NTS ABSTRACTFall2019: Difference between revisions

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Sep 5

Will Sawin

The sup-norm problem for automorphic forms over function fields and geometry

The sup-norm problem is a purely analytic question about automorphic forms, which asks for bounds on their largest value (when viewed as a function on a modular curve or similar space). We describe a new approach to this problem in the function field setting, which we carry through to provide new bounds for forms in GL_2 stronger than what can be proved for the analogous question about classical modular forms. This approach proceeds by viewing the automorphic form as a geometric object, following Drinfeld. It should be possible to prove bounds in greater generality by this approach in the future.

Sep 12

Yingkun Li

CM values of modular functions and factorization

The theory of complex multiplication tells us that the values of the j-invariant at CM points are algebraic integers. The norm of the difference of two such values has nice and explicit factorization, which was the subject of the seminal work of Gross and Zagier on singular moduli in the 1980s. In this talk, we will recall this classical result, review some recent factorization formula for other modular functions, and report some progress on a conjecture of Yui and Zagier. This is joint work with Tonghai Yang.

Sep 19

Soumya Sankar

Proportion of ordinary curves in some families

An abelian variety in characteristic [math]\displaystyle{ p }[/math] is said to be ordinary if its [math]\displaystyle{ p }[/math] torsion is as large as possible. In 2012, Cais, Ellenberg and Zureick-Brown made some conjectures about the distribution of the size of the [math]\displaystyle{ p }[/math] -torsion of an abelian variety. I will talk about some families which do not obey these heuristics, namely Jacobians of Artin-Schreier and superelliptic curves, and discuss the structure of the respective moduli spaces that make it so.

Oct 3

Patrick Allen

On the modularity of elliptic curves over imaginary quadratic fields

Wiles's proof of the modularity of semistable elliptic curves over the rationals uses the Langlands-Tunnell theorem as a starting point. In order to feed this into a modularity lifting theorem, one needs to use congruences between modular forms of weight one and modular forms of higher weight. Similar congruences are not known over imaginary quadratic fields and Wiles's strategy runs into problems right from the start. We circumvent this congruence problem and show that mod 3 Galois representations over imaginary quadratic fields arise from automorphic forms that are the analog of higher weight modular forms. Our argument relies on a 2-adic automorphy lifting theorem over CM fields together with a "2-3 switch." As an application, we deduce that a positive proportion of elliptic curves over imaginary quadratic fields are modular. This is joint work in progress with Chandrashekhar Khare and Jack Thorne.

Oct 10

Borys Kadets

Sectional monodromy groups of projective curves

Let $K$ be a field. Fix a projective curve $X \subset \mathbb{P}^r_K$ of degree $d$. A general hyperplane $H \in \mathbb{P}^{r*}$ intersects $X$ in $d$ points; the monodromy of $X \bigcap H$ as $H$ varies is a subgroup $G_X$ of $S_d$ known as the sectional monodromy group of $X$. When $K=\mathbb{C}$ (or in fact for $\mathrm{char} K = 0$), the equality $G_X=S_d$ was shown by Castelnuovo; this large monodromy fact is important in studying the degree-genus problem for projective curves. I will talk about the behaviour of sectional monodromy groups in positive characteristic. I will show that for a large class of curves the inclusion $G_X \supset A_d$ holds. On the other hand, for a seemingly simple family of curves $X_{m,n}$ given by the equation $x^n=y^mz^{n-m}$ in $\mathbb{P}^2$ I will completely characterize the possibilities for $G_{X_{n,m}}$; the list of possibilities includes linear groups $\mathrm{AGL}_n(q)$, $\mathrm{PGL}_2(q)$ as well as some sporadic simple groups.

Oct 17

Yousheng Shi

Generalized special cycles and theta series

We study generalized special cycles on Hermitian locally symmetric spaces $\Gamma \backslash D$ associated to the groups $G = U(p, q), \ \mathrm{Sp}(2n, \mathbb R)$ and $\mathrm{O}(2n)$. These cycles are algebraic and covered by symmetric spaces associated to subgroups of $G$ which are of the same type. Using the oscillator representation and the thesis of Greg Anderson, we show that Poincare duals of these generalized special cycles can be viewed as Fourier coefficients of a theta series. This gives new cases of theta lifts from the cohomology of Hermitian locally symmetric manifolds associated to $G$ to vector-valued automorphic forms associated to the groups $G' = \mathrm{U}(m, m), \ \mathrm{O}(m, m)$ or $\mathrm{Sp}(m, m)$ which are members of a dual pair with $G$ in the sense of Howe. This partially generalizes the work of Kudla and Millson on the special cycles on Hermitian locally symmetric spaces associated to the unitary groups.

