SEMINARS
Updated: 3-7-2012

MARCH 2012
 
Department Colloquium
Topic: The Surface Subgroup Theorem and the Ehrenpreis conjecture
Presenter: J. Kahn, Brown University
Date: Wednesday, March 7, 2012, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: We prove that there is a hyperbolic surface S such that for any closed hy- perbolic 2 or 3-manifold M, and  > 0, there is a nite cover ^ S of S, and a map f: ^ S ! M that is locally within  of being an isometric immersion. When dimM = 3 this implies that 1(M) has a surface subgroup, and when dimM = 2 this is the Ehrenpreis conjecture. In either case, the surface f(S) is constructed by putting together immersed pairs of pants in M, and in both cases we can construct a collection of good pants that are evenly distributed around every closed geodesic that appears as a boundary. If dimM = 3 then we can immediately assemble these pants, with a twist, to form the desired surface f(S). In the case where dimM = 2, there may be more pants on one side of a geodesic than the other. In order to determine how to correct the collection of pants, we develop the \good pants homology" of good curves modulo the boundaries of good pants, and show through a series of algebraic identities that it is equivalent to the standard homology. This is joint work with Vladimir Markovic. 1
 
Ergodic Theory and Statistical Mechanics Seminar
Topic: Effective bisector estimate for PSL(2,C) with applications to circle packings
Presenter: Ilya Vinogradov, Princeton University
Date:  Thursday, March 8, 2012, Time: 2:00 p.m., Location: Fine Hall 601
Abstract: Let Gamma be a non-elementary discrete geometrically finite subgroup of PSL(2,C). Under the assumption that the critical exponent of Gamma is greater than 1 we prove an effective bisector counting theorem for Gamma. We then apply this Theorem to the Apollonian circle packing problem to get power savings and to compute the overall constant. The proof relies on spectral theory of Gamma\PSL(2,C).
 
Discrete Mathematics Seminar
Topic: Pareto Optimal Solutions for Smoothed Analysts
Presenter: Ankur Moitra, IAS
Date: Thursday, March 8, 2012, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: Consider an optimization problem with n binary variables and d+1 linear objective functions. Each valid solution in {0,1}^n gives rise to an objective vector in R^{d+1}, and one often wants to enumerate the Pareto optima among them. In the worst case there may be exponentially many Pareto optima; however, it was recently shown that in (a generalization of) the smoothed analysis framework, the expected number is polynomial in n (Roeglin, Teng, FOCS 2009). Unfortunately, the bound obtained had a rather bad dependence on d; roughly n^{d^d}. In this paper we show a significantly improved bound of n^{2d}. Our proof is based on analyzing two algorithms. The first algorithm, on input a Pareto optimal x, outputs a "testimony" containing clues about x's objective vector, x's coordinates, and the region of space B in which x's objective vector lies. The second algorithm can be regarded as a SPECULATIVE execution of the first -- it can uniquely reconstruct x from the testimony's clues and just SOME of the probability space's outcomes. The remainder of the probability space's outcomes are just enough to bound the probability that x's objective vector falls into the region B. This is joint work with Ryan O'Donnell.
 
Algebraic Topology Seminar
Topic: Hermitian K-theory and cobordism
Presenter: Po Hu, Wayne State University
Date: Thursday, March 8, 2012, Time: 3:00 p.m., Location: Fine Hall 214
Abstract: I will discuss Z/2-equivariant motivic spectra. As an example, I will talk about a Z/2-equivariant motivic spectrum representing Karoubi's Hermitian K-theory, and my joint solution with Kriz and Ormsby of Thomason's homotopy limit problem. As another example, I will talk about motivic Hermitian cobordism, and its topological realization, topological Hermitian cobordism. This is an RO(G)-graded (Z/2 \times Z/2)-equivariant spectrum, whose RO(G)-graded homotopy groups we have computed.
 
