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| MARCH 2010 |
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| Special Algebraic Geometry Seminar ***Please note special date, time, and location |
| Topic: |
Noncommutaive Hodge structure and applications |
| Presenter: |
Ludmil Katzarkov, UC Irvine |
| Date: |
Wednesday, March 31, 2010, Time: 3:00 p.m., Location: Fine Hall 801 |
| Abstract: |
In this talk we will look at some classical problems. - rationality - from a new prospective. Our point of view will be based on Homological Mirror Symmetry. Examples will be discussed at the end. |
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| Department Colloquium |
| Topic: |
L_1 embeddings of the Heisenberg group and fast estimation of graph isoperimetry |
| Presenter: |
Assaf Naor, New York University |
| Date: |
Wednesday, March 31, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
We will show that any L_1-valued mapping of an epsilon net in the unit ball of the Heisenberg group incurs bi-Lipschitz distortion (log(1/epsilon))^c, where c is a universal constant. We will also explain how this result implies an exponential improvement to the best known integrality gap for the Goemans-Linial semidefinite relaxation of the Sparsest Cut problem. Joint work with Jeff Cheeger and Bruce Kleiner |
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| APRIL 2010 |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Independence properties of weakly mixing systems and polynomial pattersn in large sets |
| Presenter: |
Vitaly Bergelson, Ohio State University |
| Date: |
Thursday, April 1, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
| Abstract: |
Various recurrence and convergence results obtained in recent years indicate that dynamical systems exhibit regular behavior along polynomial times. In particular, weakly mixing systems turn out to always possess rather strong independence properties along certain sets of zero density. We will discuss some implications of these results in physics as well as applications to combinatorics and number theory (including polynomial extensions of Szemeredi's theorem on arithmetic progressions and recent work of Tao and Ziegler on polynomial patterns in primes). We will also formulate and discuss some natural open problems and conjectures. |
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| Joint Princeton University and Institute for Advanced Study Number Theory Seminar |
| Topic: |
On a p-adic automorphic construction of Euler systems |
| Presenter: |
Eric Urban, Columbia University |
| Date: |
Thursday, April 1, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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| Topology Seminar |
| Topic: |
Resonance for loop homology on spheres |
| Presenter: |
Nancy Hingston, The College of New Jersey |
| Date: |
Thursday, April 1, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
A Riemannian metric on a compact manifold M gives rise to a length function on the free loop space LM, whose critical points are the closed geodesics in the given metric on M. If x is a homology class on LM, the "minimax" critical level cr(x) is a critical value. Let M be a sphere, and fix a metric and a coefficient field. We prove that the limit as deg(x) goes to infinity of cr(x)/deg(x) exists. Mark Goresky and Hans-Bert Rademacher are collaborators. |
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| Discrete Mathematics Seminar *** Please note special day and time |
| Topic: |
Overlap properties of geometric expanders |
| Presenter: |
Assaf Naor, Courant Institute, NYU |
| Date: |
Friday, April 2, 2010, Time: 4:00 p.m., Location: Fine Hall 224 |
| Abstract: |
If G=(V,E) is an expander graph then for every embedding f:V\to R that is extended linearly from the vertices G to its edges, there must be a point p\in R such that the pre-image f^{-1}(p) has cardinality at least a constant multiple of the total number of edges |E| (just take p to be the median of f(V)). This property of expanders motivated Gromov to define a higher dimensional version of expansion: say that a d-dimensional simplicial complex S is "expander like" if for every embedding f:S\to R^d that is extended affinely from the vertices of S to its d-faces, there must be a point p\in R^d such that the cardinality of f^{-1}(p) is at least a constant multiple of the total number of d-faces of S. The fact that the complete d-dimensional simplicial complex is "expander like" is a classical result of Boros-Furedi (d=2) and Barany (d>2). Gromov asked the natural question whether in every dimension there exist bounded degree simplicial complexes that are "expander like". In this talk we will answer this question positively, and describe various related results and open questions. Joint work with Jacob Fox, Misha Gromov, Vincent Lafforgue, and Janos Pach. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
p-harmonic forms on complete manifolds |
| Presenter: |
Chiung-Jue Anna Sung, Tsing-Hwa University, Taiwan |
| Date: |
Friday, April 2, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
Let M be an m-dimensional complete non-compact Reimannian manifold. We prove that any bounded set of p-harmonic k-forms in L^q(M), is relatively compact with respect to the uniform convergence topology if the curvature operator of M is asymptotically non-negative. |
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| Analysis Seminar |
| Topic: |
