SEMINARS
Updated: 10-12-2010

   
OCTOBER 2010
   
Algebraic Geometry Seminar
Topic: Equivariant birational maps and resolutions of categorical quotients
Presenter: Dan Edidin, University of Missouri
Date:  Tuesday, October 12, 2010, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: If $X^{ss}$ is the set of semi-stable points for a linearized action of a reductive group on a smooth projective variety $X$ then there two procedures (Kirwan's procedure or change of linearization) for constructing a partial resolution of singularities of the categorical quotient $X^{ss}/G$. Both involve finding an equivariant birational map $\tilde{X} \to X^{ss}$ with $\tilde{X}$ smooth such that $G$ acts properly on $\tilde{X}$ and the induced map on quotients is proper and birational. A natural question to ask is whether (and to what extent) this procedure can be replicated for non-GIT quotients. We consider the problem for actions of diagonalizable groups and show that there is a simple combinatorial procedure that replicates Kirwan's construction for non-projective toric varieties. This talk is based on joint work with Yogesh More.
   
Mathematical Physics Seminar
Topic: Extended States in a Lifshitz Tail Regime for Random Operators on Trees
Presenter: Simone Warzel, Technical Univ. Munich
Date:  Tuesday, October 12, 2010, Time: 4:30 p.m., Location: Jadwin 343
Abstract: We will discuss the spectral properties of random operators on regular tree graphs. The models have have been among the earliest studied for Anderson localization, and they continue to attract attention because of analogies with localization issues for many particles. The talk will focus on the location of the mobility edge. Somewhat surprisingly, a resonance mechanism will be proven to cause the appearance of absolutely continuous spectrum in a regime extending well beyond the energy band of the operator's non-random hopping term. For weak disorder, this includes a Lifshitz tail regime of very low density of states.
   
Statistical Mechanics Seminar
Topic: Microscopic Models of Macroscopic Transport: A Selective Overview
Presenter: Joel Lebowitz, Rutgers University
Date:  Wednesday, October 13, 2010, Time: 2:00 p.m., Location: Jadwin Hall 343
Abstract: I will describe various attempts to derive, heuristically or rigorously, diffusive behavior of energy (particle) transport, i.e. Fourier's law (Fick's law) from classical microscopic models (mostly deterministic). Computer simulations showing presence or absence of such behavior in ordered and disordered systems will be described. Exact results are desperately lacking both in one and higher dimensions.
   
Department Colloquium
Topic: Incompressible Fluids: Simple Models, Complex Fluids
Presenter: Peter Constantin, University of Chicago
Date:  Wednesday, October 13, 2010, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Complex fluids are fluids with particles suspended in them. The particles are carried by the fluid, interact among themselves, and influence the fluid's behavior. I will describe some of the basic questions of existence, uniqueness, regularity and stability of solutions of models of complex fluids, in the broader context of incompressible hydrodynamic PDE.
   
Symplectic Geometry Seminar
Topic: Coherent-constructible correspondence and its applications
Presenter: Bohan Fang, Columbia University
Date:  Thursday, October 14, 2010, Time: 1:30 p.m., Location: Fine Hall 601
Abstract: I will describe a coherent-constructible correspondence, which is a monoidal dg functor between the category of equivariant perfect sheaves of a toric variety and the category of some constructible sheaves over a real vector space (dual Lie algebra of the torus). This correspondence is motivated by homological mirror symmetry - performing a T-duality on an equivariant line bundle produces a Lagrangian submanifold in the cotangent bundle of that dual Lie algebra. The Nadler-Zaslow's theorem then equates this Lagrangian to a constructible sheaf on the base. This correspondence can be extended to toric DM stacks, and as an exercise, one may show the derived categories are equivalent from the combinatorial constructible viewpoint in the case of some toric crepant resolutions. (This talk is based on the joint works with Chiu-Chu Liu, David Treumann and Eric Zaslow)
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: The Spectrum of an Hermitian Matrix With Dependent Entries Constructed from Random Independent Images
Presenter: Amit Singer and Xiuyuan Cheng, Princeton University
Date:  Thursday, October 14, 2010, Time: 2:00 p.m., Location: Fine Hall 401
Abstract: In this talk we will present a preliminary analysis and numerical results for the distribution of eigenvalues of a certain random N by N Hermitian matrix, whose construction is motivated by a problem in structural biology. The matrix is built from N images, where each image is an array of P pixels, and the pixels are i.i.d standard Gaussians. Numerical experiments suggest that the spectrum approaches Wigner's semi-circle law for P>>N, but differs significantly from the semi-circle for P<<N. We attribute this difference to the dependencies among the matrix entries. In particular, using the third moment, we show that for fixed P, the largest eigenvalue is O(N) as N goes to infinity.
   
