Colloquia 2012-2013: Difference between revisions

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All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.


== Fall 2011 ==
== Spring 2013 ==


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!align="left" | host(s)
!align="left" | host(s)
|-
|-
|Sep 9
|'''Tues, Jan 15, B139'''
|[http://www.math.ethz.ch/~einsiedl Manfred Einsiedler] (ETH-Zurich)
|[http://people.maths.ox.ac.uk/piercel/ Lillian Pierce] (Oxford)
|''Periodic orbits on homogeneous spaces''
|[[#Pierce|A new twist on the Carleson operator]]
|Fish
|Denissov
|-
|-
|Sep 16
|'''Thurs, Jan 17, 2pm, 901VV'''
|[http://www.unc.edu/~rimanyi/ Richard Rimanyi] (UNC-Chapel Hill)
|[http://www-personal.umich.edu/~jblasiak/ Jonah Blasiak] (Michigan)
|''Global singularity theory''
|[[#Blasiak|Positivity, complexity, and the Kronecker problem]]
|Maxim
|Terwilliger
|-
|-
|Sep 23
|Jan 25
|[http://www.math.wisc.edu/~andreic Andrei Caldararu] (UW-Madison)
|[http://www.maths.usyd.edu.au/u/afish/ Alexander Fish] (Sydney)
|''The Pfaffian-Grassmannian derived equivalence''
|[[#Fish|Product sets in amenable groups through a dynamical approach]]
|(local)
|Gurevich
|-
|-
|Sep 30
|Feb 1
|[http://www.math.wisc.edu/~armstron/ Scott Armstrong] (UW-Madison)
|[http://www.math.wisc.edu/~dymarz/ Tullia Dymarz] (Madison)
|''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''
|[[#Dymarz|Quasisymmetric vs Bi-Lipschitz maps]]
|(local)
|Street
|-
|-
|Oct 7
|Feb 8
|[http://www.education.wisc.edu/ci/mathEd/?folder=people&pageName=ghousseini Hala Ghousseini] (University of Wisconsin-Madison)
|[http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] (Madison)
|''Developing Mathematical Knowledge for Teaching in, from, and for Practice''
|[[#Thiffeault|pseudo-Anosovs with small or large dilatation]]
|Lempp
|Roch
|-
|-
|Oct 14
|Feb 15
|[http://www.math.sunysb.edu/~alexk/ Alex Kontorovich] (Yale)
|[http://maeresearch.ucsd.edu/lauga/ Eric Lauga] (UCSD)
|''On Zaremba's Conjecture''
|[[#Lauga|Optimization in fluid-based locomotion]]
|Shamgar
|Spagnolie
|-
|-
|'''oct 19, Wed'''
|Feb 22
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)
|[http://math.umn.edu/~svitlana/ Svitlana Mayboroda] (University of Minnesota)
|''Convex Algebraic Geometry''
|[[#Mayboroda|Elliptic PDEs, analysis, and potential theory in irregular media]]
|'''distinguished lecturer'''
|Stovall
|Shamgar 
|-
|-
|'''oct 20, Thu'''
|Mar 1
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)
|[http://www.math.harvard.edu/~kwickelg/ Kirsten Wickelgren] (Harvard)
|''Quartic Curves and Their Bitangents''
|[[#Wickelgren|Grothendieck's anabelian conjectures]]
|'''distinguished lecturer'''
|Shamgar
|-
|oct 21
|[http://math.berkeley.edu/~bernd/ Bernd Sturmfels] (UC Berkeley)
|''Multiview Geometry''
|'''distinguished lecturer'''
|Shamgar 
|-
|Oct 28
|[http://www.math.osu.edu/~romanh/ Roman Holowinsky] (OSU)
|''Equidistribution Problems and L-functions''
|Street
|Street
|-
|-
|Nov 4
|March 8
|[http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=sijue Sijue Wu] (U Michigan)
|[http://homepages.cae.wisc.edu/~negrut/ Dan Negrut] (UW - Mechanical Engineering)
|''Wellposedness of the two and three dimensional full water wave problem''
|[[#Negrut|Using Advanced Computing in Applied Dynamics: From the Dynamics of Granular Material to the Motion of the Mars Rover]]
|Qin Li
|Caldararu
|-
|-
|'''Nov 7, Mo, 3pm, SMI 133'''
|March 15
|[http://www4.stat.ncsu.edu/~pantula/ Sastry Pantula] (NSCU and DMS/NSF)
|[http://www.icmat.es/kurusch/ Kurusch Ebrahimi Fard] (Madrid)
|''Opportunities in Mathematical and Statistical Sciences at DMS''
|[[#Fard|Spitzer-type identities in non-commutative Rota-Baxter algebras]]
|'''Joint Math/Stat Colloquium'''  
|Gurvich
|-
|<strike> March 22 </strike>
|[http://www2.warwick.ac.uk/fac/sci/maths/people/staff/neil_oconnell/ Neil O'Connell] (Warwick)
|CANCELLED
|Timo Seppalainen
|-
|-
|Nov 11
|March 29
|[http://cams.ehess.fr/document.php?id=891 Henri Berestycki] (EHESS and University of Chicago)
|'''Spring Break'''
|''Reaction-diffusion equations and propagation phenomena''
|No Colloquium
|'''Wasow lecture'''
|
|-
|-
|'''Nov 16, Wed'''
|April 5
|[http://www.math.uconn.edu/~towsner/index.php Henry Towsner] (U of Conn-Storrs)
|[http://hobbes.la.asu.edu/ John Jones] (ASU)
|''An Analytic Approach to Uniformity Norms''
|[[#Jones| Number fields with prescribed ramification]]
|Steffen 
|Boston
|-
|-
|Nov 18
|April 12
|[http://pages.cs.wisc.edu/~brecht/ Benjamin Recht] (UW-Madison, CS Department)
|[http://math.mit.edu/~asnowden/ Andrew Snowden] (MIT)
|''The Convex Geometry of Inverse Problems''
|[[#Snowden|Large algebraic structures with large amounts of symmetry]]
|Jordan
|Street
|-
|-
|'''Nov 22, Tue, 2:30PM, B205'''
|April 19
|[http://math.mit.edu/~zyun/ Zhiwei Yun] (MIT)
|Moe Hirsch (Honorary Fellow -- UW Madison)
|''Motives and the inverse Galois problem''
|[[#Hirsch|The Divine Madness: Mathematics, Myths and Metaphors]]
|Tonghai 
|Street
|-
|-
|'''Nov 28, Mon, 4PM'''
|'''Tuesday, April 30, 4PM'''
|[http://guests.mpim-bonn.mpg.de/joericke/ Burglind Joricke] (Institut Fourier, Grenoble)
|[http://www.ens.fr/spip.php?article1296&lang=en Laure Saint-Raymond] (ENS)]
|''Analytic knots, satellites and the 4-ball genus''
|[[#Saint-Raymond|Wasow Lecture: The Irreversibility in Gas Dynamics, a Matter of Probability]]
|Gong
|Wasow Lecture
|-
|-
|'''Nov 29, Tue, 2:30PM, B102'''
|May 3
|[http://www.math.ucla.edu/~isaac/ Isaac Goldbring] (UCLA)
|Davesh Maulik (Columbia)
|"Nonstandard methods in Lie theory"
|[[#Maulik|Plane curve singularities and knot invariants]]
|Lempp 
|Street
|-
|-
|'''Nov 30, Wed, 4PM'''
|May 10
|Bing Wang (Simons Institute)
|[http://www.wisdom.weizmann.ac.il/~gelbar/ Steve Gelbart] (Weizmann Institute)
|''Uniformization of algebraic varieties''
|[[#Gelbart| "Zeta"]]
|Sean 
|Gurevich
|-
|Dec 2
|[http://ib.berkeley.edu/people/faculty/person_detail.php?person=61 Robert Dudley] (University of California, Berkeley)
|''From Gliding Ants to Andean Hummingbirds: The Evolution of Animal Flight Performance''
|Jean-Luc
|-
|'''Dec 5, Mon, 2:25PM, Room 901'''
|[http://math.unc.edu/people/faculty/dima-arinkin Dima Arinkin] (UNC-Chapel Hill)
|''TBA''
|Andrei 
|-
|'''Dec 7, Wed, 4PM'''
|[http://www.dam.brown.edu/people/tnguyen/index.html Toan Nguyen] (Brown University)
|''On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations''
|Misha Feldman 
|-
|Dec 9
|[http://www.math.harvard.edu/~xinwenz/ Xinwen Zhu] (Harvard University)
|''TBA''
|Tonghai
|}
|}


