
NGM Pizza Seminar: Description of the Moduli Space for U(n,0) as a Tensor Product of Categories.
Location: MSRI: Simons Auditorium Speakers: Zavosh AmirKhosravi (Fields Institute for Research in Mathematical Sciences)Shimura varieties attached to unitary groups of signature (nr,r) have integral models described by moduli spaces of certain principally polarized abelian schemes. We will consider the case r=0, and show that the corresponding moduli stack can be described as a categorical tensor product of the stack of CM elliptic curves with a category of rankn positivedefinite hermitian modules.
Updated on Sep 19, 2014 10:04 AM PDT 
GRT Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:40 PM PDT 
NGM Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:42 PM PDT 
GRT Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:42 PM PDT 
NGM Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:43 PM PDT 
GRT Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:44 PM PDT 
NGM Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:45 PM PDT 
GRT Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:45 PM PDT 
NGM Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:46 PM PDT 
GRT Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:46 PM PDT 
NGM Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:48 PM PDT 
GRT Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:48 PM PDT 
NGM Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:49 PM PDT 
GRT Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:49 PM PDT 
NGM Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:51 PM PDT 
GRT Postdoc Seminar
Location: MSRI: Simons AuditoriumCreated on Aug 22, 2014 03:53 PM PDT 
NGM Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 04:21 PM PDT 
GRT Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 04:22 PM PDT
Past other seminars

GRT Pizza Seminar: Dessins D'enfant
Location: MSRI: Simons Auditorium Speakers: Sean Rostami (University of Wisconsin)Updated on Sep 12, 2014 10:57 AM PDT 
NGM Pizza Seminar: The ArthurSelberg trace formula and the Newton stratification of Shimura varieties
Location: MSRI: Simons Auditorium Speakers: Arno Kret (Institute for Advanced Study)Updated on Sep 12, 2014 09:51 AM PDT 
GRT Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:37 PM PDT 
NGM Pizza Seminar: The padic GrossZagier formula on Shimura curves.
Location: MSRI: Simons Auditorium Speakers: Daniel Disegni (McGill University)For elliptic curves E/Q whose Lfunction L=L(E,s) vanishes to order one at s=1, the rank of E(Q) is also known to be one. This is the first prediction of the Birch and SwinnertonDyer conjecture, and the main ingredient of the proof is the formula of Gross and Zagier relating the heights of modularlyconstructed points on E to the central derivative of L. The second prediction of BSD is a formula for the central leading term of L. This is only implied by the GrossZagier formula up to a nonzero rational number. One way to go on and study the BSD formula up to pintegrality is provided by a padic analogue of the GrossZagier formula due to PerrinRiou and Kobayashi. I will explain this circle of ideas as well as its generalization to totally real fields. Time permitting, I will also discuss the representationtheoretic context.
The talk is meant to be accessible to a broad audience.
Updated on Sep 05, 2014 10:32 AM PDT 
MT Postdoc Seminar: Jet Spaces and Diophantine Geometry
Location: MSRI: Simons Auditorium Speakers: Taylor Dupuy (University of New Mexico)We will explain how to obtain effective MordellLang and ManinMumford using jet space techniques in the characteristic zero function field setting.
Updated on May 16, 2014 12:58 PM PDT 
AT Postdoc Seminar
Location: MSRI: Simons Auditorium Speakers: Joseph Hirsh (Massachusetts Institute of Technology)Created on Feb 07, 2014 09:37 AM PST 
AT Postdoc Seminar: Homotopy and arithmetic: a duality playground
Location: MSRI: Simons Auditorium Speakers: Vesna Stojanoska (Massachusetts Institute of Technology)Homotopy theory can be thought of as the study of geometric objects and continuous deformations between them, and then iterating the idea as the deformations themselves form geometric objects. One result of this iteration is that it replaces morphism sets with topological spaces, thus remembering a lot more information. There are many examples to show that the approach of replacing sets with spaces in a meaningful way can lead to remarkable developments. In this talk, I will explain some of my recent work in the case of implementing homotopy theory in arithmetic in a way which produces new results and relationships between some classical notions of duality in both fields.