Oct 24

Simon Marshall

Counting cohomological automorphic forms on $GL_3$

I will give an overview of the limit multiplicity problem for automorphic representations. I will then talk about work of mine in this area that gives a new bound for the number of cohomological cusp forms on $GL_3$ of fixed weight and growing level. My proof uses $p$-adic techniques of Calegari and Emerton.

Nov 7

Asif Zaman

A zero density estimate for Dedekind zeta functions

Given a finite group $G$, I will discuss a zero density estimate for Dedekind zeta functions associated to Galois extensions over $\mathbb{Q}$ with Galois group $G$. The result does not assume any unproven progress towards the strong Artin conjecture. Building on a recent breakthrough of Pierce, Turnage-Butterbaugh, and Wood, this has applications to $\ell$-torsion in class groups and the Chebotarev density theorem on average.

Nov 14

Liyang Yang

Holomorphic Continuation of Certain $L$-functions via Trace Formula

In this talk, we will mainly discuss two basic conjectures on entireness of certain basic $L$-functions arising from Galois representations (algebra) and automorphic representations (analysis). Although the background and definitions are quite different, we will show these $L$-functions are closely related to each other by a generalized Jacquet-Zagier trace formula. As a consequence, we obtain holomorphy of adjoint $L$-functions for $\mathrm{GL}(n),$ where $n\leq 4.$ Some applications will be provided.