Joint IAS and Princeton University Number Theory Seminar
Topic: Mod p points on Shimura varieties
Presenter: Mark Kisin, Harvard University
Date: Thursday, March 8, 2012, Time: 4:30 p.m., Location: Fine Hall 214
Abstract: A conjecture of Langlands-Rapoport predicts the structure of the mod p points on a Shimura variety. The conjecture forms part of Langlands' program to understand the zeta function of a Shimura variety in terms of automorphic L-functions. I will report on progress towards the conjecture in the case of Shimura varieties attached to non-exceptional groups.
 
Topology Seminar
Topic: Counting Connections and the Ehrenpreis conjecture
Presenter: Jeremy Kahn, Brown University
Date: Thursday, March 8, 2012, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Let S be a closed hyperbolic surface. We review the theory of counting connections on S---between points, between horocycles, and between geodesic segments---and we explain how this relates to the proof of the Ehrenpreis conjecture.
 
Differential Geometry and Geometric Analysis Seminar
Topic: The spacetime positive mass theorem in dimensions less than 8
Presenter: Dan Lee, CUNY
Date: Friday, March 9, 2012, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: After reviewing the proof of the Riemannian positive mass theorem in dimensions less than 8, I will briefly explain how to generalize the proof to slices of spacetime that are not time- symmetric. The basic idea is to replace minimal hypersurfaces by marginally outer-trapped hypersurfaces, and the main difficulty is to avoid using any minimization process. This is joint work with Eichmair, Huang, and Schoen.
 
Analysis Seminar
Topic: Finite point configurations, incidence theory and multi-linear operators
Presenter: Alex Iosevish, University of Rochester
Date: Monday, March 12, 2012, Time: 3:15 p.m., Location: Fine Hall 314
Abstract: A classical problem in geometric combinatorics is to determine how often a single distance may repeat among $n$ points in the plane. A related problem that has received much attention is how often a given triangle can repeat among $n$ points in the plane. We shall report on some partial progress on the second problem using a continuous analog, proved via a Sobolev estimate for a bilinear averaging operator and a conversion mechanism that allows us to deduce a discrete result from a sufficiently robust continuous analog.
 
Algebraic Geometry Seminar
Topic: TBA
Presenter: Karl Schwede, Penn State University
Date: Tuesday, March 13, 2012, Time: 4:30 p.m., Location: Fine Hall 322
 
Department Colloquium
Topic: A case study for critical non-linear dispersive equations: the energy critical wave equation
Presenter: Carlos Kenig, University of Chicago
Date: Wednesday, March 14, 2012, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: We will discuss recent work on the energy critical wave equation. The issues studied are global existence, scattering, finite time blow-up, universal profiles at blow-up and soliton resolution. This is viewed not as an isolated series of results, but as a way of approaching many similar critical non-linear dispersive equations.
 
Ergodic Theory and Statistical Mechanics Seminar
Topic: Noncollision singularities in planar two-center-two-body problem
Presenter: Jinxin Xue, IAS
Date:  Thursday, March 15, 2012, Time: 2:00 p.m., Location: Fine Hall 601
Abstract: In this work we study a model called planar 2-center-2-body problem. In the plane, we have two fixed centers Q_1=(-\chi,0), Q_2=(0,0) of masses 1, and two moving bodies Q_3 and Q_4 of masses \mu. They interact via Newtonian potential. Q_3 is captured by Q_2, and Q_4 travels back and forth between two centers. Based on a construction of Gerver, we prove that there is a Cantor set of initial conditions which lead to solutions of the Hamiltonian system whose velocities are accelerated to infinity within finite time avoiding all early collisions. We consider this model as a simplified model for the planar four-body problem case of the Painleve conjecture. This is a joint work with Dmity Dolgopyat.
 