Updated on Apr 25, 2014 11:19 AM PDT 
AT Postdoc Seminar: The Mirror Symmetry Conjecture and Cobordisms
Location: MSRI: Baker Board Room Speakers: Hiro Tanaka (Harvard University)This talkaimed for a general audience of neither topologists nor model theoristswill discuss applications of cobordisms to Kontsevich's mirror symmetry conjecture. We'll begin by stating a rough version of the
conjecture, which builds a bridge between symplectic geometry on one hand, and on the other hand, algebraic geometry over the complex numbers. We then discuss how the theory of cobordisms, which studies when two manifolds can be the boundary of another manifold, sheds light on how to generalize the mirror symmetry conjecture, while giving us information about objects in symplectic geometry. (For example, two Lagrangians related by a compact cobordism are equivalent in the Fukaya category.)Updated on Apr 17, 2014 05:00 PM PDT 
AT Postdoc Seminar: Galois equivariance and stable motivic homotopy theory
Location: MSRI: Simons Auditorium Speakers: Kyle Ormsby (MIT / Reed College)We will explore the relationships between Galois theory, groups acting on spaces, and motivic homotopy theory. Ultimately, for R a real closed field, we will discover that that there is a full and faithful embedding of the stable Gal(R[i]/R)equivariant homotopy category into the stable motivic homotopy category over R.
Updated on Mar 28, 2014 01:16 PM PDT 
AT Postdoc Seminar: Uses of commutative rings in homotopy theory
Location: MSRI: Simons Auditorium Speakers: Sean Tilson (Universität Osnabrück)Homotopy theorists try to gain geometric information and insight through the use of algebraic invariants. Specifically, these invariants are useful in determining whether or not two spaces can be equivalent. We will begin with an example to demonstrate the usefulness of cohomology and some of the extra structure it possesses, such as cup products and power operations. This extra structure provides a very strong invariant of the space. As these invariants are representable functors, this extra structure is coming from the representing object. Indeed, cohomology theories possess products and power operations when they are represented by objects called commutative ring spectra. We then shift focus to studying commutative ring spectra on their own and try to detect what maps of commutative ring spectra might look like.
Updated on Mar 28, 2014 10:11 AM PDT 
MT Postdoc Seminar: Strong minimality of the $j$function
Location: MSRI: Simons Auditorium Speakers: James Freitag (University of California, Berkeley)In this talk, we will be working in with the theory of differentially closed fields of characteristic zero; essentially this theory says that every differential equation which might have a solution in some field extension already has a solution in the differentially closed field. After introducing this theory in a bit of detail, we will sketch a proof of the strong minimality of the differential equation satisfied by the classical $j$function starting from Pila's modular AxLindemannWeierstrass theorem. This resolves an open question about the existence of a geometrically trivial strongly minimal set which is not $\aleph _0$categorical. If time allows, we will discuss some finiteness applications for intersections of certain sets in modular curves. This is joint work with Tom Scanlon.
Updated on Mar 21, 2014 11:13 AM PDT 
MT Postdoc Seminar: Connections between Ramsey Theory and Model Theory.
Location: MSRI: Simons Auditorium Speakers: Cameron Hill (Wesleyan University)One of the great insights of model theory is the observation that very mundanelooking "combinatorial configurations" carry a huge amount of geometric information about a structure. In this talk, I will explain what we mean by "combinatorial configuration," and then I will sketch out how configurations can be "smoothed out" to yield Ramsey classes, which can themselves be analyzed using modeltheoretic tools. I will also discuss the kinds of modeltheoretic dividing lines that can be defined just through the interaction of structures with Ramsey classes.
Updated on Mar 21, 2014 11:24 AM PDT 
AT Postdoc Seminar: Why do algebraic topologists care about categories?
Location: MSRI: Simons Auditorium Speakers: Angelica Osorno (Reed College)The study of category theory was started by Eilenberg and MacLane, in their effort to codify the axioms for homology. Category theory provides a language to express the different structures that we see in topology, and in most of mathematics. Categories also play another role in algebraic topology. Via the classifying space construction, topologists use categories to build spaces whose geometry encodes the algebraic structure of the category. This construction is a fruitful way of producing important examples of spaces used in algebraic topology. In this talk we will describe how this process works, starting from classic examples and ending with some recent work.
Updated on Mar 14, 2014 10:27 AM PDT 
AT Postdoc Seminar: Mumford Conjecture, Characteristic Classes, Manifold Bundles, and the Tautological Ring
Location: Space Science Lab Conference Room Speakers: Ilya Grigoriev (University of Chicago)I will describe a topologists' perspective on the history of the study of an object that Mumford called "the tautological ring" and its generalizations.