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private $redirectTarget = NULL; private $mExtraKey = '' }, $revision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 18367; protected $mPageId = 1466; protected $mUser = class MediaWiki\User\UserIdentityValue { private $id = 859; private $name = 'Shusterman'; private $wikiId = FALSE }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20191108164032'; protected $mDeleted = 0; protected $mSize = 9828; protected $mSha1 = 't45h0p7tdk21244zwh21adwxrm5ytyi'; protected $mParentId = 18366; protected $mComment = class CommentStoreComment { public $id = '3497'; public $text = '/* Nov 14 */'; public $message = class RawMessage { ... }; public $data = NULL }; protected $mPage = class Title { private $mTextform = 'NTS ABSTRACTFall2019'; private $mUrlform = 'NTS_ABSTRACTFall2019'; private $mDbkeyform = 'NTS_ABSTRACTFall2019'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1466; protected $mLatestID = 18492; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'NTS ABSTRACTFall2019'; protected $mLength = 13230; 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	0.1520	2446488	PoolCounterWork->execute( $skipcache = ??? )	.../ParserOutputAccess.php:299
16	0.1520	2446680	PoolWorkArticleViewOld->doWork( )	.../PoolCounterWork.php:162
17	0.1520	2446936	PoolWorkArticleView->renderRevision( )	.../PoolWorkArticleViewOld.php:66
18	0.1522	2449944	MediaWiki\Revision\RenderedRevision->getRevisionParserOutput( $hints = ??? )	.../PoolWorkArticleView.php:91
19	0.1522	2449944	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 = 18367; protected $mPageId = 1466; protected $mUser = class MediaWiki\User\UserIdentityValue { ... }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20191108164032'; protected $mDeleted = 0; protected $mSize = 9828; protected $mSha1 = 't45h0p7tdk21244zwh21adwxrm5ytyi'; protected $mParentId = 18366; 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	0.1522	2450016	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 = 18367; protected $mPageId = 1466; protected $mUser = class MediaWiki\User\UserIdentityValue { ... }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20191108164032'; protected $mDeleted = 0; protected $mSize = 9828; protected $mSha1 = 't45h0p7tdk21244zwh21adwxrm5ytyi'; protected $mParentId = 18366; 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	0.1522	2450016	MediaWiki\Revision\RevisionRenderer->combineSlotOutput( $rrev = class MediaWiki\Revision\RenderedRevision { private $revision = class MediaWiki\Revision\RevisionStoreRecord { protected $wikiId = FALSE; protected $mId = 18367; protected $mPageId = 1466; protected $mUser = class MediaWiki\User\UserIdentityValue { ... }; protected $mMinorEdit = FALSE; protected $mTimestamp = '20191108164032'; protected $mDeleted = 0; protected $mSize = 9828; protected $mSha1 = 't45h0p7tdk21244zwh21adwxrm5ytyi'; protected $mParentId = 18366; 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	0.1528	2450728	MediaWiki\Revision\RenderedRevision->getSlotParserOutput( $role = 'main', $hints = [] )	.../RevisionRenderer.php:221
23	0.1529	2450096	MediaWiki\Revision\RenderedRevision->getSlotParserOutputUncached( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = 'Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]\n\n\n== Sep 5 ==\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Will Sawin\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| The sup-norm problem for automorphic forms over function fields and geometry\n\|-\n\| bgcolor="#BCD2EE" \| \nThe sup-norm problem is a purely analytic question about \nautomorphic forms, which asks for bounds on '...; private $redirectTargetAndText = [0 => NULL, 1 => 'Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]\n\n\n== Sep 5 ==\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Will Sawin\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| The sup-norm problem for automorphic forms over function fields and geometry\n\|-\n\| bgcolor="#BCD2EE" \| \nThe sup-norm problem is a purely analytic question about \nautomorphic forms, which asks for bounds on '...]; private $preSaveTransformFlags = [] }, $withHtml = TRUE )	.../RenderedRevision.php:237
24	0.1529	2450096	MediaWiki\Content\Renderer\ContentRenderer->getParserOutput( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = 'Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]\n\n\n== Sep 5 ==\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Will Sawin\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| The sup-norm problem for automorphic forms over function fields and geometry\n\|-\n\| bgcolor="#BCD2EE" \| \nThe sup-norm problem is a purely analytic question about \nautomorphic forms, which asks for bounds on '...; private $redirectTargetAndText = [0 => NULL, 1 => 'Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]\n\n\n== Sep 5 ==\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Will Sawin\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| The sup-norm problem for automorphic forms over function fields and geometry\n\|-\n\| bgcolor="#BCD2EE" \| \nThe sup-norm problem is a purely analytic question about \nautomorphic forms, which asks for bounds on '...]; private $preSaveTransformFlags = [] }, $page = class Title { private $mTextform = 'NTS ABSTRACTFall2019'; private $mUrlform = 'NTS_ABSTRACTFall2019'; private $mDbkeyform = 'NTS_ABSTRACTFall2019'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1466; protected $mLatestID = 18492; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'NTS ABSTRACTFall2019'; protected $mLength = 13230; 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 = 18367, $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 = '20231129045038'; 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	0.1530	2450208	ContentHandler->getParserOutput( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = 'Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]\n\n\n== Sep 5 ==\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Will Sawin\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| The sup-norm problem for automorphic forms over function fields and geometry\n\|-\n\| bgcolor="#BCD2EE" \| \nThe sup-norm problem is a purely analytic question about \nautomorphic forms, which asks for bounds on '...; private $redirectTargetAndText = [0 => NULL, 1 => 'Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]\n\n\n== Sep 5 ==\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Will Sawin\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| The sup-norm problem for automorphic forms over function fields and geometry\n\|-\n\| bgcolor="#BCD2EE" \| \nThe sup-norm problem is a purely analytic question about \nautomorphic forms, which asks for bounds on '...]; private $preSaveTransformFlags = [] }, $cpoParams = class