== Spring 2012 ==
== Fall 2012 ==


{| cellpadding="8"
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!align="left" | host(s)
|-
|-
|'''Jan 26, Thu'''
|Sept 14
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)
|[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg] (Madison)
|''TBA''
|[[#Ellenberg|''FI-modules: an introduction'']]
|'''distinguished lecturer'''
|local
|-
|<strike>'''Sept 20, 4pm'''</strike>
|[http://www-stat.stanford.edu/~cgates/PERSI/ Persi Diaconis] (Stanford)
|CANCELLED
|Jean-Luc
|-
|Sept 21
|[http://eaton.math.rpi.edu/faculty/J.McLaughlin/mclauj.html Joyce McLaughlin] (RPI)
|[[#McLaughlin|''Mathematics for Imaging Biomechanical Parameters in Dynamic Elastography'']]
|WIMAW
|-
|-
|Jan 27
|Sept 28
|[http://people.cs.uchicago.edu/~const Peter Constantin] (University of Chicago)
|[http://math.mit.edu/~emarberg/ Eric Marberg] (MIT)
|''TBA''
|[[#Marberg|''Supercharacters for algebra groups: applications and extensions'']]
|'''distinguished lecturer'''
|Isaacs
|-
|-
|Feb 3
|Oct 5
|''Scheduled''
|[http://math.uchicago.edu/~masur/ Howard Masur] (Chicago)
|
|[[#Masur|''Winning games for badly approximable real numbers and billiards in polygons'']]
|Street
|Dymarz
|-
|-
|Feb 24
|'''Wed, Oct 10, 4pm'''
|[http://www.math.ubc.ca/~malabika/ Malabika Pramanik] (University of British Columbia)
|[http://www.kent.ac.uk/smsas/maths/our-people/profiles/lemmens_bas.html Bas Lemmens] (Univ. of Kent)
|''TBA''
|[[#Lemmens|From hyperbolic geometry to nonlinear Perron-Frobenius theory]]
|Benguria
|LAA lecture
|-
|-
|March 2
|'''Thur, Oct 11, 4pm'''
|[http://www.comsec.uwaterloo.ca/~ggong/ Guang Gong] (University of Waterloo)
|[http://www.ma.utexas.edu/users/gamba/ Irene Gamba] (UT-Austin)
|''TBA''
|[[#Gamba|Analytical and numerical issues associated with the dynamics of the non-linear Boltzmann equation]]
|Shamgar
|WIMAW
|-
|-
|March 16
|Oct 12
|[http://www.charlesdoran.net/ Charles Doran] (University of Alberta)
|[http://user.math.uzh.ch/rosenthal/ Joachim Rosenthal] (Univ. of Zurich)
|''TBA''
|[[#Rosenthal|Linear Random Network Codes, a Grassmannian Approach]]
|Matt Ballard
|Boston
|-
|-
|March 23
|Oct 19
|[http://www.math.temple.edu/~lorenz/ Martin Lorenz] (Temple University)
|[http://www.math.wisc.edu/~spagnolie/uw/index.html Saverio E Spagnolie] (Madison)
|''TBA''
|[[#Spagnolie|Elastic slender bodies in fluids and slender bodies in elastic fluids]]
|Don Passman
|Roch
|-
|-
|March 30
|Oct 26
|[http://www.math.fsu.edu/~aluffi/ Paolo Aluffi] (Florida State University)
|[http://math.berkeley.edu/~oeding/Home.html Luke Oeding] (UC Berkeley)
|''TBA''
|[[#Oeding|The Trifocal Variety]]
|Maxim
|Gurevich
|-
|-
|April 6
|'''Tues, Oct 30'''
|Spring recess
|[http://www.math.nyu.edu/faculty/majda/ Andrew Majda] (Courant)
|
|[[#Majda|Data Driven Methods for Complex Turbulent Systems]]
|
|Smith, Stechmann
|-
|-
|April 13
|'''Thurs, Nov 1'''
|[http://www.math.tulane.edu/~cortez/ Ricardo Cortez] (Tulane)
|[http://math.uchicago.edu/~ryzhik/ Lenya Ryzhik] (Chicago)
|''TBA''
|[[#Ryzhik|The role of a drift in elliptic and parabolic equations]]
|Mitchell
|Kiselev
|-
|-
|April 18
|Nov 2
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)
|[http://www.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota)
|''TBA''
|[[#Sverak|On scale-invariant solutions of the Navier-Stokes equations]]
|'''distinguished lecturer'''
|Kiselev
|-
|-
|April 19
|Nov 9
|[http://www.math.harvard.edu/~gross/ Benedict H. Gross] (Harvard)
|[http://www.math.wisc.edu/~andrews/ Uri Andrews] (Madison)
|''TBA''
|[[#Andrews|Computable Stability Theory]]
|'''distinguished lecturer'''
|Lempp
|-
|-
|April 20
|'''Mon, Nov 12'''
|[http://www-bcf.usc.edu/~guralnic/ Robert Guralnick] (University of South California)  
|[http://math.mit.edu/~smart/ Charles Smart] (MIT)
|''TBA''
|[[#Smart|Regularity and stochastic homogenization of fully nonlinear equations without uniform ellipticity]]
|Shamgar
|Feldman
|-
|-
|April 27
|'''Mon, Nov 26'''
|''Tentatively Scheduled''
|[http://www-personal.umich.edu/~erman/ Daniel Erman]  (U.Michigan)
|
|TBA
|Street
|Boston
|-
|-
|May 4
|'''Wed, Nov 28'''
|[http://www.math.sunysb.edu/~mde/ Mark Andrea de Cataldo] (Stony Brook)
|[http://www.nd.edu/~chill10/ Cameron Hill] (Notre Dame)
|''TBA''
|[[#Hill|Genericity in Discrete Mathematics]]
|Maxim
|Lempp
|-
|-
|May 11
|Nov 30
|''Tentatively Scheduled''
|[http://www.math.columbia.edu/~namle/ Nam Le] (Columbia)
|
|[[#Le|Boundary regularity for solutions to the linearized Monge-Ampere equations and applications]]
|Shamgar
|Feldman
|-
|-
|Dec 14
|[http://users.math.yale.edu/~alf8/ Amanda Folsom] (Yale)
|[[#Folsom|q-series and quantum modular forms]]
|Ellenberg/WIMAW
|}
|}


== Abstracts ==
== Abstracts ==


===Fri, Sept 9: Manfred Einsiedler (ETH-Zurich)===
===<span id="Ellenberg"></span>Sept 14: Jordan Ellenberg (UW-Madison) ===
''Periodic orbits on homogeneous spaces''
''FI-modules:  an introduction''
(joint work with T Church, B Farb, R Nagpal)
 
In topology and algebraic geometry one often encounters phenomena of _stability_.  A famous example is the cohomology of the moduli space of curves M_g; Harer proved in the 1980s that the sequence of vector spaces H_i(M_g,Q), with g growing and i fixed, has dimension which is eventually constant as g grows with i fixed.
 
In many similar situations one is presented with a sequence {V_n}, where the V_n are not merely vector spaces, but come with an action of S_n.  In many such situations the dimension of V_n does not become constant as n grows -- but there is still a sense in which it is eventually "always the same representation of S_n" as n grows.  The preprint
 
http://arxiv.org/abs/1204.4533
 
shows how to interpret this kind of "representation stability" as a statement of finite generation in an appropriate category; we'll discuss this set-up and some applications to the topology of configuration spaces, the representation theory of the symmetric group, and diagonal coinvariant algebras.  Finally, we'll discuss recent developments in the theory of FI-modules over general rings, which is joint work with (UW grad student) Rohit Nagpal.
 
 
<!--
===<span id="Diaconis"></span> '''Thu, Sept 20''': Persi Diaconis (Stanford) ===
''Spatial mixing: problems and progress''
 
One standard way of mixing (cards, dominos, Mahjong tiles) is to 'smoosh' them around on the table with two hands. I will introduce some models for this, present data (it's surprisingly effective) and some first theorems. The math involved is related to fluid flow and Baxendale-Harris random homeomorphisims.
-->
 
===<span id="McLaughlin"></span>Sept 21: Joyce R. McLaughlin (Rensselaer Polytechnic Institute) ===
''Mathematics for Imaging Biomechanical Parameters in Dynamic Elastography''
 
Elastography, the imaging of biomechanical parameters in
tissue, is motivated by the doctor’s palpation exam where the doctor
presses against the skin to detect stiff and abnormal tissue changes. In
dynamic elastography experiments, the tissue is in motion with
displacement amplitudes on the order of tens of microns.  The
displacement(s) are determined with sequences of MR data sets or
sequences of ultrasound RF/IQ data sets within the tissue; and the data
shows a dispersive effect indicating that tissue is viscoelastic.  A
choice of viscoelastic model must be made.  For each model the
biomechanical parameters satisfy a first order, linear or nonlinear,
partial differential equation (system) with real or complex coefficients.
We discuss the mathematical properties of these equations and how those
properties lead to successful interpretation of the data, and to
successful algorithms and images.  We show biomechanical images of breast
cancer and prostate cancer and compare those images to ultrasound images
and histology slides with marked cancerous inclusions.
 
 
===<span id="Marberg"></span>Sept 28: Eric Marberg (MIT) ===
''Supercharacters for algebra groups: applications and extensions''
 
The group U_n(F_q) of unipotent upper triangular matrices over a
finite field belongs to the same list of fundamental examples as the
symmetric or general linear groups. It comes as some surprise, therefore,
that the group's irreducible characters are unknown, and considered in some
sense unknowable. In order to tackle problems normally requiring knowledge
of a group's irreducible characters, Diaconis and Isaacs developed the
notion of the supercharacters of an algebra group, generalizing work of
Andre and Yan. Algebra groups form a well-behaved class of p-groups
including U_n(F_q) as a prototypical example, and supercharacters are
certain reducible characters which form a useful approximation to the set
of irreducible characters. In this talk I will survey several equivalent
definitions of the supercharacters of an algebra group, and discuss some
applications and extensions of these approaches. On one end of things, I
intend briefly to introduce the recent discovery of how certain
representation theoretic operations on the supercharacters of U_n(F_q)
naturally define a Hopf algebra structure, which has been studied under a
different name by combinatorialists. In another direction, I will explain
how one can view the supercharacters of an algebra group as the first step
in a more general reduction process, which can be used to shed light on
some mysterious properties of U_n(F_q).
 
===<span id="Masur"></span>Oct 04 Howard Masur (Chicago) ===
''Winning games for badly approximable real numbers and billiards in polygons''
 
Wolfgang Schmidt invented the notion of a winning subset of Euclidean space in a game between two players. Winning sets have nice
properties such as full Hausdorff dimension. The basic example of a winning set considered by Schmidt are those reals badly
approximated by rationals.  An equivalent formulation by Artin is that badly approximable reals  correspond to geodesics that stay in a bounded set in the modular curve. There is also an equivalent formulation in terms of sets of directions for  the linear flow on a square torus or equivalently, billiard trajectories in a square. In joint work with Yitwah Cheung and Jon Chaika we extend this notion of winning to flows on flat surfaces of higher genus with applications to billiards in rational angled polygons. My intention in this talk is to give the background on the Schmidt game, describe the classical results before introducing the more recent work.
 
 
===<span id="Lemmens"></span>'''Wed, Oct 10''': Bas Lemmens (University of Kent) ===
''From hyperbolic geometry to nonlinear Perron-Frobenius theory''
 
In a letter to Klein Hilbert remarked that the logarithm of the cross-ratio is a metric on
any open, bounded, convex set in Euclidean space. These metric spaces are nowadays
called Hilbert geometries. They are a natural non-Riemannian generalization of Klein's
model of the hyperbolic plane, and play a role in the solution of Hilbert's fourth problem.
In the nineteen fifties Garrett Birkhoff and Hans Samelson independently discovered that
one can use Hilbert's metric and the contraction mapping principle to prove the existence
and uniqueness of a positive eigenvector for a variety of linear operators that leave a closed
cone in a Banach space invariant. Their results are a direct extension of the classical
Perron-Frobenius theorem concerning the eigenvectors and eigenvalues of nonnegative
matrices. In the past decades this idea has been further developed and resulted in strikingly detailed nonlinear extensions of the Perron-Frobenius theorem. In this talk I will discuss
the synergy between metric geometry and (nonlinear) operator theory and some of the
recent results and open problems in this area.
 