Discrete Mathematics Seminar
Topic: Tangles, trees and flowers
Presenter: Ben Clark, Victoria University of Wellington, New Zealand
Date: Thursday, March 15, 2012, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: Identifiable regions of high connectivity in a matroid or graph are captured by the notion of ``tangles''. For a tangle of order k in a matroid or graph that satisfies a certain robustness condition, we describe a tree decomposition of the matroid or graph that displays, up to a certain natural equivalence, all of the k-separations of the matroid or graph that are non-trivial with respect to the tangle. This is joint work with Geoff Whittle.
 
Joint IAS and Princeton University Number Theory Seminar **Please note location**
Topic: TBA
Presenter: Fernando Villegas, University of Texas at Austin
Date: Thursday, March 15, 2012, Time: 4:30 p.m., Location: IAS, West Bldg. Lecture Hall **
 
Topology Seminar
Topic: A Khovanov homotopy type
Presenter: Sucharit Sarkar, Columbia University
Date: Thursday, March 15, 2012, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: We will start by describing Khovanov's categorification of the Jones polynomial from a cube of resolutions of a link diagram. We will then introduce the notion of a framed flow category, as defined by Cohen, Jones and Segal. We will see how a cube of resolutions produces a framed flow category for the Khovanov chain complex, and how the framed flow category produces a space whose reduced cohomology is the Khovanov homology. We will show that the stable homotopy type of the space is a link invariant. Time permitting, we will show that the space is often non-trivial, i.e., not a wedge sum of Moore spaces. This work is joint with Robert Lipshitz.
 
Differential Geometry and Geometric Analysis Seminar
Topic: L^p bounds for eigenfunctions on locally symmetric spaces
Presenter: Simon Marshall, Northwestern University
Date: Friday, March 16, 2012, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: There is a classical theorem of Sogge which provides bounds for the L^p norms of a Laplace eigenfunction on a compact Riemannian manifold, which are sharp on the sphere and for spectral clusters. I will present a generalization of this theorem to eigenfunctions of the full ring of invariant differential operators on a locally symmetric space, as well as a theorem on the restriction of eigenfunctions to maximal flat subspaces. Time permitting, I will discuss ways in which these bounds can be improved using inputs from number theory.
 
Analysis Seminar
Topic: Local smoothing and Strichartz estimates for manifolds with degenerate hyperbolic trapping
Presenter: Hans Cristianson, University of North Carolina at Chapel Hill
Date: Monday, March 26, 2012, Time: 3:15 p.m., Location: Fine Hall 314
Abstract: It is well known that on $\reals^n$, the Schrödinger propagator is unitary on $L2$ based spaces, but that locally in space and on average in time there is a $1/2$ derivative smoothing effect. We consider a family of manifolds with trapped geodesics which are degenerately hyperbolic and prove a sharp local smoothing estimate with loss depending on the type of trapping. Further, we construct a microlocal parametrix extended polynomially beyond Ehrenfest time, and as a consequence, we obtain Strichartz estimates with near-sharp loss depending only on the dimension of the trapping. This is partly joint work with J. Wunsch (Northwestern)
 
PACM Colloquium
Topic: Geometry and Topology in Dimension Reduction
Presenter: Sayan Mukherjee, Duke University
Date: Monday, March 26, 2012, Time: 4:30 p.m., Location: Fine Hall 214
Abstract: In the first part of the talk we describe how learning the gradient of a regression function can be used for supervised dimension reduction (SDR). We provide an algorithm for learning gradients in high-dimensional data, provide theoretical guarantees for the algorithm, and provide a statistical interpretation. Comparisons to other methods on real and simulated data are presented. In the second part of the talk we present preliminary results on using the Laplacian on forms for dimension reduction. This involves understanding higher-order versions of the isoperimetric inequality for both manfifolds and abstract simplicial complexes.
 