Discrete Mathematics Seminar
Topic: Nearly Tight Low Stretch Spanning Trees
Presenter: Ofer Neiman, Courant Institute, NYU
Date:  Thursday, October 14, 2010, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: We prove that any graph G on n vertices has a distribution over its spanning trees such that for any edge (u,v) the expected stretch E_T[d_T(u,v)] is bounded by \tilde{O}(\log n). Our result is obtained via a new approach of building ``highways'' between portals and a new strong diameter probabilistic decomposition theorem. Joint work with Ittai Abraham and Yair Bartal
   
Joint Princeton University and IAS Number Theory Seminar
Topic: Even Galois Representations and the Fontaine-Mazur conjecture
Presenter: Frank Calegari, Northwestern and IAS
Date:  Thursday, October 14, 2010, Time: 4:30 p.m., Location: IAS S-101
Abstract: Fontaine and Mazur have a remarkable conjecture that predicts which (p-adic) Galois representations arise from geometry. In the special case of two dimensional representations with distinct Hodge-Tate weights, they further conjecture that these "geometric" representations are also modular. Kisin has proven this conjecture in almost all cases under the assumption that the action of complex conjugation has determinant -1. We remove this restriction. In the case of even Galois representations, this generalizes previous work in which the representation was assumed to be ordinary.
   
Topology Seminar
Topic: Holomorphic traingle maps in sutured Floer homology
Presenter: Jacob Rasmussen, Cambridge/SUNY Stony Brook
Date:  Thursday, October 14, 2010, Time: 4:30 p.m., Location: Fine Hall 314
Abstract:

Honda, Kazez and Matic defined maps on sutured Floer homology induced by a contact structure. I'll explain how to compute these maps using holomorphic triangle counts and give some applications to computing sutured Floer homologies and sutured contact invariants.

 

Differential Geometry and Geometric Analysis Seminar
Topic: Counterexamples to Min-Oo's Conjecture
Presenter: Simon Brendle, Stanford University
Date:  Friday, October 15, 2010, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: Consider a compact Riemannian manifold $M$ of dimension $n$ whose boundary $\partial M$ is totally geodesic and is isometric to the standard sphere $S^{n-1}$. A natural conjecture of Min-Oo asserts that if the scalar curvature of $M$ is at least $n(n-1)$, then $M$ is isometric to the hemisphere $S_+^n$ equipped with its standard metric. This conjecture is inspired by the positive mass theorem in general relativity, and has been verified in many special cases. I will present joint work with F.C. Marques and A. Neves which shows that Min-Oo's conjecture fails in dimension $n \geq 3$
   
Analysis Seminar
Topic: Asymptotic Behavior of Spacetimes Approaching a Schwarzschild solution
Presenter: Gustav Holzegel, Princeton University
Date:  Monday, October 18, 2010, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: Consider a spacetime which approaches a Schwarzschild solution. We will discuss the following problem: Assuming decay of appropriate norms of the Ricci rotation coefficients and their derivatives, can one prove boundedness/ decay for the curvature components and their derivatives? The talk will give a positive answer to this question and explain some of the difficulties arising from the fact that not all curvature components decay. As an important ingredient, we generalize recent work of Dafermos and Rodnianski regarding decay for the wave equation to the setting of the Bianchi equations.
   
PACM Colloquium
Topic: Information Aggregation in Complex Networks
Presenter: Ali Jadbabaie, University of Pennsylvania
Date: Monday, October 18, 2010, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:

Over the past few years there has been a rapidly growing interest in analysis, design and optimization of various types of collective behaviors in networked dynamic systems. Collective phenomena (such as flocking, schooling, rendezvous, synchronization, and formation flight) have been studied in a diverse set of disciplines, ranging from computer graphics and statistical physics to distributed computation, and from robotics and control theory to ecology, evolutionary biology, social sciences and economics. A common underlying goal in such studies is to understand the emergence of some global phenomena from local rules and interactions.

In this talk, I will expand on such developments and present and analyze new models of consensus and agreement in random networks as well as new algorithms for information aggregation tailored to opinions and beliefs in social networks. Specifically, I will present a model of social learning in which an agent acts as rational and Bayesian with respect to her own observations, but exhibits a bias towards the average belief of its neighbors to reflect the "network effect". When the underlying social network is strongly connected all agents reach consensus in there beliefs. Moreover, I will show that when each agent's observed signal is independent from others, agents will "learn" like a Bayesian who has access to global information, hence information is correctly aggregated.

