMessage = ''; private $mParseStartTime = [...]; private $mPreventClickjacking = FALSE; private $mExtraScriptSrcs = [...]; private $mExtraDefaultSrcs = [...]; private $mExtraStyleSrcs = [...]; private $mFlags = [...]; private $mSpeculativeRevId = NULL; private $speculativePageIdUsed = NULL; private $revisionTimestampUsed = NULL; private $revisionUsedSha1Base36 = NULL; private $mWrapperDivClasses = [...]; private $mMaxAdaptiveExpiry = INF }; private $mAutonumber = 0; private $mStripState = class StripState { protected $data = [...]; protected $regex = '/\'"`UNIQ-([^<>&\'"]+)-QINU`"\'/'; protected $parser = ...; protected $circularRefGuard = [...]; protected $depth = 0; protected $highestDepth = 0; protected $expandSize = 0; protected $depthLimit = 20; protected $sizeLimit = 5000000 }; private $mLinkHolders = class LinkHolderArray { public $internals = [...]; public $interwikis = [...]; public $size = 0; public $parent = ...; private $languageConverter = class TrivialLanguageConverter { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $mLinkID = 0; private $mIncludeSizes = ['post-expand' => 0, 'arg' => 0]; public $mPPNodeCount = 11; public $mHighestExpansionDepth = 2; private $mTplRedirCache = []; public $mHeadings = [0 => [...], 1 => [...], 2 => [...], 3 => [...], 4 => [...], 5 => [...], 6 => [...]]; private $mDoubleUnderscores = []; public $mExpensiveFunctionCount = 0; private $mShowToc = TRUE; private $mForceTocPosition = FALSE; private $mTplDomCache = []; private $mUser = NULL; public $mOptions = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; public $mTitle = class Title { private $mTextform = 'PDE Geometric Analysis seminar'; private $mUrlform = 'PDE_Geometric_Analysis_seminar'; private $mDbkeyform = 'PDE_Geometric_Analysis_seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 82; protected $mLatestID = 25605; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'PDE Geometric Analysis seminar'; protected $mLength = 62882; public $mRedirect = FALSE; private $mHasSubpages = NULL; private $mPageLanguage = [...]; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $mOutputType = 1; public $ot = ['html' => TRUE, 'wiki' => FALSE, 'pre' => FALSE, 'plain' => FALSE]; private $mRevisionId = 1880; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 13566; private $mRevisionRecordObject = NULL; private $mLangLinkLanguages = []; private $currentRevisionCache = NULL; private $mInParse = '#0 /var/www/wiki_mediawiki-1.39.3/includes/parser/Parser.php(699): Parser->lock()\n#1 /var/www/wiki_mediawiki-1.39.3/includes/content/WikitextContentHandler.php(301): Parser->parse()\n#2 /var/www/wiki_mediawiki-1.39.3/includes/content/ContentHandler.php(1720): WikitextContentHandler->fillParserOutput()\n#3 /var/www/wiki_mediawiki-1.39.3/includes/content/Renderer/ContentRenderer.php(47): ContentHandler->getParserOutput()\n#4 /var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php(265): MediaWiki\\Co'...; private $mProfiler = class SectionProfiler { protected $start = NULL; protected $end = NULL; protected $stack = [...]; protected $workStack = [...]; protected $collated = [...]; protected $collateDone = FALSE; protected $errorEntry = [...]; protected $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $mLinkRenderer = NULL; private $magicWordFactory = class MagicWordFactory { private $mVariableIDsInitialised = TRUE; private $mVariableIDs = [...]; private $mCacheTTLs = [...]; private $mDoubleUnderscoreIDs = [...]; private $mSubstIDs = [...]; private $mObjects = [...]; private $mDoubleUnderscoreArray = NULL; private $contLang = class LanguageEn { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $contLang = class LanguageEn { public $mCode = 'en'; public $mMagicExtensions = [...]; private ${Language}mHtmlCode = 'en'; public $dateFormatStrings = [...]; public $mExtendedSpecialPageAliases = [...]; protected $namespaceNames = [...]; protected $mNamespaceIds = NULL; protected $namespaceAliases = NULL; private ${Language}transformData = [...]; private ${Language}namespaceInfo = class NamespaceInfo { ... }; private ${Language}localisationCache = class LocalisationCache { ... }; private ${Language}langNameUtils = class MediaWiki\Languages\LanguageNameUtils { ... }; private ${Language}langFallback = class MediaWiki\Languages\LanguageFallback { ... }; private ${Language}grammarTransformCache = NULL; private ${Language}converterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private ${Language}hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private ${Language}hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private ${Language}config = class GlobalVarConfig { ... } }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { private $cache = [...]; private $converterList = [...]; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $isConversionDisabled = FALSE; private $isTitleConversionDisabled = FALSE; private $defaultLanguage = class Closure { ... } }; private $factory = class ParserFactory { private $svcOptions = class MediaWiki\Config\ServiceOptions { ... }; private $magicWordFactory = class MagicWordFactory { ... }; private $contLang = class LanguageEn { ... }; private $urlUtils = class MediaWiki\Utils\UrlUtils { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { ... }; private $nsInfo = class NamespaceInfo { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $badFileLookup = class MediaWiki\BadFileLookup { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $titleFormatter = class MediaWikiTitleCodec { ... }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { ... }; private $trackingCategories = class TrackingCategories { ... }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $tidy = class MediaWiki\Tidy\RemexDriver { ... }; private $wanCache = class WANObjectCache { ... }; private $mainInstance = ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { private $list = [...]; private $aliases = [...]; private $options = class MediaWiki\Config\ServiceOptions { ... }; private $contLang = class LanguageEn { ... }; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $titleFactory = class TitleFactory { ... } }; private $titleFormatter = class MediaWikiTitleCodec { protected $language = class LanguageEn { ... }; protected $genderCache = class GenderCache { ... }; protected $localInterwikis = [...]; protected $interwikiLookup = class MediaWiki\Interwiki\ClassicInterwikiLookup { ... }; protected $nsInfo = class NamespaceInfo { ... }; private $createMalformedTitleException = class Closure { ... } }; private $svcOptions = class MediaWiki\Config\ServiceOptions { private $keys = [...]; private $options = [...] }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { private $titleFormatter = class MediaWikiTitleCodec { ... }; private $linkCache = class LinkCache { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... } }; private $nsInfo = class NamespaceInfo { private $alwaysCapitalizedNamespaces = [...]; private $canonicalNamespaces = [...]; private $namespaceIndexes = [...]; private $validNamespaces = [...]; private $options = class MediaWiki\Config\ServiceOptions { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $logger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'Parser'; private $minimumLevel = 999; private $isDB = FALSE }; private $badFileLookup = class MediaWiki\BadFileLookup { private $listCallback = class Closure { ... }; private $cache = class EmptyBagOStuff { ... }; private $repoGroup = class RepoGroup { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $badFiles = NULL; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { private $dynamicHandlers = [...]; private $tombstones = [...]; private $handlersByName = [...]; private $registry = class MediaWiki\HookContainer\GlobalHookRegistry { ... }; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $nextScopedRegisterId = 0 }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { private $container = class MediaWiki\HookContainer\HookContainer { ... } }; private $tidy = class MediaWiki\Tidy\RemexDriver { protected $config = [...]; private $treeMutationTrace = FALSE; private $serializerTrace = FALSE; private $mungerTrace = FALSE; private $pwrap = TRUE; private $enableLegacyMediaDOM = TRUE }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { private $serviceOptions = class MediaWiki\Config\ServiceOptions { ... }; private $defaultOptionsLookup = class MediaWiki\User\DefaultOptionsLookup { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $modifiedOptions = [...]; private $originalOptionsCache = [...]; private $optionsFromDb = [...]; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $queryFlagsUsedForCaching = [...] }; private $userFactory = class MediaWiki\User\UserFactory { private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; private $lastUserFromIdentity = NULL }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $trackingCategories = class TrackingCategories { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $namespaceInfo = class NamespaceInfo { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $extensionRegistry = class ExtensionRegistry { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { private $serviceOptions = class MediaWiki\Config\ServiceOptions { ... }; private $parserFactoryClosure = class Closure { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $titleFactory = class TitleFactory { ... } }; private $userNameUtils = class MediaWiki\User\UserNameUtils { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $contentLang = class LanguageEn { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $textFormatter = class MediaWiki\Message\TextFormatter { ... }; private $reservedUsernames = FALSE; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $tempUserConfig = class MediaWiki\User\TempUser\RealTempUserConfig { ... } }; protected $deprecatedPublicProperties = ['mLinkID' => [...], 'mIncludeSizes' => [...], 'mDoubleUnderscores' => [...], 'mShowToc' => [...], 'mRevisionId' => [...], 'mRevisionTimestamp' => [...], 'mRevisionUser' => [...], 'mRevisionSize' => [...], 'mInputSize' => [...], 'mInParse' => [...], 'mFirstCall' => [...], 'mGeneratedPPNodeCount' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE }, $frame = class PPFrame_Hash { public $parser = class Parser { private $mTagHooks = [...]; private $mFunctionHooks = [...]; private $mFunctionSynonyms = [...]; private $mStripList = [...]; private $mVarCache = [...]; private $mImageParams = [...]; private $mImageParamsMagicArray = [...]; public $mMarkerIndex = 1; private $mVariables = class MagicWordArray { ... }; private $mSubstWords = class MagicWordArray { ... }; private $mExtLinkBracketedRegex = '/\\[(((?i)bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/)(?:[0-9.]+\|\\[(?i:[0-9a-f:.]+)\\]\|[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])\\p{Zs}([^\\]\\x00-\\x08\\x0a-\\x1F\\x{FFFD}]?)\\]/Su'; private $urlUtils = class MediaWiki\Utils\UrlUtils { ... }; private $mPreprocessor = class Preprocessor_Hash { ... }; private $mOutput = class ParserOutput { ... }; private $mAutonumber = 0; private $mStripState = class StripState { ... }; private $mLinkHolders = class LinkHolderArray { ... }; private $mLinkID = 0; private $mIncludeSizes = [...]; public $mPPNodeCount = 11; public $mHighestExpansionDepth = 2; private $mTplRedirCache = [...]; public $mHeadings = [...]; private $mDoubleUnderscores = [...]; public $mExpensiveFunctionCount = 0; private $mShowToc = TRUE; private $mForceTocPosition = FALSE; private $mTplDomCache = [...]; private $mUser = NULL; public $mOptions = class ParserOptions { ... }; public $mTitle = class Title { ... }; private $mOutputType = 1; public $ot = [...]; private $mRevisionId = 1880; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 13566; private $mRevisionRecordObject = NULL; private $mLangLinkLanguages = [...]; private $currentRevisionCache = NULL; private $mInParse = '#0 /var/www/wiki_mediawiki-1.39.3/includes/parser/Parser.php(699): Parser->lock()\n#1 /var/www/wiki_mediawiki-1.39.3/includes/content/WikitextContentHandler.php(301): Parser->parse()\n#2 /var/www/wiki_mediawiki-1.39.3/includes/content/ContentHandler.php(1720): WikitextContentHandler->fillParserOutput()\n#3 /var/www/wiki_mediawiki-1.39.3/includes/content/Renderer/ContentRenderer.php(47): ContentHandler->getParserOutput()\n#4 /var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php(265): MediaWiki\\Co'...; private $mProfiler = class SectionProfiler { ... }; private $mLinkRenderer = NULL; private $magicWordFactory = class MagicWordFactory { ... }; private $contLang = class LanguageEn { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $factory = class ParserFactory { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $titleFormatter = class MediaWikiTitleCodec { ... }; private $svcOptions = class MediaWiki\Config\ServiceOptions { ... }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { ... }; private $nsInfo = class NamespaceInfo { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $badFileLookup = class MediaWiki\BadFileLookup { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $tidy = class MediaWiki\Tidy\RemexDriver { ... }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { ... }; private $trackingCategories = class TrackingCategories { ... }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; public $preprocessor = class Preprocessor_Hash { public $parser = class Parser { ... }; protected $wanCache = class WANObjectCache { ... }; protected $disableLangConversion = FALSE; protected $rules = [...]; protected $cacheThreshold = 1000 }; public $title = class Title { private $mTextform = 'PDE Geometric Analysis seminar'; private $mUrlform = 'PDE_Geometric_Analysis_seminar'; private $mDbkeyform = 'PDE_Geometric_Analysis_seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 82; protected $mLatestID = 25605; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'PDE Geometric Analysis seminar'; protected $mLength = 62882; public $mRedirect = FALSE; private $mHasSubpages = NULL; private $mPageLanguage = [...]; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; public $titleCache = [0 => 'PDE_Geometric_Analysis_seminar']; public $loopCheckHash = []; public $depth = 0; private $volatile = FALSE; private $ttl = NULL; protected $childExpansionCache = []; private $maxPPNodeCount = 1000000; private $maxPPExpandDepth = 100 } )	.../Parser.php:4023
33	0.1633	2543064	SimpleMathJaxHooks::renderTex( $tex = '\\displaystyle{ F }', $parser = class Parser { private $mTagHooks = ['pre' => [...], 'nowiki' => [...], 'gallery' => [...], 'indicator' => [...], 'langconvert' => [...], 'math' => 'SimpleMathJaxHooks::renderMath', 'chem' => 'SimpleMathJaxHooks::renderChem', 'source' => [...], 'syntaxhighlight' => [...], 'ref' => [...], 'references' => [...]]; private $mFunctionHooks = ['ns' => [...], 'nse' => [...], 'urlencode' => [...], 'lcfirst' => [...], 'ucfirst' => [...], 'lc' => [...], 'uc' => [...], 'localurl' => [...], 'localurle' => [...], 'fullurl' => [...], 'fullurle' => [...], 'canonicalurl' => [...], 'canonicalurle' => [...], 'formatnum' => [...], 'grammar' => [...], 'gender' => [...], 'plural' => [...], 'bidi' => [...], 'numberofpages' => [...], 'numberofusers' => [...], 'numberofactiveusers' => [...], 'numberofarticles' => [...], 'numberoffiles' => [...], 'numberofadmins' => [...], 'numberingroup' => [...], 'numberofedits' => [...], 'language' => [...], 'padleft' => [...], 'padright' => [...], 'anchorencode' => [...], 'defaultsort' => [...], 'filepath' => [...], 'pagesincategory' => [...], 'pagesize' => [...], 'protectionlevel' => [...], 'protectionexpiry' => [...], 'namespace' => [...], 'namespacee' => [...], 'namespacenumber' => [...], 'talkspace' => [...], 'talkspacee' => [...], 'subjectspace' => [...], 'subjectspacee' => [...], 'pagename' => [...], 'pagenamee' => [...], 'fullpagename' => [...], 'fullpagenamee' => [...], 'rootpagename' => [...], 'rootpagenamee' => [...], 'basepagename' => [...], 'basepagenamee' => [...], 'subpagename' => [...], 'subpagenamee' => [...], 'talkpagename' => [...], 'talkpagenamee' => [...], 'subjectpagename' => [...], 'subjectpagenamee' => [...], 'pageid' => [...], 'revisionid' => [...], 'revisionday' => [...], 'revisionday2' => [...], 'revisionmonth' => [...], 'revisionmonth1' => [...], 'revisionyear' => [...], 'revisiontimestamp' => [...], 'revisionuser' => [...], 'cascadingsources' => [...], 'int' => [...], 'special' => [...], 'speciale' => [...], 'tag' => [...], 'formatdate' => [...], 'displaytitle' => [...]]; private $mFunctionSynonyms = [0 => [...], 1 => [...]]; private $mStripList = [0 => 'pre', 1 => 'nowiki', 2 => 'gallery', 3 => 'indicator', 4 => 'langconvert', 5 => 'math', 6 => 'chem', 7 => 'source', 8 => 'syntaxhighlight', 9 => 'ref', 10 => 'references']; private $mVarCache = []; private $mImageParams = []; private $mImageParamsMagicArray = []; public $mMarkerIndex = 1; private $mVariables = class MagicWordArray { public $names = [...]; private $factory = class MagicWordFactory { ... }; private $hash = [...]; private $baseRegex = NULL; private $regex = NULL }; private $mSubstWords = class MagicWordArray { public $names = [...]; private $factory = class MagicWordFactory { ... }; private $hash = NULL; private $baseRegex = [...]; private $regex = NULL }; private $mExtLinkBracketedRegex = '/\\[(((?i)bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/)(?:[0-9.]+\|\\[(?i:[0-9a-f:.]+)\\]\|[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])[^][<>"\\x00-\\x20\\x7F\\p{Zs}\\x{FFFD}])\\p{Zs}([^\\]\\x00-\\x08\\x0a-\\x1F\\x{FFFD}]*?)\\]/Su'; private $urlUtils = class MediaWiki\Utils\UrlUtils { private $server = 'https://wiki.math.wisc.edu'; private $canonicalServer = 'https://wiki.math.wisc.edu'; private $internalServer = 'https://wiki.math.wisc.edu'; private $fallbackProtocol = 'http'; private $httpsPort = 443; private $validProtocols = [...]; private $validProtocolsCache = 'bitcoin\\:\|ftp\\:\\/\\/\|ftps\\:\\/\\/\|geo\\:\|git\\:\\/\\/\|gopher\\:\\/\\/\|http\\:\\/\\/\|https\\:\\/\\/\|irc\\:\\/\\/\|ircs\\:\\/\\/\|magnet\\:\|mailto\\:\|matrix\\:\|mms\\:\\/\\/\|news\\:\|nntp\\:\\/\\/\|redis\\:\\/\\/\|sftp\\:\\/\\/\|sip\\:\|sips\\:\|sms\\:\|ssh\\:\\/\\/\|svn\\:\\/\\/\|tel\\:\|telnet\\:\\/\\/\|urn\\:\|worldwind\\:\\/\\/\|xmpp\\:\|\\/\\/'; private $validAbsoluteProtocolsCache = NULL }; private $mPreprocessor = class Preprocessor_Hash { public $parser = ...; protected $wanCache = class WANObjectCache { ... }; protected $disableLangConversion = FALSE; protected $rules = [...]; protected $cacheThreshold = 1000 }; private $mOutput = class ParserOutput { protected $mParseUsedOptions = [...]; protected $mCacheTime = ''; protected $mCacheExpiry = NULL; protected $mCacheRevisionId = NULL; private $mText = NULL; private $mLanguageLinks = [...]; private $mCategories = [...]; private $mIndicators = [...]; private $mTitleText = ''; private $mLinks = [...]; private $mLinksSpecial = [...]; private $mTemplates = [...]; private $mTemplateIds = [...]; private $mImages = [...]; private $mFileSearchOptions = [...]; private $mExternalLinks = [...]; private $mInterwikiLinks = [...]; private $mNewSection = FALSE; private $mHideNewSection = FALSE; private $mNoGallery = FALSE; private $mHeadItems = [...]; private $mModules = [...]; private $mModuleStyles = [...]; private $mJsConfigVars = [...]; private $mOutputHooks = [...]; private $mWarnings = [...]; private $mWarningMsgs = [...]; private $mSections = [...]; private $mProperties = [...]; private $mTOCHTML = ''; private $mTimestamp = NULL; private $mEnableOOUI = FALSE; private $mIndexSet = FALSE; private $mNoIndexSet = FALSE; private $mExtensionData = [...]; private $mLimitReportData = [...]; private $mLimitReportJSData = [...]; private $mCacheMessage = ''; private $mParseStartTime = [...]; private $mPreventClickjacking = FALSE; private $mExtraScriptSrcs = [...]; private $mExtraDefaultSrcs = [...]; private $mExtraStyleSrcs = [...]; private $mFlags = [...]; private $mSpeculativeRevId = NULL; private $speculativePageIdUsed = NULL; private $revisionTimestampUsed = NULL; private $revisionUsedSha1Base36 = NULL; private $mWrapperDivClasses = [...]; private $mMaxAdaptiveExpiry = INF }; private $mAutonumber = 0; private $mStripState = class StripState { protected $data = [...]; protected $regex = '/\'"`UNIQ-([^<>&\'"]+)-QINU`"\'/'; protected $parser = ...; protected $circularRefGuard = [...]; protected $depth = 0; protected $highestDepth = 0; protected $expandSize = 0; protected $depthLimit = 20; protected $sizeLimit = 5000000 }; private $mLinkHolders = class LinkHolderArray { public $internals = [...]; public $interwikis = [...]; public $size = 0; public $parent = ...; private $languageConverter = class TrivialLanguageConverter { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $mLinkID = 0; private $mIncludeSizes = ['post-expand' => 0, 'arg' => 0]; public $mPPNodeCount = 11; public $mHighestExpansionDepth = 2; private $mTplRedirCache = []; public $mHeadings = [0 => [...], 1 => [...], 2 => [...], 3 => [...], 4 => [...], 5 => [...], 6 => [...]]; private $mDoubleUnderscores = []; public $mExpensiveFunctionCount = 0; private $mShowToc = TRUE; private $mForceTocPosition = FALSE; private $mTplDomCache = []; private $mUser = NULL; public $mOptions = class ParserOptions { private $options = [...]; private $mTimestamp = NULL; private $mUser = class User { ... }; private $onAccessCallback = [...]; private $redirectTarget = NULL; private $mExtraKey = '' }; public $mTitle = class Title { private $mTextform = 'PDE Geometric Analysis seminar'; private $mUrlform = 'PDE_Geometric_Analysis_seminar'; private $mDbkeyform = 'PDE_Geometric_Analysis_seminar'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 82; protected $mLatestID = 25605; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'PDE Geometric Analysis seminar'; protected $mLength = 62882; public $mRedirect = FALSE; private $mHasSubpages = NULL; private $mPageLanguage = [...]; private $mDbPageLanguage = FALSE; private $mTitleValue = NULL; private $mIsBigDeletion = NULL; private $mIsValid = NULL; private $mInstanceCacheKey = NULL; protected $deprecatedPublicProperties = [...]; private $dynamicPropertiesAccessDeprecated = FALSE }; private $mOutputType = 1; public $ot = ['html' => TRUE, 'wiki' => FALSE, 'pre' => FALSE, 'plain' => FALSE]; private $mRevisionId = 1880; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 13566; private $mRevisionRecordObject = NULL; private $mLangLinkLanguages = []; private $currentRevisionCache = NULL; private $mInParse = '#0 /var/www/wiki_mediawiki-1.39.3/includes/parser/Parser.php(699): Parser->lock()\n#1 /var/www/wiki_mediawiki-1.39.3/includes/content/WikitextContentHandler.php(301): Parser->parse()\n#2 /var/www/wiki_mediawiki-1.39.3/includes/content/ContentHandler.php(1720): WikitextContentHandler->fillParserOutput()\n#3 /var/www/wiki_mediawiki-1.39.3/includes/content/Renderer/ContentRenderer.php(47): ContentHandler->getParserOutput()\n#4 /var/www/wiki_mediawiki-1.39.3/includes/Revision/RenderedRevision.php(265): MediaWiki\\Co'...; private $mProfiler = class SectionProfiler { protected $start = NULL; protected $end = NULL; protected $stack = [...]; protected $workStack = [...]; protected $collated = [...]; protected $collateDone = FALSE; protected $errorEntry = [...]; protected $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $mLinkRenderer = NULL; private $magicWordFactory = class MagicWordFactory { private $mVariableIDsInitialised = TRUE; private $mVariableIDs = [...]; private $mCacheTTLs = [...]; private $mDoubleUnderscoreIDs = [...]; private $mSubstIDs = [...]; private $mObjects = [...]; private $mDoubleUnderscoreArray = NULL; private $contLang = class LanguageEn { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $contLang = class LanguageEn { public $mCode = 'en'; public $mMagicExtensions = [...]; private ${Language}mHtmlCode = 'en'; public $dateFormatStrings = [...]; public $mExtendedSpecialPageAliases = [...]; protected $namespaceNames = [...]; protected $mNamespaceIds = NULL; protected $namespaceAliases = NULL; private ${Language}transformData = [...]; private ${Language}namespaceInfo = class NamespaceInfo { ... }; private ${Language}localisationCache = class LocalisationCache { ... }; private ${Language}langNameUtils = class MediaWiki\Languages\LanguageNameUtils { ... }; private ${Language}langFallback = class MediaWiki\Languages\LanguageFallback { ... }; private ${Language}grammarTransformCache = NULL; private ${Language}converterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private ${Language}hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private ${Language}hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private ${Language}config = class GlobalVarConfig { ... } }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { private $cache = [...]; private $converterList = [...]; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $isConversionDisabled = FALSE; private $isTitleConversionDisabled = FALSE; private $defaultLanguage = class Closure { ... } }; private $factory = class ParserFactory { private $svcOptions = class MediaWiki\Config\ServiceOptions { ... }; private $magicWordFactory = class MagicWordFactory { ... }; private $contLang = class LanguageEn { ... }; private $urlUtils = class MediaWiki\Utils\UrlUtils { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { ... }; private $nsInfo = class NamespaceInfo { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $badFileLookup = class MediaWiki\BadFileLookup { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $titleFormatter = class MediaWikiTitleCodec { ... }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { ... }; private $trackingCategories = class TrackingCategories { ... }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $tidy = class MediaWiki\Tidy\RemexDriver { ... }; private $wanCache = class WANObjectCache { ... }; private $mainInstance = ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { private $list = [...]; private $aliases = [...]; private $options = class