MediaWiki\Content\Renderer\ContentParseParams { private $page = class Title { private $mTextform = 'NTS ABSTRACTFall2019'; private $mUrlform = 'NTS_ABSTRACTFall2019'; private $mDbkeyform = 'NTS_ABSTRACTFall2019'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1466; protected $mLatestID = 18492; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'NTS ABSTRACTFall2019'; protected $mLength = 13230; 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 = 18367; 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	0.1531	2452304	WikitextContentHandler->fillParserOutput( $content = class WikitextContent { protected $model_id = 'wikitext'; protected $mText = 'Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]\n\n\n== Sep 5 ==\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Will Sawin\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| The sup-norm problem for automorphic forms over function fields and geometry\n\|-\n\| bgcolor="#BCD2EE" \| \nThe sup-norm problem is a purely analytic question about \nautomorphic forms, which asks for bounds on '...; private $redirectTargetAndText = [0 => NULL, 1 => 'Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]\n\n\n== Sep 5 ==\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Will Sawin\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| The sup-norm problem for automorphic forms over function fields and geometry\n\|-\n\| bgcolor="#BCD2EE" \| \nThe sup-norm problem is a purely analytic question about \nautomorphic forms, which asks for bounds on '...]; private $preSaveTransformFlags = [] }, $cpoParams = class MediaWiki\Content\Renderer\ContentParseParams { private $page = class Title { private $mTextform = 'NTS ABSTRACTFall2019'; private $mUrlform = 'NTS_ABSTRACTFall2019'; private $mDbkeyform = 'NTS_ABSTRACTFall2019'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1466; protected $mLatestID = 18492; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'NTS ABSTRACTFall2019'; protected $mLength = 13230; 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 = 18367; 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	0.1532	2452304	Parser->parse( $text = 'Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]\n\n\n== Sep 5 ==\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Will Sawin\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| The sup-norm problem for automorphic forms over function fields and geometry\n\|-\n\| bgcolor="#BCD2EE" \| \nThe sup-norm problem is a purely analytic question about \nautomorphic forms, which asks for bounds on '..., $page = class Title { private $mTextform = 'NTS ABSTRACTFall2019'; private $mUrlform = 'NTS_ABSTRACTFall2019'; private $mDbkeyform = 'NTS_ABSTRACTFall2019'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1466; protected $mLatestID = 18492; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'NTS ABSTRACTFall2019'; protected $mLength = 13230; 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 = '20231129045038'; 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 = 18367 )	.../WikitextContentHandler.php:301
28	0.1533	2459576	Parser->internalParse( $text = 'Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]\n\n\n== Sep 5 ==\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Will Sawin\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| The sup-norm problem for automorphic forms over function fields and geometry\n\|-\n\| bgcolor="#BCD2EE" \| \nThe sup-norm problem is a purely analytic question about \nautomorphic forms, which asks for bounds on '..., $isMain = ???, $frame = ??? )	.../Parser.php:724
29	0.1533	2459608	Parser->replaceVariables( $text = 'Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]\n\n\n== Sep 5 ==\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Will Sawin\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| The sup-norm problem for automorphic forms over function fields and geometry\n\|-\n\| bgcolor="#BCD2EE" \| \nThe sup-norm problem is a purely analytic question about \nautomorphic forms, which asks for bounds on '..., $frame = ???, $argsOnly = ??? )	.../Parser.php:1610
30	0.1554	2493312	PPFrame_Hash->expand( $root = class PPNode_Hash_Tree { public $name = 'root'; private $rawChildren = [0 => 'Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]\n\n\n', 1 => [...], 2 => '\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Will Sawin\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| The sup-norm problem for automorphic forms over function fields and geometry\n\|-\n\| bgcolor="#BCD2EE" \| \nThe sup-norm problem is a purely analytic question about \nautomorphic forms, which asks for bounds on their largest value (when \nviewed as a function on a modular curve or s'..., 3 => [...], 4 => '\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Yingkun Li\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| CM values of modular functions and factorization\n\|-\n\| bgcolor="#BCD2EE" \| \nThe theory of complex multiplication tells us that the values of the j-invariant at CM points are algebraic integers. The norm of the difference of two such values has nice and explicit factorization, '..., 5 => [...], 6 => '\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Soumya Sankar\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| Proportion of ordinary curves in some families \n\|-\n\| bgcolor="#BCD2EE" \| \nAn abelian variety in characteristic ', 7 => [...], 8 => ' is said to be ordinary if its ', 9 => [...], 10 => ' torsion is as large as possible. In 2012, Cais, Ellenberg and Zureick-Brown made some conjectures about the distribution of the size of the ', 11 => [...], 12 => ' -torsion of an abelian variety. I will talk about some families which do not obey these heuristics, namely Jacobians of Artin-Schreier and superelliptic curves, and discuss the structure of the respective moduli spaces that make it so. \n\|} \n</center>\n\n<br>\n\n', 13 => [...], 14 => '\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Patrick Allen\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| On the modularity of elliptic curves over imaginary quadratic fields\n\|-\n\| bgcolor="#BCD2EE" \| \n\nWiles\'s proof of the modularity of semistable elliptic curves over the rationals uses the Langlands-Tunnell theorem as a starting point. In order to feed this into a modularity '..., 15 => [...], 16 => '\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Borys Kadets\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| Sectional monodromy groups of projective curves\n\|-\n\| bgcolor="#BCD2EE" \| Let $K$ be a field. Fix a projective curve $X \\subset \\mathbb{P}^r_K$ of degree $d$. A general hyperplane $H \\in \\mathbb{P}^{r*}$ intersects $X$ in $d$ points; the monodromy of $X \\bigcap H$ as $H$ vari'..., 17 => [...], 18 => '\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Yousheng