The tautological ring was originally defined as a subring of the cohomology of the moduli space of Riemann surfaces, but can also be studied as a ring of characteristic classes of topological bundles. This point of view led to a proof of Mumford's conjecture, stating that the tautological ring coincides with the entire cohomology of the moduli space in a "stable range", as well as to some generalizations of this result. If time permits, I will explain what we know about the tautological ring outside the stable range.
Updated on Feb 21, 2014 09:07 AM PST 
MT Postdoc Seminar
Location: Space Science Lab Conference Room Speakers: Artem Chernikov (L'Institut de Mathématiques de Jussieu)Updated on Feb 07, 2014 03:51 PM PST 
AT Postdoc Seminar: Groups, Fixed Points, and Algebraic Topology
Location: MSRI: Simons Auditorium Speakers: Anna Marie Bohmann (Northwestern University)In algebraic topology, one key way of understanding group actions on spaces is by considering families of fixed points under subgroups. In this talk, we will discuss this basic structure and its fundamental role in understanding equivariant algebraic topology. I will then describe some recent joint work with A. Osorno that builds on fixed point information to create equivariant cohomology theories.
Updated on Feb 21, 2014 09:02 AM PST 
MT Postdoc Seminar: Finite VCdimension in model theory and elsewhere
Location: MSRI: Simons Auditorium Speakers: Pierre Simon (Centre National de la Recherche Scientifique (CNRS))I will present a combinatorial propertyfinite VCdimensionwhich appeared independently in various parts of mathematics.
In model theory it is called "NIP" and is used notably in the study of ordered and valued fields. In probability theory, it is related to "learnable classes". In combinatorics, classes of finite VCdimension behave a lot like families of convex subsets of euclidean space. I will also talk about Banach spaces and topological dynamics.
The talk will be accessible to postdocs of both programs.
Updated on Feb 20, 2014 02:34 PM PST 
PD Seminar: 4stochastic measures and polyconvexity
Location: MSRI: Simons Auditorium Speakers: Romeo Awi (Georgia Institute of Technology)Speaker: Romeo Awi
Updated on Dec 12, 2013 01:57 PM PST 
PD Seminar: Regularity of shadows and the singular set associated to a MongeAmpere equation
Location: 740 Evans Hall Speakers: Emanuel Indrei (Carnegie Mellon University)Updated on Nov 15, 2013 09:42 AM PST 
PD Seminar: The spherically symmetric SU(2) EinsteinYangMills equations
Location: 740 Evans Hall Speakers: Daniel Jackson (Monash University)Updated on Nov 15, 2013 09:41 AM PST 
PD Seminar: The geodesic hypothesis in general relativity
Location: 740 Evans Hall Speakers: Shiwu Yang (University of Cambridge)Updated on Nov 08, 2013 12:39 PM PST 
PD Seminar: Martingales, robust hedging and the Skorokhod embedding
Location: 740 Evans Hall Speakers: Martin Huesmann (Universität Bonn)Updated on Nov 07, 2013 10:24 AM PST 
PD Seminar: The EinsteinYangMills phase space and the First Law of black hole mechanics
Location: 740 Evans Hall Speakers: Stephen McCormick (Monash University)Updated on Oct 30, 2013 03:07 PM PDT 
PD Seminar: Adding a vanishing Dirichlet energy to the Monge cost: some surprising effects
Location: 740 Evans Hall Speakers: Jean Louet (Université ParisSud (Orsay))Updated on Oct 30, 2013 03:07 PM PDT 
PD Seminar: Convergence of harmonic maps.
Location: 740 Evans Hall Speakers: Zahra Sinaei (École Polytechnique Fédérale de Lausanne (EPFL))Updated on Oct 23, 2013 04:36 PM PDT 
PD Seminar: Rigidity of singularities and Lorentzian splitting geometry.