MediaWiki\Config\ServiceOptions { ... }; private $contLang = class LanguageEn { ... }; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $titleFactory = class TitleFactory { ... } }; private $titleFormatter = class MediaWikiTitleCodec { protected $language = class LanguageEn { ... }; protected $genderCache = class GenderCache { ... }; protected $localInterwikis = [...]; protected $interwikiLookup = class MediaWiki\Interwiki\ClassicInterwikiLookup { ... }; protected $nsInfo = class NamespaceInfo { ... }; private $createMalformedTitleException = class Closure { ... } }; private $svcOptions = class MediaWiki\Config\ServiceOptions { private $keys = [...]; private $options = [...] }; private $linkRendererFactory = class MediaWiki\Linker\LinkRendererFactory { private $titleFormatter = class MediaWikiTitleCodec { ... }; private $linkCache = class LinkCache { ... }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... } }; private $nsInfo = class NamespaceInfo { private $alwaysCapitalizedNamespaces = [...]; private $canonicalNamespaces = [...]; private $namespaceIndexes = [...]; private $validNamespaces = [...]; private $options = class MediaWiki\Config\ServiceOptions { ... }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $logger = class MediaWiki\Logger\LegacyLogger { protected $channel = 'Parser'; private $minimumLevel = 999; private $isDB = FALSE }; private $badFileLookup = class MediaWiki\BadFileLookup { private $listCallback = class Closure { ... }; private $cache = class EmptyBagOStuff { ... }; private $repoGroup = class RepoGroup { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $badFiles = NULL; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... } }; private $hookContainer = class MediaWiki\HookContainer\HookContainer { private $dynamicHandlers = [...]; private $tombstones = [...]; private $handlersByName = [...]; private $registry = class MediaWiki\HookContainer\GlobalHookRegistry { ... }; private $objectFactory = class Wikimedia\ObjectFactory\ObjectFactory { ... }; private $nextScopedRegisterId = 0 }; private $hookRunner = class MediaWiki\HookContainer\HookRunner { private $container = class MediaWiki\HookContainer\HookContainer { ... } }; private $tidy = class MediaWiki\Tidy\RemexDriver { protected $config = [...]; private $treeMutationTrace = FALSE; private $serializerTrace = FALSE; private $mungerTrace = FALSE; private $pwrap = TRUE; private $enableLegacyMediaDOM = TRUE }; private $userOptionsLookup = class MediaWiki\User\UserOptionsManager { private $serviceOptions = class MediaWiki\Config\ServiceOptions { ... }; private $defaultOptionsLookup = class MediaWiki\User\DefaultOptionsLookup { ... }; private $languageConverterFactory = class MediaWiki\Languages\LanguageConverterFactory { ... }; private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $userFactory = class MediaWiki\User\UserFactory { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $modifiedOptions = [...]; private $originalOptionsCache = [...]; private $optionsFromDb = [...]; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $queryFlagsUsedForCaching = [...] }; private $userFactory = class MediaWiki\User\UserFactory { private $loadBalancer = class Wikimedia\Rdbms\LoadBalancer { ... }; private $userNameUtils = class MediaWiki\User\UserNameUtils { ... }; private $lastUserFromIdentity = NULL }; private $httpRequestFactory = class MediaWiki\Http\HttpRequestFactory { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $trackingCategories = class TrackingCategories { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $namespaceInfo = class NamespaceInfo { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $extensionRegistry = class ExtensionRegistry { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... } }; private $signatureValidatorFactory = class MediaWiki\Preferences\SignatureValidatorFactory { private $serviceOptions = class MediaWiki\Config\ServiceOptions { ... }; private $parserFactoryClosure = class Closure { ... }; private $specialPageFactory = class MediaWiki\SpecialPage\SpecialPageFactory { ... }; private $titleFactory = class TitleFactory { ... } }; private $userNameUtils = class MediaWiki\User\UserNameUtils { private $options = class MediaWiki\Config\ServiceOptions { ... }; private $contentLang = class LanguageEn { ... }; private $logger = class MediaWiki\Logger\LegacyLogger { ... }; private $titleParser = class MediaWikiTitleCodec { ... }; private $textFormatter = class MediaWiki\Message\TextFormatter { ... }; private $reservedUsernames = FALSE; private $hookRunner = class MediaWiki\HookContainer\HookRunner { ... }; private $tempUserConfig = class MediaWiki\User\TempUser\RealTempUserConfig { ... } }; protected $deprecatedPublicProperties = ['mLinkID' => [...], 'mIncludeSizes' => [...], 'mDoubleUnderscores' => [...], 'mShowToc' => [...], 'mRevisionId' => [...], 'mRevisionTimestamp' => [...], 'mRevisionUser' => [...], 'mRevisionSize' => [...], 'mInputSize' => [...], 'mInParse' => [...], 'mFirstCall' => [...], 'mGeneratedPPNodeCount' => [...]]; private $dynamicPropertiesAccessDeprecated = FALSE } )	.../SimpleMathJaxHooks.php:26
34	0.1633	2543064	ParserOutput->addModules( $modules = 'ext.SimpleMathJax' )	.../SimpleMathJaxHooks.php:34
35	0.1633	2543064	wfDeprecated( $function = 'ParserOutput::addModules with non-array argument', $version = '1.38', $component = ???, $callerOffset = ??? )	.../ParserOutput.php:1180
36	0.1633	2543064	MWDebug::deprecated( $function = 'ParserOutput::addModules with non-array argument', $version = '1.38', $component = FALSE, $callerOffset = 3 )	.../GlobalFunctions.php:765
37	0.1633	2543192	MWDebug::deprecatedMsg( $msg = 'Use of ParserOutput::addModules with non-array argument was deprecated in MediaWiki 1.38.', $version = '1.38', $component = 'MediaWiki', $callerOffset = 4 )	.../MWDebug.php:233
38	0.1633	2544888	MWDebug::sendRawDeprecated( $msg = 'Use of ParserOutput::addModules with non-array argument was deprecated in MediaWiki 1.38. [Called from SimpleMathJaxHooks::renderTex in /var/www/wiki_mediawiki-1.39.3/extensions/SimpleMathJax/SimpleMathJaxHooks.php at line 34]', $sendToLog = TRUE, $callerFunc = 'SimpleMathJaxHooks::renderTex' )	.../MWDebug.php:351
39	0.1633	2544888	trigger_error( $message = 'Use of ParserOutput::addModules with non-array argument was deprecated in MediaWiki 1.38. [Called from SimpleMathJaxHooks::renderTex in /var/www/wiki_mediawiki-1.39.3/extensions/SimpleMathJax/SimpleMathJaxHooks.php at line 34]', $error_level = 16384 )	.../MWDebug.php:381