Shi\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| Generalized special cycles and theta series\n\|-\n\| bgcolor="#BCD2EE" \| We study generalized special cycles on Hermitian locally symmetric spaces $\\Gamma \\backslash D$ associated to the groups $G = U(p, q), \\ \\mathrm{Sp}(2n, \\mathbb R)$ and $\\mathrm{O}(2n)$. These cycles are al'..., 19 => [...], 20 => '\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Simon Marshall\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| Counting cohomological automorphic forms on $GL_3$\n\|-\n\| bgcolor="#BCD2EE" \| I will give an overview of the limit multiplicity problem for automorphic representations. I will then talk about work of mine in this area that gives a new bound for the number of cohomological c'..., 21 => [...], 22 => '\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Asif Zaman\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| A zero density estimate for Dedekind zeta functions\n\|-\n\| bgcolor="#BCD2EE" \| Given a finite group $G$, I will discuss a zero density estimate for Dedekind zeta functions associated to Galois extensions over $\\mathbb{Q}$ with Galois group $G$. The result does not assume any un'..., 23 => [...], 24 => '\n\n<center>\n{\| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"\n\|-\n\| bgcolor="#F0A0A0" align="center" style="font-size:125%" \| \'\'\'Liyang Yang\'\'\'\n\|-\n\| bgcolor="#BCD2EE" align="center" \| Holomorphic Continuation of Certain $L$-functions via Trace Formula\n\|-\n\| bgcolor="#BCD2EE" \| In this talk, we will mainly discuss two basic conjectures on entireness of certain basic $L$-functions arising from Galois representations (algebra) and automorphic representations '...]; private $store = [0 => [...]]; private $index = 0 }, $flags = 0 )	.../Parser.php:2955
31	0.1555	2499360	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 = 7; 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 = 18367; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 9828; 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 = 'NTS ABSTRACTFall2019'; private $mUrlform = 'NTS_ABSTRACTFall2019'; private $mDbkeyform = 'NTS_ABSTRACTFall2019'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1466; protected $mLatestID = 18492; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'NTS ABSTRACTFall2019'; protected $mLength = 13230; 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 => 'NTS_ABSTRACTFall2019']; 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	0.1555	2499864	SimpleMathJaxHooks::renderMath( $tex = 'p', $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 = 7; public $mHighestExpansionDepth = 2; private $mTplRedirCache = []; public $mHeadings = [0 => [...], 1 => [...], 2 => [...]]; 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 = 'NTS ABSTRACTFall2019'; private $mUrlform = 'NTS_ABSTRACTFall2019'; private $mDbkeyform = 'NTS_ABSTRACTFall2019'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1466; protected $mLatestID = 18492; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'NTS ABSTRACTFall2019'; protected $mLength = 13230; 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 = 18367; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 9828; 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 = 7; 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 = 18367; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 9828; 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 = 'NTS ABSTRACTFall2019'; private $mUrlform = 'NTS_ABSTRACTFall2019'; private $mDbkeyform = 'NTS_ABSTRACTFall2019'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1466; protected $mLatestID = 18492; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'NTS ABSTRACTFall2019'; protected $mLength = 13230; 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 => 'NTS_ABSTRACTFall2019']; public $loopCheckHash = []; public $depth = 0; private $volatile = FALSE; private $ttl = NULL; protected $childExpansionCache = []; private $maxPPNodeCount = 1000000; private $maxPPExpandDepth = 100 } )	.../Parser.php:4023
33	0.1556	2499944	SimpleMathJaxHooks::renderTex( $tex = '\\displaystyle{ p }', $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 = 7; public $mHighestExpansionDepth = 2; private $mTplRedirCache = []; public $mHeadings = [0 => [...], 1 => [...], 2 => [...]]; 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 = 'NTS ABSTRACTFall2019'; private $mUrlform = 'NTS_ABSTRACTFall2019'; private $mDbkeyform = 'NTS_ABSTRACTFall2019'; private $mNamespace = 0; private $mInterwiki = ''; private $mLocalInterwiki = FALSE; private $mFragment = ''; public $mArticleID = 1466; protected $mLatestID = 18492; private $mContentModel = 'wikitext'; private $mForcedContentModel = FALSE; private $mEstimateRevisions = NULL; public $prefixedText = 'NTS ABSTRACTFall2019'; protected $mLength = 13230; 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 = 18367; private $mRevisionTimestamp = NULL; private $mRevisionUser = NULL; private $mRevisionSize = NULL; private $mInputSize = 9828; 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	0.1556	2499944	ParserOutput->addModules( $modules = 'ext.SimpleMathJax' )	.../SimpleMathJaxHooks.php:34
35	0.1556	2499944	wfDeprecated( $function = 'ParserOutput::addModules with non-array argument', $version = '1.38', $component = ???, $callerOffset = ??? )	.../ParserOutput.php:1180
36	0.1556	2499944	MWDebug::deprecated( $function = 'ParserOutput::addModules with non-array argument', $version = '1.38', $component = FALSE, $callerOffset = 3 )	.../GlobalFunctions.php:765
37	0.1556	2500072	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	0.1556	2501768	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	0.1556	2501768	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	357752	{main}( )	.../index.php:0
2	0.0447	1478536	wfIndexMain( )	.../index.php:46
3	0.0447	1478648	MediaWiki->run( )	.../index.php:50
4	0.0447	1478648	MediaWiki->main( )	.../MediaWiki.php:562
5	0.2188	2843336	OutputPage->output( $return = TRUE )	.../MediaWiki.php:922
6	0.2188	2859912	WebResponse->header( $string = 'Content-type: text/html; charset=UTF-8', $replace = ???, $http_response_code = ??? )	.../OutputPage.php:2825
7	0.2188	2860104	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	357752	{main}( )	.../index.php:0
2	0.0447	1478536	wfIndexMain( )	.../index.php:46
3	0.0447	1478648	MediaWiki->run( )	.../index.php:50
4	0.0447	1478648	MediaWiki->main( )	.../MediaWiki.php:562
5	0.2188	2843336	OutputPage->output( $return = TRUE )	.../MediaWiki.php:922
6	0.2191	2860024	WebResponse->header( $string = 'Content-language: en', $replace = ???, $http_response_code = ??? )	.../OutputPage.php:2826
7	0.2191	2860024	header( $header = 'Content-language: en', $replace = TRUE )	.../WebResponse.php:75