 
===<span id="Gamba"></span>'''Thur, Oct 11''': Irene Gamba (University of Texas-Austin) ===
''Analytical and numerical issues associated with the dynamics of the non-linear Boltzmann equation''
 
The non-linear Boltzmann equation models the evolution of a statistical flow associated with particle systems in a rarefied or mesoscopic regimes. Its analytical local as well as long time behavior depends strongly on the growth conditions of the collisional kernels, as functions of the intermolecular potentials and scattering mechanisms. We will present  recent analytical results, such as classical convolutional inequalities and sharp moments estimates, which imply propagation of $W^{k,p}$ norms and exponential decay of high energy tails, and their consequences on the existence, regularity, and stability of solutions for initial value problems as well as control of decay rates to equilibrium. In particular we present a numerical approximation to the non-linear Boltzmann problem by a conservative spectral scheme, and show spectral accuracy as well as error estimates.
 
===<span id="Rosenthal"></span>Oct 12: Joachim Rosenthal (Univ of Zurich) ===
''Linear Random Network Codes, a Grassmannian Approach''
 
Elastography, the imaging of biomechanical parameters in
A novel framework for random network coding has been introduced by
Koetter and Kschischang.  In this framework information is encoded in
subspaces of a given ambient space over a finite field. A natural
metric is introduced where two subspaces are `close to each other' as
soon as their dimension of intersection is large. This framework poses
the challenge to come up with new codes with optimal or near optimal
distance and to develop efficient decoding algorithms.
 
In a first part of the talk we will provide a survey. In a second part
of the talk we report on progress constructing spread codes
and orbit codes. The decoding problem of orbit codes can be
interpreted as a problem in Schubert calculus over a finite field.
 
 
===<span id="Spagnolie"></span>'''Fri, Oct 19''': Saverio E. Spagnolie (Madison) ===
''Elastic slender bodies in fluids and slender bodies in elastic fluids''
 
Abstract:
 
The scientific study of elastic materials dates back to Galileo, and fluid mechanics to Archimedes, but the interaction of elastic bodies and viscous fluids remains a topic at the frontier of modern research. We will discuss two problems on this topic of recent interest. First, when a flexible filament is confined to a fluid interface, the balance between capillary attraction, bending resistance, and tension from an external source can lead to a self-buckling instability. We will walk through an analysis of this elastocapillary instability, and analytical formulae will be shown that compare favorably with the results of detailed numerical computations.  Second, we will discuss the motility of a swimming helical body in a viscoelastic fluid, wherein the fluid itself exhibits an elastic response to deformation. The helical geometry is exploited to generate a highly accurate numerical method, and we will show that the introduction of viscoelasticity can either enhance or retard the swimming speed depending on the body geometry and the properties of the fluid (through a dimensionless Deborah number). Our findings bridge the gap between studies showing situationally dependent enhancement or retardation of swimming speed, and may help to clarify phenomena observed in systems from spermatozoan swimming to mechanical drilling.
 
===<span id="Oeding"></span>'''Fri, Oct 26''': Luke Oeding (UC Berkeley) ===
''The Trifocal Variety''
 
Abstract:
In Computer Vision one considers many cameras looking at the same scene.  From this setup many interesting geometric and algebraic questions arise.  In this talk we will focus on the case of 3 cameras and study the so called trifocal tensors.  Trifocal tensors are constructed from a bilinear map defined using the trifocal setup.  A natural question is, given a particular tensor, how can one determine if it is a trifocal tensor?  This question can be answered by finding implicit defining equations for the trifocal variety. From an algebraic standpoint, it is also interesting to know the minimal generators of the defining ideal of the trifocal variety.
 
In this talk I will explain our use of symbolic and numerical computations aided by Representation Theory and Numerical Algebraic Geometry to find the minimal generators of the ideal of the trifocal variety. This is joint work with Chris Aholt (Washington).  Our work builds on the work of others (such as Hartley-Zisserman, Alzati-Tortora and Papadopoulo-Faugeras) who have already considered this problem set-theoretically.
 
My goal is to make most of the talk accessible to anyone with a modest background in Linear Algebra.
 
 
===<span id="Majda"></span>'''Tues, Oct 30''': Andrew Majda (Courant) ===
''Data Driven Methods for Complex Turbulent Systems''
 
An important contemporary research topic is the development of physics
constrained data driven methods for complex, large-dimensional turbulent
systems such as the equations for climate change science. Three new
approaches to various aspects of this topic are emphasized here. 1) The
systematic development of physics constrained quadratic regression models
with memory for low-frequency components of complex systems; 2) Novel
dynamic stochastic superresolution algorithms for real time filtering of
turbulent systems; 3) New nonlinear Laplacian spectral analysis (NLSA) for
large-dimensional time series which capture both intermittency and
low-frequency variability unlike conventional EOF or principal component
analysis. This is joint work with John Harlim (1,2), Michal Branicki (2),
and Dimitri Giannakis (3).
 
=== <span id="Ryzhik"></span>'''Thurs, Nov 1''': Lenya Ryzhik (Chicago) ===
''The role of a drift in elliptic and parabolic equations''
 
The first order partial differential equations are closely connected to the underlying characteristic ODEs. The second order elliptic and parabolic equations are as closely connected to the Brownian motion and more general diffusions with a drift. From a variety of points of view, the drift does not really matter - all diffusions look more or less similar. As a caveat to this reasonable line of thought, I will describe a menagerie of problems: linear and nonlinear, steady and time-dependent, compressible and incompressible, where the drift and diffusion confirm the Mayakovsky thesis "Woe to one alone!" Together, they lead to enhanced mixing and improved regularity that are impossible
for each one of them to attain.
 
===<span id="Sverak"></span>Nov 2: Vladimir Sverak (Minnesota) ===
''On scale-invariant solutions of the Navier-Stokes equations''
 
The solutions of the Navier-Stokes equations which are invariant under the scaling symmetry of the equations provide an interesting window into non-linear regimes which are not accessible by perturbation theory. They appear to give valuable hints concerning the old question about the uniqueness of weak solutions. In the lecture we outline a recent proof of the result that for every scale-invariant initial data there is a global scale-invariant solution (smooth for positive times), and we explain connections to the uniqueness problem. This is joint work with Hao Jia.
 
===<span id="Andrews"></span>Nov 9: Uri Andrews (Madison) ===
''Computable Stability Theory''
 
Stability theory attempts to classify the underlying structure of
mathematical objects. The goal of computable mathematics is to understand
when mathematical objects or constructions can be demonstrated computably.
I'll talk about the relationship between underlying structure and
computation of mathematical objects.
 
===<span id="Smart"></span>Monday, Nov 12: Charles Smart (MIT) ===
''Regularity and stochastic homogenization of fully nonlinear equations without uniform ellipticity''


We call an orbit xH of a subgroup H<G on a quotient space Gamma \ G
I will discuss regularity of fully nonlinear elliptic
periodic if it has finite H-invariant volume. These orbits have
equations when the usual uniform upper bound on the ellipticity is
intimate connections to a variety of number theoretic problems, e.g.
replaced by bound on its $L^d$ norm, where $d$ is the dimension of the
both integer quadratic forms and number fields give rise periodic
ambient space. Our
orbits and these periodic orbits then relate to local-global problems
estimates refine the classical theory and require several new ideas
for the quadratic forms or to special values of L-functions.  We will
that we believe are of independent interest. As an application, we
discuss whether a sequence of periodic orbits equidistribute in Gamma
prove homogenization for a class of stationary ergodic strictly
\ G assuming the orbits become more complicated (which can be measured
elliptic equations.
by a discriminant). If H is a diagonal subgroup (also called torus or
Cartan subgroup), this is not always the case but can be true with a
bit more averaging. As a theorem of Mozes and Shah show the case where
H is generated by unipotents is well understand and is closely related
to the work of M. Ratner. We then ask about the rate of approximation,
where the situation is much more complex. The talk is based on several
papers which are  joint work with E.Lindenstrauss, Ph. Michel, and A.
Venkatesh resp. with G. Margulis and A. Venkatesh.


===Fri, Sept 16: Richard Rimanyi (UNC)===
''Global singularity theory''


The topology of the spaces A and B may force every map from A to B to have certain singularities. For example, a map from the Klein bottle to 3-space must have double points. A map from the projective plane to the plane must have an odd number of cusp points.
===<span id="Hill"></span>Wednesday, Nov 28: Cameron Hill (Notre Dame) ===
''Genericity in Discrete Mathematics''


To a singularity one may associate a polynomial (its Thom polynomial) which measures how topology forces this particular singularity. In the lecture we will explore the theory of Thom polynomials and their applications in enumerative geometry. Along the way, we will meet a wide spectrum of mathematical concepts from geometric theorems of the ancient Greeks to the cohomology ring of moduli spaces.
I will discuss the intriguing role that ``generic'' objects can play in finitary discrete mathematics. Using the framework of model theory, we will see that there are at least two reasonable but very different notions of genericity relative to a class of finite structures (like a class of finite graphs or a class of finite groups). Through discussions of zero-one laws and structural Ramsey theory, I will try to illustrate the importance of generically-categorical classes -- those for which the various notions of genericity coincide. To finish, I will state some results that follow from the assumption of generic-categoricity.


===Fri, Sept 23: Andrei Caldararu (UW-Madison)===
===<span id="Le"></span>Nov 30: Nam Le (Columbia) ===
''The Pfaffian-Grassmannian derived equivalence''
''Boundary regularity for solutions to the linearized Monge-Ampere equations and applications''


String theory relates certain seemingly different manifolds through a relationship called mirror symmetry. Discovered about 25 years ago, this story is still very mysterious from a mathematical point of view. Despite the name, mirror symmetry is not entirely symmetric -- several distinct spaces can be mirrors to a given one. When this happens it is expected that certain invariants of these "double mirrors" match up. For a long time the only known examples of double mirrors arose through a simple construction called a flop, which led to the conjecture that this would be a general phenomenon. In joint work with Lev Borisov we constructed the first counterexample to this, which I shall present. Explicitly, I shall construct two Calabi-Yau threefolds which are not related by flops, but are derived equivalent, and therefore are expected to arise through a double mirror construction. The talk will be accessible to a wide audience, in particular to graduate students. There will even be several pictures!
In this talk, I will discuss boundary regularity of solutions to the linearized Monge-Ampere equations, and their applications to nonlinear, fourth order, geometric Partial Differential Equations (PDE).  
First, I will present my regularity results in joint work with O. Savin and T. Nguyen including:
boundary Holder gradient estimates and global $C^{1,\alpha}$ estimates, global Holder estimates and global $W^{2,p}$ estimates.
Then, I will describe applications of the above regularity results to several nonlinear, fourth order, geometric PDE such as:  global second derivative estimates for the second
boundary value problem of the prescribed affine mean curvature and Abreu's equations; and global regularity for minimizers having prescribed determinant of certain convex functionals motivated by
the Mabuchi functional in complex geometry.