Mathematical Physics Seminar **Please note new time**
Topic: TBA
Presenter: Sourav Chatterjee, Courant Institute
Date:  Tuesday, March 27, 2012, Time: 3:30 p.m. **, Location: A06 - Jadwin Hall
 
Algebraic Geometry Seminar
Topic: The integral Hodge conjecture for 3-folds
Presenter: Burt Totaro DPMMS, Cambridge University
Date: Tuesday, March 27, 2012, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: The Hodge conjecture predicts which rational homology classes on a smooth complex projective variety can be represented by linear combinations of complex subvarieties. In other words, it is about the difference between topology and algebraic geometry. The integral Hodge conjecture, the analogous conjecture for integral homology classes, is false in general. We discuss negative results and some new positive results on the integral Hodge conjecture for 3-folds
 
Department Colloquium
Topic: TBA
Presenter: G. Margulis, Yale University
Date: Wednesday, March 28, 2012, Time: 4:30 p.m., Location: Fine Hall 314
 
Ergodic Theory and Statistical Mechanics Seminar
Topic: TBA
Presenter: Jon Fickenscher, Princeton University
Date:  Thursday, March 29, 2012, Time: 2:00 p.m., Location: Fine Hall 601
 
Discrete Mathematics Seminar
Topic: TBA
Presenter: Benjamin Matschke, IAS
Date: Thursday, March 29, 2012, Time: 2:15 p.m., Location: Fine Hall 224
 
Joint IAS and Princeton University Number Theory Seminar
Topic: TBA
Presenter: Payman Kassaei, King's College London
Date: Thursday, March 29, 2012, Time: 4:30 p.m., Location: IAS, Room S-101
 
Topology Seminar
Topic: TBA
Presenter: Joan Licata, Stanford University
Date: Thursday, March 29, 2012, Time: 4:30 p.m., Location: Fine Hall 314
 
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Mattias Jonsson, University of Michigan
Date: Friday, March 30, 2012, Time: 3:00 p.m., Location: Fine Hall 314
 
APRIL 2012
 
Analysis Seminar
Topic: TBA
Presenter: Brian Street, University of Wisconsin, Madison
Date: Monday, April 2, 2012, Time: 3:15 p.m., Location: Fine Hall 314
 
Algebraic Geometry Seminar
Topic: TBA
Presenter: Lev Borisov, Rutgers University
Date: Tuesday, April 3, 2012, Time: 4:30 p.m., Location: Fine Hall 322
 
Department Colloquium
Topic: TBA
Presenter: J. Quastel, University of Toronto
Date: Wednesday, April 4, 2012, Time: 4:30 p.m., Location: Fine Hall 314
 
Ergodic Theory and Statistical Mechanics Seminar
Topic: TBA
Presenter: Xiuyuan Cheng, Princeton University
Date:  Thursday, April 5, 2012, Time: 2:00 p.m., Location: Fine Hall 601
 
Discrete Mathematics Seminar
Topic: TBA
Presenter: Jeff Kahn, Rutgers University
Date: Thursday, April 5, 2012, Time: 2:15 p.m., Location: Fine Hall 224
 
Algebraic Topology Seminar
Topic: TBA
Presenter: Chuck Weibel, Rutgers University
Date: Thursday, April 5, 2012, Time: 3:00 p.m., Location: Fine Hall 214
 
Joint IAS and Princeton University Number Theory Seminar
Topic: TBA
Presenter: Julia Gordon, University of British Columbia
Date: Thursday, April 5, 2012, Time: 4:30 p.m., Location: Fine Hall 214
 
Topology Seminar
Topic: TBA
Presenter: Joshua Greene, Boston College
Date: Thursday, April 5, 2012, Time: 4:30 p.m., Location: Fine Hall 314
 
Differential Geometry and Geometric Analysis Seminar
Topic: An extension of Hardy-Littlewood-Sobolev inequality
Presenter: Meijun Zhu, University of Oklahoma
Date: Friday, April 6, 2012, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: The classical Hardy-Littlewood-Sobolev inequality implies Sobolev and other geometric inequalities and has a great impact to geometric analysis. Recent results on Sobolev inequalities with negative power indicate the existence of certain extensions to the classical HLS inequality. In this talk, we shall reveal one extension. The existence of sharp constant, as well as the classification of certain extremal functions via the method of moving sphere are also obtained. This is a joint work with J. Dou.
 