( ! ) Warning: Cannot modify header information - headers already sent by (output started at /var/www/wiki_mediawiki-1.39.3/includes/debug/MWDebug.php:381) in /var/www/wiki_mediawiki-1.39.3/includes/WebResponse.php on line 75
Call Stack
#	Time	Memory	Function	Location
1	0.0001	357800	{main}( )	.../index.php:0
2	0.0446	1478576	wfIndexMain( )	.../index.php:46
3	0.0446	1478688	MediaWiki->run( )	.../index.php:50
4	0.0446	1478688	MediaWiki->main( )	.../MediaWiki.php:562
5	0.2597	2932888	OutputPage->output( $return = TRUE )	.../MediaWiki.php:922
6	0.2597	2949464	WebResponse->header( $string = 'Content-type: text/html; charset=UTF-8', $replace = ???, $http_response_code = ??? )	.../OutputPage.php:2825
7	0.2597	2949656	header( $header = 'Content-type: text/html; charset=UTF-8', $replace = TRUE )	.../WebResponse.php:75

( ! ) Warning: Cannot modify header information - headers already sent by (output started at /var/www/wiki_mediawiki-1.39.3/includes/debug/MWDebug.php:381) in /var/www/wiki_mediawiki-1.39.3/includes/WebResponse.php on line 75
Call Stack
#	Time	Memory	Function	Location
1	0.0001	357800	{main}( )	.../index.php:0
2	0.0446	1478576	wfIndexMain( )	.../index.php:46
3	0.0446	1478688	MediaWiki->run( )	.../index.php:50
4	0.0446	1478688	MediaWiki->main( )	.../MediaWiki.php:562
5	0.2597	2932888	OutputPage->output( $return = TRUE )	.../MediaWiki.php:922
6	0.2600	2949576	WebResponse->header( $string = 'Content-language: en', $replace = ???, $http_response_code = ??? )	.../OutputPage.php:2826
7	0.2600	2949576	header( $header = 'Content-language: en', $replace = TRUE )	.../WebResponse.php:75