===Fri, Sept 30: Scott Armstrong (UW-Madison)===
===<span id="Folsom"></span>Dec 14: Amanda Folsom (Yale) ===
''Optimal Lipschitz extensions, the infinity Laplacian, and tug-of-war games''
''q-series and quantum modular forms''


Given a nice bounded domain, and a Lipschitz function
While the theory of mock modular forms has seen great advances in the last decade, questions remain. We revisit Ramanujan's last letter to Hardy, and prove one of his remaining conjectures as a special case of a more general result. Surprisingly, Dyson's combinatorial rank function, the Andrews-Garvan crank functions, mock theta functions, and quantum modular forms, all play key roles. Along these lines, we also show that the Rogers-Fine false theta functions, functions that have not been well understood within the theory of modular forms, specialize to quantum modular forms. This is joint work with K. Ono (Emory U.) and R.C. Rhoades (Stanford U.).
defined on its boundary, consider the problem of finding an extension
of this function to the closure of the domain which has minimal
Lipschitz constant. This is the archetypal problem of the calculus of
variations
"in the sup-norm". There can be many such minimal Lipschitz
extensions, but there is there is a unique minimizer once we properly
"localize" this Lipschitz minimizing property. This minimizer is
characterized by the infinity Laplace equation: the Euler-Lagrange
equation for our optimization problem. This PDE is a very highly
degenerate nonlinear elliptic equation which does not possess smooth
solutions in general. In this talk I will discuss what we know about
the infinity Laplace equation, what the important open questions are,
and some interesting recent developments. We will even play a
probabilistic game called "tug-of-war".


===Fri, Oct 7: Hala Ghousseini (University of Wisconsin-Madison)===
===<span id="Pierce"></span>Tues, Jan 15, B139: Lillian Pierce (Oxford) ===
''Developing Mathematical Knowledge for Teaching in, from, and for Practice''
''A new twist on the Carleson operator''


Recent research in mathematics education has established that successful teaching requires a specialized kind of professional knowledge known as Mathematical Knowledge for Teaching (MKT). The mathematics education community, however, is beginning to appreciate that to be effective, teachers not only need to know MKT but also be able to use it in interaction with students (Hill & Ball, 2010). Very few examples exist at the level of actual practice of how novice teachers develop such knowledge for use. I will report on my current work on the Learning in, from, and for Practice project to develop, implement, and study what mathematics teacher educators can do to support novice teachers in acquiring and using Mathematical Knowledge for Teaching.
Must the Fourier series of an L^2 function converge pointwise almost everywhere? In the 1960's, Carleson answered this question in the affirmative, by studying a particular type of maximal singular integral operator, which has since become known as a Carleson operator. In the past 40 years, a number of important results have been proved for generalizations of the original Carleson operator. In this talk we will introduce the Carleson operator and survey several of its generalizations, and then describe new joint work with Po Lam Yung that introduces curved structure to the setting of Carleson operators.


===Fri, Oct 14: Alex Kontorovich (Yale)===
===<span id="Blasiak"></span>Thurs, Jan 17, 2pm, 901VV: Jonah Blasiak (Michigan) ===
''On Zaremba's Conjecture''
''Positivity, complexity, and the Kronecker problem''


It is folklore that modular multiplication is "random". This concept is useful for many applications, such as generating pseudorandom sequences, or in quasi-Monte Carlo methods for multi-dimensional numerical integration. Zaremba's theorem quantifies the quality of this "randomness" in terms of certain Diophantine properties involving continued fractions. His 40-year old conjecture predicts the ubiquity of moduli for which this Diophantine property is uniform. It is connected to Markoff and Lagrange spectra, as well as to families of "low-lying" divergent geodesics on the modular surface. We prove that a density one set satisfies Zaremba's conjecture, using recent advances such as the circle method and estimates for bilinear forms in the Affine Sieve, as well as a "congruence" analog of the renewal method in the thermodynamical formalism. This is joint work with Jean Bourgain.
Positivity problems in algebraic combinatorics ask to find positive combinatorial formulae
for nonnegative quantities arising in geometry and representation theory like cohomological dimensions and dimensions of algebras and their irreducible representations.
A famous open positivity problem in representation theory is the Kronecker problem, which asks for a positive combinatorial formula for decomposing tensor products of irreducible representations of the symmetric group.
We will begin with a general discussion of positivity problems and an intriguing new motivation for these problems from complexity theory.
We will then present our solution to a special case of the Kronecker problem that substantially improves on previous results.


===Wed, Oct 19: Bernd Sturmfels (Berkeley)===
===<span id="Fish"></span>Fri, Jan 25: Alexander Fish (Sydney) ===
''Convex Algebraic Geometry''
''Product sets in amenable groups through a dynamical approach''


This lecture concerns convex bodies with an interesting algebraic structure.
We will describe a new correspondence between product sets in a countable amenable group and product sets in compact groups. This approach enables us to obtain quantitative results concerning product sets in amenable groups. The talk is for general mathematical audience.  
A primary focus lies on the geometry of semidefinite optimization. Starting
(based on a joint work with M. Bjorklund)
with elementary questions about ellipses in the plane, we move on to discuss
the geometry of spectrahedra, orbitopes, and convex hulls of real varieties.


===Thu, Oct 20: Bernd Sturmfels (Berkeley)===
===<span id="Dymarz"></span>Fri, Feb 1: Tullia Dymarz (Madison) ===
''Quartic Curves and Their Bitangents''
''Quasisymmetric vs Bi-Lipschitz maps''


We present a computational study of plane curves of degree four, with
On a metric space, there are various classes of functions which respect aspects of the metric space structure.  One of the most basic classes is the bi-Lipschitz maps (Lipschitz maps whose inverses are also Lipschitz).  Another possibly much larger class consists of the so-called quasisymmetric maps (these are closely related quasiconformal maps).  On both Euclidean space and the p-adics, there are many quasisymmetric maps which are not bi-Lipschitz.  However, on the product of Euclidean space with the p-adics, we show that all quasisymmetric maps are bi-Lipschitz.  Furthermore,  our proof does not use any direct analysis
primary focus on writing their defining polynomials as sums of squares
but instead uses coarse topology and results from negative curvature.
and as symmetric determinants. Number theorists will enjoy the appearance
of the Weyl group <math>E_7</math> as the Galois group of the 28 bitangents. Based
===<span id="Thiffeault"></span>Feb 8: Jean-Luc Thiffeault (Madison) ===
on joint work with Daniel Plaumann and Cynthia Vinzant, this lecture
''pseudo-Anosovs with small or large dilatation''
spans a bridge from 19th century algebra to 21st century optimization.


===Fri, Oct 21: Bernd Sturmfels (Berkeley)===
Homeomorphisms of a surface to itself can be classified using the
''Multiview Geometry''
well-known Thurston-Nielsen theorem.  The most interesting topological
class contains pseudo-Anosov mappings: they stabilize a pair of
transverse singular foliations with a finite number of singularities.
These foliations are called unstable and stable, and are respectively
expanded and compressed by an algebraic constant called the
dilatation.  Characterizing the possible values of these dilatations
for a given suface is an open problem.  Here I discuss a method to
find the minimum value of the dilatation on closed surfaces of a given
genus, for the special case where the foliations are orientable.  I
will then address the opposite problem: how to find pseudo-Anosovs
with large dilatations.  Unlike the minimizer problem, this is not
well-defined -- the answer is infinity -- unless we add a constraint.
Constraints can arise from practical optimization problems in
engineering, and I will show some optimal solutions that can be
incorporated in devices called taffy pullers. (This is joint work with
Erwan Lanneau and Matt Finn.)


The study of two-dimensional images of three-dimensional scenes is foundational
===<span id="Lauga"></span>Feb 15: Eric Lauga (UCSD) ===
for computer vision. We present work with Chris Aholt and Rekha Thomas on the
''Optimization in fluid-based locomotion''
polynomials characterizing images taken by <math>n</math> cameras. Our varieties are
threefolds that vary in a family of dimension <math>11n-15</math> when the cameras are
moving. We use toric geometry and Hilbert schemes to characterize
degenerations of camera positions.


===Fri, Oct 28: Roman Holowinsky (OSU)===
The world of self-propelled low-Reynolds number swimmers is inhabited by a myriad of microorganisms such as bacteria, spermatozoa, ciliates, and plankton. In this talk, we focus on the locomotion of ciliated cells. Cilia are short slender whiplike appendages (a few microns long, one tenth of a micron wide) internally actuated by molecular motors (dyneins) which generate a distribution of bending moments along the cilium length and produce time-varying shape deformations. In most cases cilia are not found individually but instead in densely packed arrays on surfaces. In this work we will ask the question: can the individual and collective dynamics of cilia on the surface of an individual microorganism be rationalized as the solution to an optimization problem? We first address the deformation of individual cilia anchored on surfaces before characterizing the locomotion and feeding by surface distortions of swimmers covered by cilia array. We demonstrate, as solution to the optimization procedure, the appearance of the well-known two-stroke kinematics of an individual cilium, as well as waves in cilia array reminiscent of experimentally-observed metachronal waves.
''Equidistribution Problems and L-functions''


There are several equidistribution problems of arithmetic nature which have had shared interest between the fields of Ergodic Theory and Number Theory. The relation of such problems to homogeneous flows and the reduction to analysis of special values of automorphic L-functions has resulted in increased collaboration between these two fields of mathematics.  We will discuss two such equidistribution problems: the equidistribution of Heegner points for negative quadratic discriminants and the equidistribution of mass of Hecke eigenforms.  Equidistribution follows upon establishing subconvexity bounds for the associated L-functions and are fine examples as to why one might be interested in such objects.
===<span id="Mayboroda"></span>Feb 22: Svitlana Mayboroda (University of Minnesota) ===
''Elliptic PDEs, analysis, and potential theory in irregular media''


===Fri, Nov 4: Sijue Wu (U Michigan)===
Elliptic boundary value problems are well-understood in the
''Wellposedness of the two and three dimensional full water wave problem''
case when the boundary, the data, and the coefficients exhibit
smoothness. However, perfectly uniform smooth systems do not exist in
nature, and every real object inadvertently possesses irregularities
(a sharp edge of the boundary, an abrupt change of the medium, a
defect of the construction).