Analysis Seminar
Topic: Growth of Sobolev norms for the cubic defocusing nonlinear Schrodinger equation in polynomial time
Presenter: Marcel Guardia, Universitat Politecnica de Catalunya / IAS
Date: Monday, April 9, 2012, Time: 3:15 p.m., Location: Fine Hall 314
Abstract: We consider the cubic defocusing nonlinear Schrodinger equation in the two dimensional torus. Fix s>1. Colliander, Keel, Staffilani, Tao and Takaoka (2010) proved existence of solutions with s-Sobolev norm growing in time by any given factor R. Refining their methods in several aspects we find solutions with s-Sobolev norm growing in polynomial time in R. This is a joint work with V. Kaloshin.
 
Algebraic Geometry Seminar
Topic: TBA
Presenter: Daniel Erman, Stanford University
Date: Tuesday, April 10, 2012, Time: 4:30 p.m., Location: Fine Hall 322
 
Department Colloquium
Topic: TBA
Presenter: A. Kiselev, University of Wisconsin - Madison
Date: Wednesday, April 11, 2012, Time: 4:30 p.m., Location: Fine Hall 314
 
Ergodic Theory and Statistical Mechanics Seminar
Topic: Local semicircle law in the bulk for Gaussian $β$-ensemble
Presenter: Percy Wong, Princeton University
Date:  Thursday, April 12, 2012, Time: 2:00 p.m., Location: Fine Hall 601
Abstract: Paper available at: http://arxiv.org/abs/1112.2016v1
 
Algebraic Topology Seminar
Topic: TBA
Presenter: Paul Baum, Penn State University
Date: Thursday, April 12, 2012, Time: 3:00 p.m., Location: Fine Hall 214
 
Joint IAS and Princeton University Number Theory Seminar
Topic: TBA
Presenter: Xinwen Zhu, Harvard University
Date: Thursday, April 12, 2012, Time: 4:30 p.m., Location: Fine Hall 214
 
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: John Head, Courant Institute
Date: Friday, April 13, 2012, Time: 3:00 p.m., Location: Fine Hall 314
 
IAS-PU Symplectic Geometry Seminar **Please note location**
Topic: A Mathematical Theory of Quantum Sheaf Cohomology
Presenter: Ron Donagi, University of Pennsylvania.
Date: Friday, April 13, 2012, Time: 4:30 p.m., Location: Fine Hall 322 **
 
Analysis Seminar
Topic: TBA
Presenter: Michael Lacey, Georgia Institute of Technology
Date: Monday, April 16, 2012, Time: 3:15 p.m., Location: Fine Hall 314
 
Department Colloquium
Topic: On Kolmogorov's conjecture and Hausdorff dimension of oscillatory motions for certain restricted three body problems
Presenter: V. Kaloshin, University of Maryland - College Park
Date: Wednesday, April 18, 2012, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Consider the classical Newtonian 3-body problem, namely, bodies are mutually attracted by the Newton graviation. Call motion oscillatory if as time tends to infinity limsup of maximal distance among the bodies is infinite, while liminf is finite. In the 50's Sitnikov presented the first rigorous example of ocsillatory motions for the so-called restricted 3-body problem. Later in the 60's Alexeev extended this example to the full 3-body problem. A long-standing conjecture of Kolmogorov is that oscillatory motions have measure zero. We show that for the Sitnikov example and for the so-called restricted planar circular 3-body problem these motions often form a set of maximal possible Hausdorff dimension. This is a joint work with A. Gorodetski.
 