@@ Line 25: / Line 25: @@
 |Juraj Foldes (Vanderbilt)
 |[[#Juraj Foldes (Vanderbilt)|
-  ''TBA'']]
+  ''Symmetry properties of parabolic problems and their applications'']]
 |Zlatos
 |-
@@ Line 285: / Line 285: @@
 The talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of <math>R^n</math>. To each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new symmetrization technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.
+===Juraj Foldes (Vanderbilt)===
+''Symmetry properties of parabolic problems and their applications''
+Positive solutions of nonlinear parabolic problems can have a very complex behavior. However, assuming certain symmetry  conditions, it is possible to prove that the solutions converge to the space of symmetric functions. We show that this property is 'stable'; more specifically if the symmetry conditions are replaced by asymptotically symmetric ones, the solutions still approach the space of symmetric functions. As an application, we show new results on convergence of solutions to a single equilibrium.

( ! ) Warning: Cannot modify header information - headers already sent by (output started at /var/www/wiki_mediawiki-1.39.3/includes/debug/MWDebug.php:381) in /var/www/wiki_mediawiki-1.39.3/includes/WebResponse.php on line 75
Call Stack
#	Time	Memory	Function	Location
1	0.0001	357800	{main}( )	.../index.php:0
2	0.0446	1478576	wfIndexMain( )	.../index.php:46
3	0.0446	1478688	MediaWiki->run( )	.../index.php:50
4	0.0446	1478688	MediaWiki->main( )	.../MediaWiki.php:562
5	0.2597	2932888	OutputPage->output( $return = TRUE )	.../MediaWiki.php:922
6	0.3662	3763320	OutputPage->sendCacheControl( )	.../OutputPage.php:2891
7	0.3663	3764336	WebResponse->header( $string = 'Vary: Accept-Encoding, Cookie', $replace = ???, $http_response_code = ??? )	.../OutputPage.php:2691
8	0.3663	3764336	header( $header = 'Vary: Accept-Encoding, Cookie', $replace = TRUE )	.../WebResponse.php:75