We consider the question of global in time existence and uniqueness of solutions of the infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial data that is small in its kinetic energy and height, we show that the 2-D full water wave equation is uniquely solvable almost globally in time. And for any initial interface that is small in its steepness and velocity, we show that the 3-D full water wave equation is uniquely solvable globally in time.
The analysis of general non-smooth elliptic PDEs gives rise to
decisively new challenges: possible failure of maximal principle and
positivity,
breakdown of boundary regularity, lack of the classical L^2 estimates,
to mention just a few. Further progress builds on an involved blend of
harmonic analysis, potential theory and geometric measure theory
techniques. In this talk we are going to discuss some highlights of
the history, conjectures, paradoxes, and recent discoveries such as
the higher-order Wiener criterion and maximum principle for higher
order PDEs, solvability of rough elliptic boundary problems, as well
as an intriguing phenomenon of localization of eigenfunctions --
within and beyond the limits of the famous Anderson localization.


===Mo, Nov 7: Sastry Pantula (DMS/NSF, NCSU)===
Parts of the talk are based on joint work with S. Hofmann, M. Filoche,
''Opportunities in Mathematical and Statistical Sciences at DMS''
C. Kenig, V. Maz'ya, and J. Pipher.


In this talk, I will give you an overview of the funding and
===<span id="Wickelgren"></span>March 1: Kirsten Wickelgren (Harvard) ===
other opportunities at DMS for mathematicians and statisticians. I will
''Grothendieck's anabelian conjectures''
also talk about our new program in computational and data-enabled science
and engineering in mathematical and statistical sciences (CDS&E-MSS).


===Fri, Nov 11: Henri Berestycki (EHESS and University of Chicago)===
Grothendieck's anabelian conjectures predict that the solutions to certain polynomial equations over Q are determined by the loops on the corresponding space of all solutions, or more precisely that the etale fundamental group is a fully faithful functor from certain anabelian schemes to profinite groups with Galois action. This is analogous to an equivalence between fixed points and homotopy fixed points for Galois actions. We will introduce the anabelian conjectures and their topological analogues, and relate certain nilpotent obstructions to the existence of rational points introduced by Jordan Ellenberg to higher cohomology operations. These cohomology operations encode when the existence of particular Galois extensions implies the existence of others, and are connected with the formality of the etale cochains. As a corollary one has that the order n Massey product <x,x,..x,1-x,x,...x> vanishes, where x denotes the image of x in k* under the Kummer map k* -> H^1(Gal(kbar/k), Z_l(1)).
''Reaction-diffusion equations and propagation phenomena''


Starting with the description of reaction-diffusion mechanisms in physics, biology and ecology, I will explain the motivation for this class of non-linear partial differential equations and mention some of the interesting history of these systems. Then, I will review classical results in the homogeneous setting and discuss their relevance. The second part of the lecture will be concerned with recent developments in non-homogeneous settings, in particular for Fisher-KPP type equations. Such problems are encountered in models from ecology. The mathematical theory will be seen to shed light on questions arising in this context.
===<span id="Negrut"></span>March 8: Dan Negrut (UW-Mechanical Engineering)===
''Using Advanced Computing in Applied Dynamics: From the Dynamics of Granular Material to the Motion of the Mars Rover''


===Wed, Nov 16: Henry Towsner (U of Conn-Storrs)===
This talk outlines numerical solution methods and their implementation in a high performance computing-enabled software infrastructure aimed at supporting physics-based simulation for virtual design in Engineering. The applications of interest include granular dynamics, rigid/flexible many-body dynamics, and fluid-solid interaction problems. CHRONO, the software infrastructure developed as part of this ongoing effort, partitions the problem of interest into a number of sub-problems that are solved in parallel using Graphics Processing Unit (GPU) cards, or multi-core CPUs. The five components at the cornerstone of the vision that eventually led to CHRONO are: (a) modeling support for multi-physics phenomena; (b) scalable numerical methods for multi-GPU and multi-core hardware architectures; (c) methods for proximity computation and collision detection; (d) support for domain decomposition and load balance; and (e) tools for carrying out visualization and post-processing in a distributed manner. Several engineering applications will be used to demonstrate how these five components are implemented to leverage a heterogeneous CPU/GPU supercomputer available at the Wisconsin Applied Computing Center. The talk will conclude with a brief discussion of current trends in high performance computing and how they are poised to change the field of Computational Science in the near future.
''An Analytic Approach to Uniformity Norms''


The Gowers uniformity norms have proven to be a powerful tool in extremal combinatorics, and a number of "structure theorems" have been given showing that the uniformity norms provide a dichotomy between "structured" objects and "random" objects.  While analogous norms (the Gowers-Host-Kra norms) exist in dynamical systems, they do not quite correspond to the uniformity norms in the finite setting.  We describe an analytic approach to the uniformity norms in which the "correspondence principle" between the finite setting and the infinite analytic setting remains valid.
===<span id="Fard"></span>March 15: Kurusch Ebrahimi Fard (Madrid) ===
''Spitzer-type identities in non-commutative Rota-Baxter algebras''


===Fri, Nov 18: Ben Recht (UW-Madison)===
Gian-Carlo Rota suggested in one of his last articles the problem of developing the notion of integration algebra, complementary to the already existing theory of differential algebras. This idea was mainly motivated by Rota's deep appreciation for Chen's fundamental work on iterated integrals. As a starting point for such a theory Rota proposed to consider a particular operator identity first introduced in 1960 by the mathematician Glen Baxter. It was later coined Rota-Baxter identity. Examples range from algebras with a direct decomposition into subalgebras to algebras of functions equipped with the ordinary Riemann integral or its discrete analogs.
''The Convex Geometry of Inverse Problems''
Rota-Baxter algebras feature a genuine factorization property. It is intimately related to linear fixpoint equations, such as those, for instance, appearing in the renormalization problem in perturbative quantum field theory. For arbitrary commutative Rota-Baxter algebras, proper exponential solutions of such fixpoint equations are described by what is known as the classical Spitzer identity. The similar classical Bohnenblust-Spitzer identity involves the symmetric group, and generalizes the simple observation that the n-fold iterated integral of a function is proportional to the n-fold product of the primitive of this function. Recently, the seminal Cartier-Rota theory of classical Spitzer-type identities has been generalized to noncommutative Rota-Baxter algebras. Pre-Lie algebras (also known as Vinberg or Gerstenhaber algebras) play a crucial role in this approach.
In this talk we will provide a short introduction to Rota-Baxter algebras, and review recent work on Spitzer-type identities.
This talk is based on joint work with Frederic Patras (CNRS, Nice, France) and Dominique Manchon (CNRS, Clermont-Ferrand, France).


Deducing the state or structure of a system from partial, noisy measurements is a fundamental task throughout the sciences and engineering. The resulting inverse problems are often ill-posed because there are fewer measurements available than the ambient dimension of the model to be estimated. In practice, however, many interesting signals or models contain few degrees of freedom relative to their ambient dimension: a small number of genes may constitute the signature of a disease, very few parameters may specify the correlation structure of a time series, or a sparse collection of geometric constraints may determine a molecular configuration. Discovering, leveraging, or recognizing such low-dimensional structure plays an important role in making inverse problems well-posed.
===<span id="Jones"></span>April 5: John Jones (ASU) ===
''Number fields with prescribed ramification''


In this talk, I will propose a unified approach to transform notions of simplicity and latent low-dimensionality into convex penalty functionsThis approach builds on the success of generalizing compressed sensing to matrix completion, and greatly extends the catalog of objects and structures that can be recovered from partial information. I will focus on a suite of data analysis algorithms designed to decompose general signals into sums of atoms from a simple---but not necessarily discrete---set. These algorithms are derived in a convex optimization framework that encompasses previous methods based on l1-norm minimization and nuclear norm minimization for recovering sparse vectors and low-rank matricesI will provide sharp estimates of the number of generic measurements required for exact and robust recovery of a variety of structured models.  I will then detail several example applications and describe how to scale the corresponding inference algorithms to massive data sets.
Finite extensions of the rational numbers are basic objects of algebra and
number theoryWe discuss the interaction of two basic invariants
associated to such a field, its set of ramified primes and its Galois
groupAfter describing the basic problem, we present computational and
theoretical results.


===Tue, Nov 22: Zhiwei Yun (MIT)===
===<span id="Snowden"></span>April 12: Andrew Snowden (MIT) ===
"Motives and the inverse Galois problem"


We will use geometric Langlands theory to solve two problems
In recent years, it has been realized that various large algebraic
simultaneously. One is Serre's question about whether there
structures admitting large amounts of symmetry behave as if they were
exist motives over Q with motivic Galois groups of type E_8 or G_2; the other
small. For example, when symmetries are taken into account, polynomial
is whether there are Galois extensions of Q with Galois groups E_8(p)
rings in infinitely many variables retain some of the favorable
or G_2(p) (the finite simple groups of Lie type). The answers to both
properties of polynomial rings in finitely many variables. This
questions are YES. No familiarity with either motives or geometric
observation has been applied to obtain uniformity results in diverse
Langlands or E_8 will be assumed.
fields. I will describe some of the recent work in this area.


===Mon, Nov 28: Burglind Joricke (Institut Fourier, Grenoble)===
===<span id="Hirsch"></span>April 19: Moe Hirsch (Honorary Fellow -- UW Madison) ===
"Analytic knots, satellites and the 4-ball genus"


After introducing classical geometric knot invariants and satellites
I will discuss various ideas about mathematics which many of its
I will concentrate on knots or links in the unit sphere in $\mathbb
practitioners seem to believe, including the Myth of Truth, the Myth of
C^2$ which bound a complex curve (respectively, a smooth complex
Proof, the Myth of Certainty, and so forth.
curve) in the unit ball. Such a knot or link will be called analytic
(respectively, smoothly analytic). For analytic satellite links of
smoothly analytic knots there is a sharp lower bound for the 4-ball
genus. It is given in terms of the 4-ball genus of the companion and
the winding number. No such estimate is true in the general case.
There is a natural relation to the theory of holomorphic mappings
from open Riemann surfaces into the space of monic polynomials
without multiple zeros. I will briefly touch related problems.


===Tue, Nov 29: Isaac Goldbring (UCLA)===
This talk is available as a pdf file:
"Nonstandard methods in Lie theory"


Nonstandard analysis is a way of rigorously using "ideal" elements, such as infinitely small and infinitely large elements, in mathematics. In this talk, I will survey the use of nonstandard methods in Lie theory. I will focus on two applications in particular:  the positive solution to Hilbert's fifth problem (which establishes that locally euclidean groups are Lie groups) and nonstandard hulls of infinite-dimensional Lie groups and algebras.  I will also briefly discuss the recent work of Breuillard, Green, and Tao (extending work of Hrushovski) concerning the classification of approximate groups, which utilizes nonstandard methods and the local version of Hilbert's fifth problem in an integral way. I will assume no prior knowledge of nonstandard analysis or Lie theory.
<http://sprott.physics.wisc.edu/chaos-complexity/hirsch12.pdf>.