The space time resonance method and global existence of small surface waves. |
| Presenter: |
Jalal Shatah, Courant Institute |
| Date: |
Monday, April 5, 2010, Time: 4:00 p.m., Location: Fine Hall 110 |
| Abstract: |
We will present a new approach to proving global existence of small solutions to dispersive equations. This approach combines the well established methods of vector fields and normal forms and extend them to show global existence of small amplitude surface water waves. We will also show how many of the well known results of existence of small solutions of dispersive equations can be simply established by the space time resonance method. |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
Y. Ruan, Michigan |
| Date: |
Monday, April 5, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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| PACM Colloquium |
| Topic: |
Combinatorial Phase Transition |
| Presenter: |
Peter Winkler, AT&T Labs Research, Florham Park NJ |
| Date: |
Monday, April 5, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
| Abstract: |
The past fifteen years have seen a huge boom in work at the interface of statistical physics, combinatorics, probability, and the theory of computing. A unifying objective has been understanding phase transition, especially in discrete models with hard constraints. We will give some indication of why the notion is so interesting to diverse groups of researchers, and some examples where there has been recent progress. |
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| Group Actions Seminar |
| Topic: |
Compact forms of homogeneous spaces and group actions |
| Presenter: |
David Constantine, University of Chicago |
| Date: |
Tuesday, April 6, 2010, Time: 12:30 p.m., Location: Fine Hall 322 |
| Abstract: |
Given a homogeneous space J\H, does there exist a discrete subgroup \Gamma in H such that J\H/Gamma is a compact manifold? These compact forms of homogeneous spaces turn out to be rare outside of a few natural cases. Their existence has been studied by a very wide range of techniques, one of which is via the action of the centralizer of J in H. In this talk I'll show that no compact form exists when H is a simple Lie group, J is reductive and the acting group is higher-rank and semisimple. The proof uses cocycle superrigidity, Ratner's theorem and techniques from partially hyperbolic dynamics. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
James McKernan, MIT |
| Date: |
Tuesday, April 6, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Concentration inequalities for dynamical systems |
| Presenter: |
Jean-René Chazottes, CNRS and École-Polytechnique |
| Date: |
Thursday, April 8, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
| Abstract: |
Concentration inequalities are a powerful tool to estimate the fluctuations of observables more general than ergodic sums: one can consider any observable F(x,...,T^n x) provided it is separately Lipschitz. Such inequalities can be established for non-uniformly hyperbolic systems and we shall present some applications. |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Alexandra Kolla, IAS |
| Date: |
Thursday, April 8, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Joint Princeton University and Institute for Advanced Study Number Theory Seminar |
| Topic: |
Proof, via smooth homology, of the existence of rational families of H-invariant linear forms on G-induced representations, when G/H is a symetric, reductive, p-adic space, via smooth homology |
| Presenter: |
Philippe Blanc, Institut de Mathématiques de Luminy |
| Date: |
Thursday, April 8, 2010, Time: 4:30 p.m., Location: IAS S-101 |
| Abstract: |
We fix F a local non archmedean field of characteristic zero, G the points over F of an algebraic reductive group defined over F and s a rational involution of G defined over F. We note H the group of fixed points of G under the action of s and X(G,s) the connected component on the neutral element of the set of complex characters of G antiinvariant under the action of s. Let P be a s-parabolic subgroup of G, id est the intersection M of P with s(P) is a s-stable Levi subgroup, we construct from a irreducible, smooth representation r of M, a rational family of distributions above the algebraic variety X(G,s), which are H-invariant linear forms on tne smooth induced representation ind(P,G; r ). Our main trick is the use of homology of groups. |
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| Topology Seminar |
| Topic: |
Rank and genus of amalgamated 3-manifolds |
| Presenter: |
Tao Li, Boston College |
| Date: |
Thursday, April 8, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
A fundamental question in 3-manifold topology is whether or not the rank of the fundamental group of a closed 3-manifold is equal to the Heegaard genus. We use hyperbolic JSJ pieces to construct closed 3-manifolds with rank smaller than genus. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
Ricci flow and the determinant of the Laplacian on non-compact surfaces |
| Presenter: |
Pierre Albin, Courant |
| Date: |
Friday, April 9, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