Location: 740 Evans Hall Speakers: Carlos Vega (University of Miami)Updated on Oct 23, 2013 04:35 PM PDT 
PD Seminar: Linear waves on Kerrde Sitter cosmologies
Location: 740 Evans Hall Speakers: Volker Schlue (University of Toronto)Updated on Oct 17, 2013 11:27 AM PDT 
PD Seminar: Interior curvature estimates and the asymptotic Plateau problem in hyperbolic space
Location: 740 Evans Hall Speakers: Ling Xiao (Johns Hopkins University)Updated on Oct 17, 2013 11:26 AM PDT 
PD Seminar: Strict convexity properties of solutions to MongeAmpere type equations
Location: 740 Evans Hall Speakers: Jun Kitagawa (MSRI  Mathematical Sciences Research Institute)Updated on Oct 10, 2013 12:57 PM PDT 
PD Seminar: Far from constant mean curvature solutions to the Einstein constraint equations on compact manifolds
Location: 740 Evans Hall Speakers: Caleb Meier (University of California, San Diego)Updated on Oct 03, 2013 11:19 AM PDT 
PD Seminar: TypeII singularities for Ricci flow on $R^n$
Location: 740 Evans Hall Speakers: Haotian Wu (University of Oregon)Updated on Sep 26, 2013 02:39 PM PDT 
PD Seminar: Noncollision singularities in the Newtonian Nbody problem
Location: 740 Evans Hall Speakers: Jinxin Xue (University of Chicago)Updated on Sep 26, 2013 02:38 PM PDT 
PD Seminar: Bochner inequality and the entropic curvature dimension condition for metric measure spaces.
Location: 740 Evans Hall Speakers: Matthias Erbar (Rheinische FriedrichWilhelmsUniversität Bonn)Updated on Sep 26, 2013 09:02 AM PDT 
PD Seminar: Microlocal analysis of radial points.
Location: 740 Evans Hall Speakers: Nick Haber (Stanford University)Updated on Sep 26, 2013 09:02 AM PDT 
PD Seminar: On the mass/angular momentum inequality
Location: 939 Evans Hall Speakers: Xin Zhou (Massachusetts Institute of Technology)Updated on Sep 13, 2013 10:44 AM PDT 
PD Seminar: Multimarginal optimal transport on Riemannian manifolds.
Location: 939 Evans Hall Speakers: Brendan Pass (University of Alberta)Updated on Sep 13, 2013 10:42 AM PDT 
Growth of groups using Euler characteristics
Location: MSRI: Simons Auditorium Speakers: Alexander Young (University of Washington)A new method, currently under development, is brought forward to establish an upper bound on the growth of any finitely generated group, using a variant of monoid categories and analagous CWcomplexes.
Updated on May 10, 2013 10:59 AM PDT 
Computing critical values of quadratic Dirichlet Lfunctions, with an eye toward their moments.
Location: MSRI: Simons Auditorium Speakers: Matthew AldersonMoments of Lfunctions has been a topic of intense research in recent years. Through the integration of random matrix theory and multiple Dirichlet series with traditional number theoretic arguments, methods for studying the moments of Lfunctions have been developed and, in turn, have lead to many wellposed conjectures for their behavior. In my talk, I will discuss the (integral) moments of quadratic DIrichlet Lfunctions evaluated at the critical point s=1/2. In particular, I will present formulas for computing the critical values for such Lfunctions and then compare the data for the corresponding moments to the (aforementioned) conjectured moments.Created on Apr 15, 2011 09:13 AM PDT 
New computations of the Riemann zeta function
Location: MSRI: Simons Auditorium Speakers: Jonathan BoberI'll describe the implementation of Hiary's O(t1/3) algorithm and the computations that we have been running using it. Some highlights include the 10^32nd zero (and a few hundred of its neighbors, all of which lie on the critical line), values of S(T) which are larger than 3, and values of zeta larger than 14000.Updated on Feb 19, 2014 08:53 AM PST 
Review and recent works on the large time asymptotics for HamiltonJacobi equations
Location: MSRI: Baker Board Room Speakers: Hiroyoshi MITAKECreated on Apr 08, 2011 06:19 AM PDT 
FBPInformal Seminar
Location: MSRI: Baker Board Room Speakers: TBA, Lihe WangUpdated on Apr 01, 2011 03:03 AM PDT 
Moment Polynomials for the Riemann Zeta Function
Location: MSRI: Simons Auditorium Speakers: Shuntaro YamagishiI will explain how we calculated the coefficients of moment
polynomials for the Riemann zeta function for k = 4,5.., 13
and numerically tested them against the moment polynomial conjecture.