===Wed, Nov 30: Bing Wang (Simons Center for Geometry and Physics)===
===<span id="Maulik"></span>May 3: Davesh Maulik (Columbia) ===
''Uniformization of algebraic varieties''
'''Plane curve singularities and knot invariants'''


For algebraic varieties of general type with
Given a polynomial function $f(x,y)$ in two complex variables, with a critical point at the origin, by studying the nearby points, one can associate a knot (or link) inside $\mathbb{R}^3$.  In nice situations, we can try to understand analytic properties of the singularity in terms of topological properties of this knot. For example, Milnor showed that the codimension of the ideal generated by the partial derivatives is related to the degree of the Alexander polynomial of the link.  I will explain a broad generalization of this example, first conjectured by Oblomkov and Shende, which relates the geometry of the Hilbert scheme of the singularity to the HOMFLY polynomial of the link.  As time permits, I will discuss further extensions (some known, some conjectural).
mild singularities, we show the Bogmolov-Yau inequality
holds. If equality is attained, then this variety is a
global quotient of complex hyperbolic space away from
a subvariety.


===Wed, Dec 7: Toan Nguyen (Brown University)===
===<span id="Gelbart"></span>May 10: Steve Gelbart (Weizmann Institute, Israel) ===
"On the stability of Prandtl boundary layers and the inviscid limit of the Navier-Stokes equations"
''"Zeta"''


In fluid dynamics, one of the most classical issues is to understand the dynamics of viscous fluid flows past solid bodies (e.g., aircrafts, ships, etc...), especially in the regime of very high Reynolds numbers (or small viscosity). Boundary layers are typically formed in a thin layer near the boundary. In this talk, I shall present various ill-posedness results on the classical Prandtl boundary-layer equation, and discuss the relevance of boundary-layer expansions and the vanishing viscosity limit problem of the Navier-Stokes equations. I will also discuss viscosity effects in destabilizing stable inviscid flows.
This will be an introductory (and incomplete) lecture on the story of “zeta”. Starting with
the fundamental work of Euler, Kummer and Riemann, and the telling work of Artin, Hecke and Hasse-Weil, we end up with the ever growing mysteries of Iwasawa, Langlands, and beyond.

Latest revision as of 21:01, 23 February 2020


Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.

Spring 2013

date speaker title host(s)
Tues, Jan 15, B139 Lillian Pierce (Oxford) A new twist on the Carleson operator Denissov
Thurs, Jan 17, 2pm, 901VV Jonah Blasiak (Michigan) Positivity, complexity, and the Kronecker problem Terwilliger
Jan 25 Alexander Fish (Sydney) Product sets in amenable groups through a dynamical approach Gurevich
Feb 1 Tullia Dymarz (Madison) Quasisymmetric vs Bi-Lipschitz maps Street
Feb 8 Jean-Luc Thiffeault (Madison) pseudo-Anosovs with small or large dilatation Roch
Feb 15 Eric Lauga (UCSD) Optimization in fluid-based locomotion Spagnolie
Feb 22 Svitlana Mayboroda (University of Minnesota) Elliptic PDEs, analysis, and potential theory in irregular media Stovall
Mar 1 Kirsten Wickelgren (Harvard) Grothendieck's anabelian conjectures Street
March 8 Dan Negrut (UW - Mechanical Engineering) Using Advanced Computing in Applied Dynamics: From the Dynamics of Granular Material to the Motion of the Mars Rover Caldararu
March 15 Kurusch Ebrahimi Fard (Madrid) Spitzer-type identities in non-commutative Rota-Baxter algebras Gurvich
March 22 Neil O'Connell (Warwick) CANCELLED Timo Seppalainen
March 29 Spring Break No Colloquium
April 5 John Jones (ASU) Number fields with prescribed ramification Boston
April 12 Andrew Snowden (MIT) Large algebraic structures with large amounts of symmetry Street
April 19 Moe Hirsch (Honorary Fellow -- UW Madison) The Divine Madness: Mathematics, Myths and Metaphors Street
Tuesday, April 30, 4PM Laure Saint-Raymond (ENS)] Wasow Lecture: The Irreversibility in Gas Dynamics, a Matter of Probability Wasow Lecture
May 3 Davesh Maulik (Columbia) Plane curve singularities and knot invariants Street
May 10 Steve Gelbart (Weizmann Institute) "Zeta" Gurevich

Fall 2012

date speaker title host(s)
Sept 14 Jordan Ellenberg (Madison) FI-modules: an introduction local
Sept 20, 4pm Persi Diaconis (Stanford) CANCELLED Jean-Luc
Sept 21 Joyce McLaughlin (RPI) Mathematics for Imaging Biomechanical Parameters in Dynamic Elastography WIMAW
Sept 28 Eric Marberg (MIT) Supercharacters for algebra groups: applications and extensions Isaacs
Oct 5 Howard Masur (Chicago) Winning games for badly approximable real numbers and billiards in polygons Dymarz
Wed, Oct 10, 4pm Bas Lemmens (Univ. of Kent) From hyperbolic geometry to nonlinear Perron-Frobenius theory LAA lecture
Thur, Oct 11, 4pm Irene Gamba (UT-Austin) Analytical and numerical issues associated with the dynamics of the non-linear Boltzmann equation WIMAW
Oct 12 Joachim Rosenthal (Univ. of Zurich) Linear Random Network Codes, a Grassmannian Approach Boston
Oct 19 Saverio E Spagnolie (Madison) Elastic slender bodies in fluids and slender bodies in elastic fluids Roch
Oct 26 Luke Oeding (UC Berkeley) The Trifocal Variety Gurevich
Tues, Oct 30 Andrew Majda (Courant) Data Driven Methods for Complex Turbulent Systems Smith, Stechmann
Thurs, Nov 1 Lenya Ryzhik (Chicago) The role of a drift in elliptic and parabolic equations Kiselev
Nov 2 Vladimir Sverak (Minnesota) On scale-invariant solutions of the Navier-Stokes equations Kiselev
Nov 9 Uri Andrews (Madison) Computable Stability Theory Lempp
Mon, Nov 12 Charles Smart (MIT) Regularity and stochastic homogenization of fully nonlinear equations without uniform ellipticity Feldman
Mon, Nov 26 Daniel Erman (U.Michigan) TBA Boston
Wed, Nov 28 Cameron Hill (Notre Dame) Genericity in Discrete Mathematics Lempp
Nov 30 Nam Le (Columbia) Boundary regularity for solutions to the linearized Monge-Ampere equations and applications Feldman
Dec 14 Amanda Folsom (Yale) q-series and quantum modular forms Ellenberg/WIMAW

Abstracts

Sept 14: Jordan Ellenberg (UW-Madison)

FI-modules: an introduction (joint work with T Church, B Farb, R Nagpal)

In topology and algebraic geometry one often encounters phenomena of _stability_. A famous example is the cohomology of the moduli space of curves M_g; Harer proved in the 1980s that the sequence of vector spaces H_i(M_g,Q), with g growing and i fixed, has dimension which is eventually constant as g grows with i fixed.

In many similar situations one is presented with a sequence {V_n}, where the V_n are not merely vector spaces, but come with an action of S_n. In many such situations the dimension of V_n does not become constant as n grows -- but there is still a sense in which it is eventually "always the same representation of S_n" as n grows. The preprint

http://arxiv.org/abs/1204.4533

shows how to interpret this kind of "representation stability" as a statement of finite generation in an appropriate category; we'll discuss this set-up and some applications to the topology of configuration spaces, the representation theory of the symmetric group, and diagonal coinvariant algebras. Finally, we'll discuss recent developments in the theory of FI-modules over general rings, which is joint work with (UW grad student) Rohit Nagpal.


Sept 21: Joyce R. McLaughlin (Rensselaer Polytechnic Institute)

Mathematics for Imaging Biomechanical Parameters in Dynamic Elastography

Elastography, the imaging of biomechanical parameters in tissue, is motivated by the doctor’s palpation exam where the doctor presses against the skin to detect stiff and abnormal tissue changes. In dynamic elastography experiments, the tissue is in motion with displacement amplitudes on the order of tens of microns. The displacement(s) are determined with sequences of MR data sets or sequences of ultrasound RF/IQ data sets within the tissue; and the data shows a dispersive effect indicating that tissue is viscoelastic. A choice of viscoelastic model must be made. For each model the biomechanical parameters satisfy a first order, linear or nonlinear, partial differential equation (system) with real or complex coefficients. We discuss the mathematical properties of these equations and how those properties lead to successful interpretation of the data, and to successful algorithms and images. We show biomechanical images of breast cancer and prostate cancer and compare those images to ultrasound images and histology slides with marked cancerous inclusions.


Sept 28: Eric Marberg (MIT)

Supercharacters for algebra groups: applications and extensions

The group U_n(F_q) of unipotent upper triangular matrices over a finite field belongs to the same list of fundamental examples as the symmetric or general linear groups. It comes as some surprise, therefore, that the group's irreducible characters are unknown, and considered in some sense unknowable. In order to tackle problems normally requiring knowledge of a group's irreducible characters, Diaconis and Isaacs developed the notion of the supercharacters of an algebra group, generalizing work of Andre and Yan. Algebra groups form a well-behaved class of p-groups including U_n(F_q) as a prototypical example, and supercharacters are certain reducible characters which form a useful approximation to the set of irreducible characters. In this talk I will survey several equivalent definitions of the supercharacters of an algebra group, and discuss some applications and extensions of these approaches. On one end of things, I intend briefly to introduce the recent discovery of how certain representation theoretic operations on the supercharacters of U_n(F_q) naturally define a Hopf algebra structure, which has been studied under a different name by combinatorialists. In another direction, I will explain how one can view the supercharacters of an algebra group as the first step in a more general reduction process, which can be used to shed light on some mysterious properties of U_n(F_q).