The determinant of the Laplacian is an important invariant of closed surfaces and has connections to the dynamics of geodesics, Ricci flow, and physics. Its definition is somewhat intricate as the Laplacian has infinitely many eigenvalues. I'll explain how to extend the determinant of the Laplacian to non-compact surfaces where one has to deal with additional difficulties like continuous spectrum and divergence of the trace of the heat kernel. On surfaces (even non-compact) this determinant has a simple variation when the metric varies conformally. I'll explain how to use Ricci flow to see that the largest value of the determinant occurs at constant curvature metrics.This is joint work with Clara Aldana and Frederic Rochon. |
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| Analysis Seminar |
| Topic: |
Interaction of Light with Arbitrarily Shaped Dielectric Media: Compactness and Robustness in Electromagnetic Scattering |
| Presenter: |
Yajun Zhou, Princeton University |
| Date: |
Monday, April 12, 2010, Time: 4:00 p.m., Location: Fine Hall 110 |
| Abstract: |
The scattering of electromagnetic waves by homogeneous dielectric media is characterized by a strongly singular integral equation, corresponding to the identity operator perturbed by a non-compact Green operator. Using the Kondrachov-Rellich compact imbedding and the Calderon-Zygmund theory, we prove that the Green operator is polynomially compact if the dielectric boundary is a compact smooth manifold. We then show that the electromagnetic scattering problem admits a robust solution for all non-accretive media ($\mathrm{Im}\chi\leq0$) satisfying certain geometric and topological constraints, except for the critical point $\chi=-2$, where unbounded electromagnetic enhancement may occur. Combining the polynomial compactness of the Green operator with the Arendt-Batty-Lyubich-Vu theorem in semigroup theory, we devise a non-perturbative approach to the solution of electromagnetic scattering problem, as an improvement of the Born approximation.
This work was part of the speaker's PhD thesis project completed at Harvard University. |
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| PACM Colloquium |
| Topic: |
Internet Traffic Matrices and Compressive Sensing |
| Presenter: |
Walter Willinger, Mathematics and Computer Science, Darthmouth College |
| Date: |
Monday, April 12, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
| Abstract: |
Internet traffic matrices (TMs) specify the traffic volumes between origins and destinations in a network over some time period. For example, origins and destinations can be individual IP addresses, prefixes, routers, points-of-presence (PoPs), or entire networks or Autonomous Systems (ASes). Past work on TMs has almost exclusively focused on large ASes such as AS7018 (AT&T) and their router- or PoP-level TMs, mainly because the latter are critical inputs to many basic network engineering tasks, and the thrust of much of this work has been on measurement and inference of TMs. A key remaining challenge in this area is how to cope with missing values that frequently arise in real-world TMs. This problem brings TM research into the realm of compressive sensing, a generic technique for dealing with missing observations that exploits the presence of structure or redundancy in data from many real-world systems. In particular, since real-world TMs have been found to be of low rank, the concept of compressive sensing is directly applicable, at least in theory. In this talk, I will report on novel applications of compressive sensing to TM interpolation and inference and discuss how the resulting techniques work in practice. I will end by describing some challenging open problems concerning measuring and inferring the completely unknown Internet-wide AS-level TM. (This is joint work with Y. Zhang and L. Qiu (Univ. of Texas) and M. Roughan (Univ. od Adelaide).) |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
Y. Tachikawa, IAS |
| Date: |
Monday, April 12, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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| Group Actions Seminar |
| Topic: |
TBA |
| Presenter: |
Daryl Cooper, University of California, Santa Barbara |
| Date: |
Tuesday, April 13, 2010, Time: 12:30 p.m., Location: Fine Hall 322 |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Shin-Yao Jow, University of Pennsylvania |
| Date: |
Tuesday, April 13, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Discrete Mathematics Seminar *** Please note special day |
| Topic: |
Eigenvalues, connectivity and matchings in regular graphs |
| Presenter: |
Sebastian Cioaba, University of Delaware |
| Date: |
Wednesday, April 14, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: |
The spectrum of a graph contains a lot of relevant information regarding its structure. In this talk, I will describe some relationships between the eigenvalues of a regular graph, its matching number and connectivity. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Alex Kontorovich, Brown University and IAS |
| Date: |
Thursday, April 15, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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| Topology Seminar |
| Topic: |
A combinatorial approach to Heegaard Floer invariants |
| Presenter: |
Ciprian Manolescu, UCLA |
| Date: |
Thursday, April 15, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
I will present a combinatorial description of the Heegaard Floer invariants of three- and four-manifolds (mod 2). The idea is to represent the manifolds in terms of links in S3, and then to use grid diagrams to represent the links. Counting holomorphic polygons in symmetric products boils down to counting certain domains on the grids. This is based on joint work with P. Ozsvath and D. Thurston. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Julie Rowlett, Bonn |