Updated on Mar 31, 2011 04:37 AM PDT 
Averages of central Lvalues
Location: MSRI: Simons Auditorium Speakers: TBAUpdated on Apr 01, 2011 08:17 AM PDT 
NonDegeneracy of an EllipticFree Boundary Problem
Location: MSRI: Simons Auditorium Speakers: Betul Orcan (University of Texas)In this talk, we will consider a free boundary problem with a
very general free boundary condition and analyze the nondegeneracy of the
largest subsolution near the free boundary.Updated on Jul 07, 2014 08:16 AM PDT 
"Computing Lfunctions in SAGE"
Location: MSRI: Simons Auditorium Speakers: RishikeshCreated on Mar 23, 2011 08:26 AM PDT 
Elliptic curves of arbitrarily large rank (Over Function Fields)
Speakers: Kevin Wilson
Updated on Mar 14, 2011 08:03 AM PDT 
Empirical Evidence for an Arithmetic Analogue of Nevanlinna's Five Value Theorem
Location: MSRI: Baker Board Room Speakers: James Weigandt
Updated on Feb 28, 2011 07:57 AM PST 
Postdoctoral Seminars FBP
Created on Feb 18, 2011 04:31 AM PST 
A problem related to the ABC conjecture
Speakers: Danial Kane (Harvard University)
Updated on Feb 13, 2011 03:01 AM PST 
Nonlocal equations and new notions of curvature
Location: MSRI: Baker Board Room Speakers: Nestor Guillen
Updated on Feb 13, 2011 03:00 AM PST 
Brandt module of ternary quadratic forms
Location: MSRI: Baker Board Room Speakers: Gonzalo Tornaría
Updated on Feb 13, 2011 02:59 AM PST 
Regularity for Elliptic Equations with Discontinous BMO Coefficients in Reifenberg Flat Domains
Location: MSRI: Simons AuditoriumPizza Lunch
Updated on Feb 04, 2011 05:25 AM PST 
"Lowlying zeros of Dedekind zeta functions"
Location: MSRI: Simons Auditorium Speakers: Andrew YangPizza Lunch
Updated on Feb 04, 2011 05:52 AM PST 
Postdoctoral Seminars FBP
Location: MSRI: Baker Board RoomPizza Lunch
Updated on Jan 24, 2011 08:17 AM PST 
Postdoctoral and Graduate Student Seminar TBA
Location: MSRI: Simons AuditoriumPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
Gluing semiclassical resolvent estimates via propagation of singularities.
Location: MSRI: Baker Board Room Speakers: Kiril DatchevPizza Lunch
Updated on Aug 14, 2014 02:45 PM PDT 
Lower bounds for the volume of the nodal sets
Location: MSRI: Simons Auditorium Speakers: Hamid HezariPizza Lunch
Updated on Dec 19, 2013 01:12 PM PST 
Nonintersecting Brownian Motions at a Tacnode: Soft and Hard Edge Case.
Location: MSRI: Simons AuditoriumPizza Lunch
Updated on Nov 29, 2010 03:22 AM PST 
Harmonic maps into conic surfaces with cone angles less than $2\pi$
Updated on Nov 22, 2010 03:33 AM PST 
A tale of two tiling problems
Speakers: Benjamin Young
Updated on May 29, 2013 09:25 AM PDT 
Postdoctoral and Graduate Student Seminar TBA
Location: MSRI: Baker Board RoomPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
Dihedral symmetry and the RazumovStroganov ExConjecture
Location: MSRI: Baker Board RoomPizza Lunch
Updated on Nov 05, 2010 07:12 AM PDT 
Geometric structures in the study of the geodesic ray transform
Location: MSRI: Simons Auditorium Speakers: JuhaMatti PerkkioPizza Lunch
Updated on Oct 29, 2010 06:27 AM PDT 
"Edge scaling limits for nonHermitian random matrices"
Location: MSRI: Simons Auditorium Speakers: Martin Bender
Updated on Oct 29, 2010 07:57 AM PDT 
Postdoctoral and Graduate Student Seminar TBA
Location: MSRI: Simons AuditoriumPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
From Oscillatory Integrals to a Cubic Random Matrix Model"
Speakers: Alfredo DeañoPizza Lunch
Updated on Oct 23, 2010 05:07 AM PDT 
Application of RiemannHilbert Problems in Modelling of Cavitating Flow
Location: MSRI: Simons Auditorium Speakers: Anna ZemlyanovaPizza Lunch
Updated on Oct 18, 2010 02:57 AM PDT 
Albrecht Durer, Magic Squares, and Unitary Matrix Integrals
Location: MSRI: Simons Auditorium Speakers: Jonathan NovakPizza Lunch
Updated on Dec 04, 2013 12:45 PM PST 
Imaging Edges in Random Media
Location: MSRI: Simons Auditorium Speakers: Fernando Guevara VasquezPizza Lunch
Consider the problem of imaging a reflector (target) from recordings of the echoes resulting from probing the medium with waves emanating from an array of transducers (the array response matrix). We present an algorithm that selectively illuminates the edges or the interior of an extended target by choosing particular subspaces of the array response matrix. For a homogeneous background medium, we characterize these subspaces in terms of the singular functions of a space and wave number restricting operator, which are also called generalized prolate spheroidal wave functions. We discuss results indicating what can be expected from using this algorithm when the medium fluctuates around a constant background medium and the fluctuations can be modeled as a random field.Updated on May 13, 2013 11:01 PM PDT 