Joint IAS and Princeton University Number Theory Seminar
Topic: TBA
Presenter: Francis Brown, CNRS/Jussieu
Date: Thursday, April 19, 2012, Time: 4:30 p.m., Location: IAS - Room S-101
 
Topology Seminar
Topic: TBA
Presenter: Liam Watson, UCLA
Date: Thursday, April 19, 2012, Time: 4:30 p.m., Location: Fine Hall 314
 
Department Colloquium
Topic: TBA
Presenter: T. Wooley, University of Bristol
Date: Wednesday, April 25, 2012, Time: 4:30 p.m., Location: Fine Hall 314
 
Ergodic Theory and Statistical Mechanics Seminar
Topic: Invariant Measures, Conjugations and Renormalizations of Circle Maps with Break points
Presenter: Akhtam Dzhalilov, Samarkand State University
Date:  Thursday, April 26, 2012, Time: 2:00 p.m., Location: Fine Hall 601
 
Algebraic Topology Seminar
Topic: TBA
Presenter: Nancy Hingston, IAS
Date: Thursday, April 26, 2012, Time: 3:00 p.m., Location: Fine Hall 214
 
Joint IAS and Princeton University Number Theory Seminar
Topic: TBA
Presenter: Mitya Boyarchenko, University of Michigan
Date: Thursday, April 26, 2012, Time: 4:30 p.m., Location: Fine Hall 214
 
Topology Seminar
Topic: TBA
Presenter: Joshua Batson, MIT
Date: Thursday, April 26, 2012, Time: 4:30 p.m., Location: Fine Hall 314
 
Analysis Seminar
Topic: The Cauchy problem for the Benjamin-Ono equation in L^2 revisited (Joint work with Luc Molinet)
Presenter: Didier Pilod, Universidade Federal do Rio de Janeiro / University of Chicago
Date: Monday, April 30, 2012, Time: 3:15 p.m., Location: Fine Hall 314
Abstract: The Benjamin-Ono equation models the unidirectional evolution of weakly nonlinear dispersive internal long waves at the interface of a two-layer system, one being in finitely deep. The Cauchy problem associated to this equation presents interesting mathematical difficulties and has been extensively studied in the recent years. In a recent work (2007), Ionescu and Kenig proved well-posedness for real-valued initial data in L^2(R). In this talk, we will give another proof of Ionescu and Kenig's result, which moreover provides stronger uniqueness results. In particular, we prove unconditional well-posedness in H^s(R), for s > 1/4 . Note that our approach also permits to simplify the proof of the global well-posedness in L^2(T) by Molinet (2008) and yields unconditional well-posedness in H^{1/2}(T). Finally, it is worthwhile to mention that our technique of proof also apply for a higher-order Benjamin-Ono equation. We prove that the associated Cauchy problem is globally well-posed in the energy space H^1(R).
 
MAY 2012
 
Algebraic Geometry Seminar
Topic: TBA
Presenter: Bhargav Bhatt, University of Michigan
Date: Tuesday, May 1, 2012, Time: 4:30 p.m., Location: Fine Hall 322
 
Department Colloquium
Topic: TBA
Presenter: T. Tao, University of California - Los Angeles
Date: Wednesday, May 2, 2012, Time: 4:30 p.m., Location: Fine Hall 314
 
Discrete Mathematics Seminar
Topic: TBA
Presenter: Maria Chudnovsky, Columbia University
Date: Thursday, May 3, 2012, Time: 2:15 p.m., Location: Fine Hall 224
 
Joint IAS and Princeton University Number Theory Seminar
Topic: TBA
Presenter: Steven D. Miller, Rutgers University
Date: Thursday, May 3, 2012, Time: 4:30 p.m., Location: IAS - Room S-101
 
Joint IAS and Princeton University Number Theory Seminar
Topic: TBA
Presenter: Jack Thorne, Harvard University
Date: Thursday, May 10, 2012, Time: 4:30 p.m., Location: Fine Hall 214