PDE Geometric Analysis seminar: Difference between revisions

Revision as of 16:33, 24 March 2011

Contents

PDE and Geometric Analysis Seminar

Seminar Schedule Spring 2011

Seminar Schedule Fall 2010

Abstracts

Fausto Ferrari (Bologna)

Arshak Petrosyan (Purdue)

Changyou Wang (U. of Kentucky)

Philippe LeFloch (Paris VI)

Irina Mitrea

Panagiota Daskalopoulos (Columbia U)

Maria Gualdani (UT Austin)

Hiroshi Matano (Tokyo University)

Ian Tice (Brown University)

Hoai Minh Nguyen (NYU-Courant Institute)

Bing Wang (Princeton)

Francois Hamel (Marseille)

Juraj Foldes (Vanderbilt)

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PDE Geometric Analysis seminar: Difference between revisions

Revision as of 16:33, 24 March 2011

PDE and Geometric Analysis Seminar

Seminar Schedule Spring 2011

Seminar Schedule Fall 2010

Abstracts

Fausto Ferrari (Bologna)

Arshak Petrosyan (Purdue)

Changyou Wang (U. of Kentucky)

Philippe LeFloch (Paris VI)

Irina Mitrea

Panagiota Daskalopoulos (Columbia U)

Maria Gualdani (UT Austin)

Hiroshi Matano (Tokyo University)

Ian Tice (Brown University)

Hoai Minh Nguyen (NYU-Courant Institute)

Bing Wang (Princeton)

Francois Hamel (Marseille)

Juraj Foldes (Vanderbilt)

Navigation menu

Search