| Date: |
Friday, April 16, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
G. Bellamy, Edinburgh |
| Date: |
Monday, April 19, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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| Group Actions Seminar |
| Topic: |
TBA |
| Presenter: |
Nir Avni, Harvard University |
| Date: |
Tuesday, April 20, 2010, Time: 12:30 p.m., Location: Fine Hall 322 |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Dragos Oprea, UCSD |
| Date: |
Tuesday, April 20, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Robin Thomas, Georgia Tech |
| Date: |
Thursday, April 22, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Guofang We, UCSB |
| Date: |
Friday, April 23, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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| Topology Seminar ***Please note special date and time |
| Topic: |
TBA |
| Presenter: |
Olga Plamenevskaya, SUNY Stony Brook |
| Date: |
Friday, April 23, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Justin Holmer, Brown University |
| Date: |
Monday, April 26, 2010, Time: 4:00 p.m., Location: Fine Hall 110 |
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| PACM Colloquium |
| Topic: |
Toward practical rare event simulation in high dimensions |
| Presenter: |
Jonathan Weare, Courant Institute for Mathematics, NYC |
| Date: |
Monday, April 26, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
| Abstract: |
Prof. Weare will discuss an importance sampling method for certain rare event problems involving small noise diffusions. Standard Monte Carlo schemes for these problems behave exponentially poorly in the small noise limit. Previous work in rare event simulation has focused on developing, in specific situations, estimators with optimal exponential variance decay rates. He will introduce an estimator related to a deterministic control problem that not only has an optimal variance decay rate under certain conditions, but that can even have vanishingly small statistical relative error in the small noise limit. The method can be seen as the limit of a well known zero variance importance sampling scheme for diffusions which requires the solution of a second order partial differential equation. |
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| Mathematical Physics Seminar |
| Topic: |
Quasi-adiabatic continuation and the Topology of Many-body Quantum Systems |
| Presenter: |
Matthew Hastings, Microsoft Research |
| Date: |
Tuesday, April 27, 2010, Time: 4:30 p.m., Location: Jadwin 343 |
| Abstract: |
Topological arguments play a key role in understanding quantum systems. For example, recently it has been shown that K-theory provides a tool for classifying different phases of non-interacting, or single-particle, systems. However, topological arguments have also been applied to interacting systems. I will explain the technique of quasi-adiabatic continuation, which provides a way to rigourously formulate many of the topological arguments made by physicists for these systems. In particular, I will discuss its application to a higher dimensional Lieb-Schultz-Mattis theorem (a statement about degeneracy of ground states, which can arise for topological reasons), where this technique was introduced in 2004, and its more recent application to proving quantum Hall conductance quantization for interacting systems. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Valentino Tosatti, Columbia University |
| Date: |
Friday, April 30, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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| MAY 2010 |
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| PACM Colloquium |
| Topic: |
TBA |
| Presenter: |
Stephen Howard, University of Melbourne, Australia |
| Date: |
Monday, May 3, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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| Group Actions Seminar |
| Topic: |
TBA |
| Presenter: |
Yves Cornulier, CNRS, Université de Rennes 1 |
| Date: |
Tuesday, May 4, 2010, Time: 12:30 p.m., Location: Fine Hall 322 |
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| Joint Princeton University and Institute for Advanced Study Number Theory Seminar |
| Topic: |
Selmer ranks of twists of elliptic curves |
| Presenter: |
Karl Rubin, UC Irvine |
| Date: |
Thursday, May 6, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
| Abstract: |
In joint work with Barry Mazur, we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions for an elliptic curve to have twists of arbitrary 2-Selmer rank, and we give lower bounds for the number of twists (with bounded conductor) that have a given 2-Selmer rank. As a consequence, under appropriate hypotheses there are many twists with Mordell-Weil rank zero, and (assuming the Shafarevich-Tate conjecture) many others with Mordell-Weil rank one. The talk will conclude with some speculation about the density of twists with a given Selmer rank. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Xavier Cabre, Universitat Politècnica de Catalunya |
| Date: |
Friday, May 7, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium |
| Topic: |
TBA |
| Presenter: |
Anthony Peirce, University of British Columbia |
| Date: |
Monday, May 17, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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