Oct 04 Howard Masur (Chicago)

Winning games for badly approximable real numbers and billiards in polygons

Wolfgang Schmidt invented the notion of a winning subset of Euclidean space in a game between two players. Winning sets have nice properties such as full Hausdorff dimension. The basic example of a winning set considered by Schmidt are those reals badly approximated by rationals. An equivalent formulation by Artin is that badly approximable reals correspond to geodesics that stay in a bounded set in the modular curve. There is also an equivalent formulation in terms of sets of directions for the linear flow on a square torus or equivalently, billiard trajectories in a square. In joint work with Yitwah Cheung and Jon Chaika we extend this notion of winning to flows on flat surfaces of higher genus with applications to billiards in rational angled polygons. My intention in this talk is to give the background on the Schmidt game, describe the classical results before introducing the more recent work.


Wed, Oct 10: Bas Lemmens (University of Kent)

From hyperbolic geometry to nonlinear Perron-Frobenius theory

In a letter to Klein Hilbert remarked that the logarithm of the cross-ratio is a metric on any open, bounded, convex set in Euclidean space. These metric spaces are nowadays called Hilbert geometries. They are a natural non-Riemannian generalization of Klein's model of the hyperbolic plane, and play a role in the solution of Hilbert's fourth problem.

In the nineteen fifties Garrett Birkhoff and Hans Samelson independently discovered that one can use Hilbert's metric and the contraction mapping principle to prove the existence and uniqueness of a positive eigenvector for a variety of linear operators that leave a closed cone in a Banach space invariant. Their results are a direct extension of the classical Perron-Frobenius theorem concerning the eigenvectors and eigenvalues of nonnegative matrices. In the past decades this idea has been further developed and resulted in strikingly detailed nonlinear extensions of the Perron-Frobenius theorem. In this talk I will discuss the synergy between metric geometry and (nonlinear) operator theory and some of the recent results and open problems in this area.


Thur, Oct 11: Irene Gamba (University of Texas-Austin)

Analytical and numerical issues associated with the dynamics of the non-linear Boltzmann equation

The non-linear Boltzmann equation models the evolution of a statistical flow associated with particle systems in a rarefied or mesoscopic regimes. Its analytical local as well as long time behavior depends strongly on the growth conditions of the collisional kernels, as functions of the intermolecular potentials and scattering mechanisms. We will present recent analytical results, such as classical convolutional inequalities and sharp moments estimates, which imply propagation of $W^{k,p}$ norms and exponential decay of high energy tails, and their consequences on the existence, regularity, and stability of solutions for initial value problems as well as control of decay rates to equilibrium. In particular we present a numerical approximation to the non-linear Boltzmann problem by a conservative spectral scheme, and show spectral accuracy as well as error estimates.

Oct 12: Joachim Rosenthal (Univ of Zurich)

Linear Random Network Codes, a Grassmannian Approach

Elastography, the imaging of biomechanical parameters in A novel framework for random network coding has been introduced by Koetter and Kschischang. In this framework information is encoded in subspaces of a given ambient space over a finite field. A natural metric is introduced where two subspaces are `close to each other' as soon as their dimension of intersection is large. This framework poses the challenge to come up with new codes with optimal or near optimal distance and to develop efficient decoding algorithms.

In a first part of the talk we will provide a survey. In a second part of the talk we report on progress constructing spread codes and orbit codes. The decoding problem of orbit codes can be interpreted as a problem in Schubert calculus over a finite field.


Fri, Oct 19: Saverio E. Spagnolie (Madison)

Elastic slender bodies in fluids and slender bodies in elastic fluids

Abstract:

The scientific study of elastic materials dates back to Galileo, and fluid mechanics to Archimedes, but the interaction of elastic bodies and viscous fluids remains a topic at the frontier of modern research. We will discuss two problems on this topic of recent interest. First, when a flexible filament is confined to a fluid interface, the balance between capillary attraction, bending resistance, and tension from an external source can lead to a self-buckling instability. We will walk through an analysis of this elastocapillary instability, and analytical formulae will be shown that compare favorably with the results of detailed numerical computations. Second, we will discuss the motility of a swimming helical body in a viscoelastic fluid, wherein the fluid itself exhibits an elastic response to deformation. The helical geometry is exploited to generate a highly accurate numerical method, and we will show that the introduction of viscoelasticity can either enhance or retard the swimming speed depending on the body geometry and the properties of the fluid (through a dimensionless Deborah number). Our findings bridge the gap between studies showing situationally dependent enhancement or retardation of swimming speed, and may help to clarify phenomena observed in systems from spermatozoan swimming to mechanical drilling.

Fri, Oct 26: Luke Oeding (UC Berkeley)

The Trifocal Variety

Abstract: In Computer Vision one considers many cameras looking at the same scene. From this setup many interesting geometric and algebraic questions arise. In this talk we will focus on the case of 3 cameras and study the so called trifocal tensors. Trifocal tensors are constructed from a bilinear map defined using the trifocal setup. A natural question is, given a particular tensor, how can one determine if it is a trifocal tensor? This question can be answered by finding implicit defining equations for the trifocal variety. From an algebraic standpoint, it is also interesting to know the minimal generators of the defining ideal of the trifocal variety.

In this talk I will explain our use of symbolic and numerical computations aided by Representation Theory and Numerical Algebraic Geometry to find the minimal generators of the ideal of the trifocal variety. This is joint work with Chris Aholt (Washington). Our work builds on the work of others (such as Hartley-Zisserman, Alzati-Tortora and Papadopoulo-Faugeras) who have already considered this problem set-theoretically.

My goal is to make most of the talk accessible to anyone with a modest background in Linear Algebra.


Tues, Oct 30: Andrew Majda (Courant)

Data Driven Methods for Complex Turbulent Systems

An important contemporary research topic is the development of physics constrained data driven methods for complex, large-dimensional turbulent systems such as the equations for climate change science. Three new approaches to various aspects of this topic are emphasized here. 1) The systematic development of physics constrained quadratic regression models with memory for low-frequency components of complex systems; 2) Novel dynamic stochastic superresolution algorithms for real time filtering of turbulent systems; 3) New nonlinear Laplacian spectral analysis (NLSA) for large-dimensional time series which capture both intermittency and low-frequency variability unlike conventional EOF or principal component analysis. This is joint work with John Harlim (1,2), Michal Branicki (2), and Dimitri Giannakis (3).

Thurs, Nov 1: Lenya Ryzhik (Chicago)

The role of a drift in elliptic and parabolic equations

The first order partial differential equations are closely connected to the underlying characteristic ODEs. The second order elliptic and parabolic equations are as closely connected to the Brownian motion and more general diffusions with a drift. From a variety of points of view, the drift does not really matter - all diffusions look more or less similar. As a caveat to this reasonable line of thought, I will describe a menagerie of problems: linear and nonlinear, steady and time-dependent, compressible and incompressible, where the drift and diffusion confirm the Mayakovsky thesis "Woe to one alone!" Together, they lead to enhanced mixing and improved regularity that are impossible for each one of them to attain.

Nov 2: Vladimir Sverak (Minnesota)

On scale-invariant solutions of the Navier-Stokes equations

The solutions of the Navier-Stokes equations which are invariant under the scaling symmetry of the equations provide an interesting window into non-linear regimes which are not accessible by perturbation theory. They appear to give valuable hints concerning the old question about the uniqueness of weak solutions. In the lecture we outline a recent proof of the result that for every scale-invariant initial data there is a global scale-invariant solution (smooth for positive times), and we explain connections to the uniqueness problem. This is joint work with Hao Jia.

Nov 9: Uri Andrews (Madison)

Computable Stability Theory

Stability theory attempts to classify the underlying structure of mathematical objects. The goal of computable mathematics is to understand when mathematical objects or constructions can be demonstrated computably. I'll talk about the relationship between underlying structure and computation of mathematical objects.

Monday, Nov 12: Charles Smart (MIT)

Regularity and stochastic homogenization of fully nonlinear equations without uniform ellipticity

I will discuss regularity of fully nonlinear elliptic equations when the usual uniform upper bound on the ellipticity is replaced by bound on its $L^d$ norm, where $d$ is the dimension of the ambient space. Our estimates refine the classical theory and require several new ideas that we believe are of independent interest. As an application, we prove homogenization for a class of stationary ergodic strictly elliptic equations.


Wednesday, Nov 28: Cameron Hill (Notre Dame)

Genericity in Discrete Mathematics

I will discuss the intriguing role that ``generic objects can play in finitary discrete mathematics. Using the framework of model theory, we will see that there are at least two reasonable but very different notions of genericity relative to a class of finite structures (like a class of finite graphs or a class of finite groups). Through discussions of zero-one laws and structural Ramsey theory, I will try to illustrate the importance of generically-categorical classes -- those for which the various notions of genericity coincide. To finish, I will state some results that follow from the assumption of generic-categoricity.

Nov 30: Nam Le (Columbia)

Boundary regularity for solutions to the linearized Monge-Ampere equations and applications

In this talk, I will discuss boundary regularity of solutions to the linearized Monge-Ampere equations, and their applications to nonlinear, fourth order, geometric Partial Differential Equations (PDE). First, I will present my regularity results in joint work with O. Savin and T. Nguyen including: boundary Holder gradient estimates and global $C^{1,\alpha}$ estimates, global Holder estimates and global $W^{2,p}$ estimates. Then, I will describe applications of the above regularity results to several nonlinear, fourth order, geometric PDE such as: global second derivative estimates for the second boundary value problem of the prescribed affine mean curvature and Abreu's equations; and global regularity for minimizers having prescribed determinant of certain convex functionals motivated by the Mabuchi functional in complex geometry.

Dec 14: Amanda Folsom (Yale)

q-series and quantum modular forms

While the theory of mock modular forms has seen great advances in the last decade, questions remain. We revisit Ramanujan's last letter to Hardy, and prove one of his remaining conjectures as a special case of a more general result. Surprisingly, Dyson's combinatorial rank function, the Andrews-Garvan crank functions, mock theta functions, and quantum modular forms, all play key roles. Along these lines, we also show that the Rogers-Fine false theta functions, functions that have not been well understood within the theory of modular forms, specialize to quantum modular forms. This is joint work with K. Ono (Emory U.) and R.C. Rhoades (Stanford U.).

Tues, Jan 15, B139: Lillian Pierce (Oxford)

A new twist on the Carleson operator

Must the Fourier series of an L^2 function converge pointwise almost everywhere? In the 1960's, Carleson answered this question in the affirmative, by studying a particular type of maximal singular integral operator, which has since become known as a Carleson operator. In the past 40 years, a number of important results have been proved for generalizations of the original Carleson operator. In this talk we will introduce the Carleson operator and survey several of its generalizations, and then describe new joint work with Po Lam Yung that introduces curved structure to the setting of Carleson operators.