@@ Line 168: / Line 168: @@
 | bgcolor="#BCD2EE"  align="center" | Holomorphic Continuation of Certain $L$-functions via Trace Formula
 |-
-| bgcolor="#BCD2EE"  |  In this talk, we will mainly discuss two basic conjectures on entireness of certain basic $L$-functions arising from Galois representation (algebra) and automorphic representation (analysis). Although the background and definitions are quite different, we will show these $L$-functions are closely related to each other by a generalized Jacquet-Zagier trace formula. As a consequence, we obtain holomorphy of adjoint $L$-functions for $\mathrm{GL}(n),$ where $n\leq 4.$ Some applications will be provided.
+| bgcolor="#BCD2EE"  |  In this talk, we will mainly discuss two basic conjectures on entireness of certain basic $L$-functions arising from Galois representations (algebra) and automorphic representations (analysis). Although the background and definitions are quite different, we will show these $L$-functions are closely related to each other by a generalized Jacquet-Zagier trace formula. As a consequence, we obtain holomorphy of adjoint $L$-functions for $\mathrm{GL}(n),$ where $n\leq 4.$ Some applications will be provided.

( ! ) 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	357752	{main}( )	.../index.php:0
2	0.0447	1478536	wfIndexMain( )	.../index.php:46
3	0.0447	1478648	MediaWiki->run( )	.../index.php:50
4	0.0447	1478648	MediaWiki->main( )	.../MediaWiki.php:562
5	0.2188	2843336	OutputPage->output( $return = TRUE )	.../MediaWiki.php:922
6	0.3217	3661376	OutputPage->sendCacheControl( )	.../OutputPage.php:2891
7	0.3218	3662392	WebResponse->header( $string = 'Vary: Accept-Encoding, Cookie', $replace = ???, $http_response_code = ??? )	.../OutputPage.php:2691
8	0.3218	3662392	header( $header = 'Vary: Accept-Encoding, Cookie', $replace = TRUE )	.../WebResponse.php:75

NTS ABSTRACTFall2019: Difference between revisions

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