Integrable Equations for Random Matrix Spectral Gap Probabilities
Location: MSRI: Simons Auditorium Speakers: Igor RumanovPizza Lunch
Connections are exposed between integrable equations for spectral gap probabilities of unitary invariant ensembles of random matrices (UE) derived by different  TracyWidom (TW) and AdlerShiotavan Moerbeke (ASvM)  methods. Simple universal relations are obtained between these probabilities and their ratios on one side, and variables of the approach using resolvent kernels of Fredholm operators on the other side. A unified description of UE is developed in terms of universal, i.e. independent of the specific probability measure, PDEs for gap probabilities, using the correspondence of TW and ASvM variables. These considerations are based on the threeterm recurrence for orthogonal polynomials (OP) and onedimensional Toda lattice (or TodaAKNS) integrable hierarchy whose flows are the continuous transformations between different OP bases. Similar connections exist for coupled UE. The gap probabilities for onematrix Gaussian UE (GUE) or joint gap probabilities for coupled GUE satisfy various PDEs whose number grows with the number of spectral endpoints. With the above connections serving as a guide, minimal complete sets of independent lowest order PDEs for the GUE and for the largest eigenvalues of twomatrix coupled GUE are found.Updated on May 13, 2013 11:01 PM PDT 
The Inverse Calderon Problem for Schrödinger Operator on Riemann Surfaces
Location: MSRI: Simons Auditorium Speakers: Leo tzouPizza Lunch
We show that on a smooth compact Riemann surface with boundary (M0, g) the Dirichletto Neumann map of the Schrödinger operator â g + V determines uniquely the potential V . This seemingly analytical problem turns out to have connections with ideas in symplectic geometry and differential topology. We will discuss how these geometrical features arise and the techniques we use to treat them. This is joint work with Colin Guillarmou of CNRS Nice. The speaker is partially supported by NSF Grant No. DMS0807502 during this work.Updated on May 13, 2013 11:01 PM PDT 
E. Nordenstam's Talk
Location: MSRI: Simons Auditorium Speakers: Eric NordenstamPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
Resistor Networks and Optimal Grids for Electrical Impedance Tomography with Partial Boundary Measurements
Location: MSRI: Baker Board Room Speakers: Alexander MamonovPizza Lunch
The problem of Electrical Impedance Tomography (EIT) with partial boundary measurements is to determine the electric conductivity inside a body from the simultaneous measurements of direct currents and voltages on a subset of its boundary. Even in the case of full boundary measurements the nonlinear inverse problem is known to be exponentially illconditioned. Thus, any numerical method of solving the EIT problem must employ some form of regularization. We propose to regularize the problem by using sparse representations of the unknown conductivity on adaptive finite volume grids known as the optimal grids. Then the discretized partial data EIT problem can be reduced to solving the discrete inverse problems for resistor networks. Two distinct approaches implementing this strategy are presented. The first approach uses the results for the EIT problem with full boundary measurements, which rely on the use of resistor networks with circular graph topology. The optimal grids for such networks are essentially one dimensional objects, which can be computed explicitly. We solve the partial data problem by reducing it to the full data case using the theory of extremal quasiconformal (Teichmuller) mappings. The second approach is based on resistor networks with the pyramidal graph topology. Such network topology is better suited for the partial data problem, since it allows for explicit treatment of the inaccessible part of the boundary. We present a method of computing the optimal grids for the networks with general topology (including pyramidal), which is based on the sensitivity analysis of both the continuum and the discrete EIT problems. We present extensive numerical results for the two approaches. We demonstrate both the optimal grids and the reconstructions of smooth and discontinuous conductivities in a variety of domains. The numerical results show two main advantages of our approaches compared to the traditional optimizationbased methods. First, the inversion based on resistor networks is orders of magnitude faster than any iterative algorithm. Second, our approaches are able to correctly reconstruct the conductivities of very high contrast, which usually present a challenge to the iterative or linearizationbased inversion methods.Updated on May 13, 2013 11:01 PM PDT