Thurs, Jan 17, 2pm, 901VV: Jonah Blasiak (Michigan)

Positivity, complexity, and the Kronecker problem

Positivity problems in algebraic combinatorics ask to find positive combinatorial formulae for nonnegative quantities arising in geometry and representation theory like cohomological dimensions and dimensions of algebras and their irreducible representations. A famous open positivity problem in representation theory is the Kronecker problem, which asks for a positive combinatorial formula for decomposing tensor products of irreducible representations of the symmetric group. We will begin with a general discussion of positivity problems and an intriguing new motivation for these problems from complexity theory. We will then present our solution to a special case of the Kronecker problem that substantially improves on previous results.

Fri, Jan 25: Alexander Fish (Sydney)

Product sets in amenable groups through a dynamical approach

We will describe a new correspondence between product sets in a countable amenable group and product sets in compact groups. This approach enables us to obtain quantitative results concerning product sets in amenable groups. The talk is for general mathematical audience. (based on a joint work with M. Bjorklund)

Fri, Feb 1: Tullia Dymarz (Madison)

Quasisymmetric vs Bi-Lipschitz maps

On a metric space, there are various classes of functions which respect aspects of the metric space structure. One of the most basic classes is the bi-Lipschitz maps (Lipschitz maps whose inverses are also Lipschitz). Another possibly much larger class consists of the so-called quasisymmetric maps (these are closely related quasiconformal maps). On both Euclidean space and the p-adics, there are many quasisymmetric maps which are not bi-Lipschitz. However, on the product of Euclidean space with the p-adics, we show that all quasisymmetric maps are bi-Lipschitz. Furthermore, our proof does not use any direct analysis but instead uses coarse topology and results from negative curvature.

Feb 8: Jean-Luc Thiffeault (Madison)

pseudo-Anosovs with small or large dilatation

Homeomorphisms of a surface to itself can be classified using the well-known Thurston-Nielsen theorem. The most interesting topological class contains pseudo-Anosov mappings: they stabilize a pair of transverse singular foliations with a finite number of singularities. These foliations are called unstable and stable, and are respectively expanded and compressed by an algebraic constant called the dilatation. Characterizing the possible values of these dilatations for a given suface is an open problem. Here I discuss a method to find the minimum value of the dilatation on closed surfaces of a given genus, for the special case where the foliations are orientable. I will then address the opposite problem: how to find pseudo-Anosovs with large dilatations. Unlike the minimizer problem, this is not well-defined -- the answer is infinity -- unless we add a constraint. Constraints can arise from practical optimization problems in engineering, and I will show some optimal solutions that can be incorporated in devices called taffy pullers. (This is joint work with Erwan Lanneau and Matt Finn.)

Feb 15: Eric Lauga (UCSD)

Optimization in fluid-based locomotion

The world of self-propelled low-Reynolds number swimmers is inhabited by a myriad of microorganisms such as bacteria, spermatozoa, ciliates, and plankton. In this talk, we focus on the locomotion of ciliated cells. Cilia are short slender whiplike appendages (a few microns long, one tenth of a micron wide) internally actuated by molecular motors (dyneins) which generate a distribution of bending moments along the cilium length and produce time-varying shape deformations. In most cases cilia are not found individually but instead in densely packed arrays on surfaces. In this work we will ask the question: can the individual and collective dynamics of cilia on the surface of an individual microorganism be rationalized as the solution to an optimization problem? We first address the deformation of individual cilia anchored on surfaces before characterizing the locomotion and feeding by surface distortions of swimmers covered by cilia array. We demonstrate, as solution to the optimization procedure, the appearance of the well-known two-stroke kinematics of an individual cilium, as well as waves in cilia array reminiscent of experimentally-observed metachronal waves.

Feb 22: Svitlana Mayboroda (University of Minnesota)

Elliptic PDEs, analysis, and potential theory in irregular media

Elliptic boundary value problems are well-understood in the case when the boundary, the data, and the coefficients exhibit smoothness. However, perfectly uniform smooth systems do not exist in nature, and every real object inadvertently possesses irregularities (a sharp edge of the boundary, an abrupt change of the medium, a defect of the construction).

The analysis of general non-smooth elliptic PDEs gives rise to decisively new challenges: possible failure of maximal principle and positivity, breakdown of boundary regularity, lack of the classical L^2 estimates, to mention just a few. Further progress builds on an involved blend of harmonic analysis, potential theory and geometric measure theory techniques. In this talk we are going to discuss some highlights of the history, conjectures, paradoxes, and recent discoveries such as the higher-order Wiener criterion and maximum principle for higher order PDEs, solvability of rough elliptic boundary problems, as well as an intriguing phenomenon of localization of eigenfunctions -- within and beyond the limits of the famous Anderson localization.

Parts of the talk are based on joint work with S. Hofmann, M. Filoche, C. Kenig, V. Maz'ya, and J. Pipher.

March 1: Kirsten Wickelgren (Harvard)

Grothendieck's anabelian conjectures

Grothendieck's anabelian conjectures predict that the solutions to certain polynomial equations over Q are determined by the loops on the corresponding space of all solutions, or more precisely that the etale fundamental group is a fully faithful functor from certain anabelian schemes to profinite groups with Galois action. This is analogous to an equivalence between fixed points and homotopy fixed points for Galois actions. We will introduce the anabelian conjectures and their topological analogues, and relate certain nilpotent obstructions to the existence of rational points introduced by Jordan Ellenberg to higher cohomology operations. These cohomology operations encode when the existence of particular Galois extensions implies the existence of others, and are connected with the formality of the etale cochains. As a corollary one has that the order n Massey product <x,x,..x,1-x,x,...x> vanishes, where x denotes the image of x in k* under the Kummer map k* -> H^1(Gal(kbar/k), Z_l(1)).

March 8: Dan Negrut (UW-Mechanical Engineering)

Using Advanced Computing in Applied Dynamics: From the Dynamics of Granular Material to the Motion of the Mars Rover

This talk outlines numerical solution methods and their implementation in a high performance computing-enabled software infrastructure aimed at supporting physics-based simulation for virtual design in Engineering. The applications of interest include granular dynamics, rigid/flexible many-body dynamics, and fluid-solid interaction problems. CHRONO, the software infrastructure developed as part of this ongoing effort, partitions the problem of interest into a number of sub-problems that are solved in parallel using Graphics Processing Unit (GPU) cards, or multi-core CPUs. The five components at the cornerstone of the vision that eventually led to CHRONO are: (a) modeling support for multi-physics phenomena; (b) scalable numerical methods for multi-GPU and multi-core hardware architectures; (c) methods for proximity computation and collision detection; (d) support for domain decomposition and load balance; and (e) tools for carrying out visualization and post-processing in a distributed manner. Several engineering applications will be used to demonstrate how these five components are implemented to leverage a heterogeneous CPU/GPU supercomputer available at the Wisconsin Applied Computing Center. The talk will conclude with a brief discussion of current trends in high performance computing and how they are poised to change the field of Computational Science in the near future.

March 15: Kurusch Ebrahimi Fard (Madrid)

Spitzer-type identities in non-commutative Rota-Baxter algebras

Gian-Carlo Rota suggested in one of his last articles the problem of developing the notion of integration algebra, complementary to the already existing theory of differential algebras. This idea was mainly motivated by Rota's deep appreciation for Chen's fundamental work on iterated integrals. As a starting point for such a theory Rota proposed to consider a particular operator identity first introduced in 1960 by the mathematician Glen Baxter. It was later coined Rota-Baxter identity. Examples range from algebras with a direct decomposition into subalgebras to algebras of functions equipped with the ordinary Riemann integral or its discrete analogs. Rota-Baxter algebras feature a genuine factorization property. It is intimately related to linear fixpoint equations, such as those, for instance, appearing in the renormalization problem in perturbative quantum field theory. For arbitrary commutative Rota-Baxter algebras, proper exponential solutions of such fixpoint equations are described by what is known as the classical Spitzer identity. The similar classical Bohnenblust-Spitzer identity involves the symmetric group, and generalizes the simple observation that the n-fold iterated integral of a function is proportional to the n-fold product of the primitive of this function. Recently, the seminal Cartier-Rota theory of classical Spitzer-type identities has been generalized to noncommutative Rota-Baxter algebras. Pre-Lie algebras (also known as Vinberg or Gerstenhaber algebras) play a crucial role in this approach. In this talk we will provide a short introduction to Rota-Baxter algebras, and review recent work on Spitzer-type identities. This talk is based on joint work with Frederic Patras (CNRS, Nice, France) and Dominique Manchon (CNRS, Clermont-Ferrand, France).

April 5: John Jones (ASU)

Number fields with prescribed ramification

Finite extensions of the rational numbers are basic objects of algebra and number theory. We discuss the interaction of two basic invariants associated to such a field, its set of ramified primes and its Galois group. After describing the basic problem, we present computational and theoretical results.

April 12: Andrew Snowden (MIT)

In recent years, it has been realized that various large algebraic structures admitting large amounts of symmetry behave as if they were small. For example, when symmetries are taken into account, polynomial rings in infinitely many variables retain some of the favorable properties of polynomial rings in finitely many variables. This observation has been applied to obtain uniformity results in diverse fields. I will describe some of the recent work in this area.

April 19: Moe Hirsch (Honorary Fellow -- UW Madison)

I will discuss various ideas about mathematics which many of its practitioners seem to believe, including the Myth of Truth, the Myth of Proof, the Myth of Certainty, and so forth.

This talk is available as a pdf file:

<http://sprott.physics.wisc.edu/chaos-complexity/hirsch12.pdf>.

May 3: Davesh Maulik (Columbia)

Plane curve singularities and knot invariants

Given a polynomial function $f(x,y)$ in two complex variables, with a critical point at the origin, by studying the nearby points, one can associate a knot (or link) inside $\mathbb{R}^3$. In nice situations, we can try to understand analytic properties of the singularity in terms of topological properties of this knot. For example, Milnor showed that the codimension of the ideal generated by the partial derivatives is related to the degree of the Alexander polynomial of the link. I will explain a broad generalization of this example, first conjectured by Oblomkov and Shende, which relates the geometry of the Hilbert scheme of the singularity to the HOMFLY polynomial of the link. As time permits, I will discuss further extensions (some known, some conjectural).

May 10: Steve Gelbart (Weizmann Institute, Israel)

"Zeta"

This will be an introductory (and incomplete) lecture on the story of “zeta”. Starting with the fundamental work of Euler, Kummer and Riemann, and the telling work of Artin, Hecke and Hasse-Weil, we end up with the ever growing mysteries of Iwasawa, Langlands, and beyond.