Joint work with Pooya Molavi, Alireza Tahbaz-Salehi, Alvaro Sandroni and Victor Preciado

   
Analysis Seminar *** Please note special time
Topic: Global wellposedness and scattering for the inhomogeneous fourth-order Schrodinger equation
Presenter: Benoit Pausader, Brown University
Date:  Monday, October 18, 2010, Time: 5:00 p.m., Location: Fine Hall 314
Abstract: Fourth-order Schrodinger equations were proposed as a correction to the standard model for propagation of laser in nonlinear media and have since appeared in different contexts. In this talk, I will consider the inhomogeneous mass-critical fourth-order Schrodinger equation iu_t+D^2u-Du+|u|^{8/n}u=0 and prove global existence and scattering in L^2 in high dimensions. The main analysis is reduced to a good understanding of the scaling limit problems which are scale invariant. This is a joint work with Shuanglin Shao.
   
Algebraic Geometry Seminar
Topic: A vanishing theorem in characteristic p
Presenter: Junecue Suh, IAS
Date:  Tuesday, October 19, 2010, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: While the classical Kodaira vanishing theorem is false in general in characteristic p>0, Deligne, Illusie and Raynaud proved that it remains true under some mild (liftability and dimension) conditions. It has then been generalized in two directions: (1) Esnault and Viehweg allowed the line bundle to be somewhat less than ample and (2) Illusie covered the case with some nontrivial coefficients. We prove a common generalization of the two, which then yields a vanishing theorem of Kollár type.
   
Statistical Mechanics Seminar
Topic: From microscopic hamiltonian dynamics to heat equation
Presenter: Stefano Olla, Universite Paris-Dauphine
Date:  Wednesday, October 20, 2010, Time: 2:00 p.m., Location: Jadwin Hall 343
Abstract: One of the main problems in non-equilibrium statistical mechanics is to derive, by space-time rescaling, macroscopic irreversible diffusive evolution for the co nserved quantities of an (large) hamiltonian system. I will describe the mathematical setup of the problem, and some recent progress when the hamiltonian dynamics is perturbed by energy conserving stochastic collisions.
   
Department Colloquium
Topic: Rearrangement and convection
Presenter: Yann Brenier, University of Nice Sophia Antipolis
Date:  Wednesday, October 20, 2010, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Rearrangement theory is about reorganizing a given function (or map) in some specific order (monotonicity, cycle monotonicity etc...). This is somewhat similar to the convection phenomenon in fluid mechanics, where fluid parcels are continuously reorganized in a stabler way (heavy fluid at bottom and light fluid at top). Convection theory is one of the most important piece of geo-sciences, related to weather forecasting, oceanography, volcanism, earthquake etc... In our talk, we make these analogies more precise by analyzing the Navier-Stokes equations with buoyancy and Coriolis forces. We will see how these approximations are related to the concept, well known in optimal transport theory, of rearrangement of maps as gradient of convex functions.
   
Symplectic Geometry Seminar
Topic: Schrodinger equation, deformation theory and tt^* geometry
Presenter: Huijun Fan, Beijing University
Date:  Thursday, October 21, 2010, Time: 1:30 p.m., Location: Fine Hall 601
Abstract: I will talk about my recent work on the deformation theory of Schrodinger equations. This is an attempt to construct the rigorous mathematical foundation for topological B model, which has tight relation to the deformation theory of complex structure and the singularity theory.
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: From random tilings to representation theory
Presenter: Vadim Gorin, Moscow State University
Date:  Thursday, October 21, 2010, Time: 2:00 p.m., Location: Fine Hall 401
Abstract:

Lozenge tilings of planar domains provide a simple, yet sophisticated model of random surfaces. Asymptotic behavior of such models has been extensively studied in recent years.

We will start from recent results about q-distributions on tilings of a hexagon or, equivalently, on boxed plane partitions. (This part is based on the joint work with A.Borodin and E.Rains).

In the second part of the talk we will explain how representation theory of the infinite-dimensional unitary group is related to random lozenge tilings with a certain Gibbs property. We will discuss applications of this correspondence and results on the classification of Gibbs measures on tilings of the half-plane.

   
Discrete Mathematics Seminar
Topic: The size Ramsey number of a directed path
Presenter: Ido Ben-Eliezer, Tel-Aviv University
Date:  Thursday, October 21, 2010, Time: 2:15 p.m., Location: Fine Hall 224
Abstract:

Given a graph H, the size Ramsey number r_e(H,q) is the minimal number m for which there is a graph G with m edges such that every q-coloring of G contains a monochromatic copy of H. We study the size Ramsey number of the directed path of length n in oriented graphs, where no antiparallel edges are allowed. We give nearly tight bounds for every fixed number of colors. For the case of two colors we show that there are constants c_1,c_2 such that \frac{c_1 n^{2} \log n}{(\log\log n)^3} \leq r_e(P_n,2) \leq c_2 n^{2}(\log n)^2.

Joint work with Michael Krivelevich and Benny Sudakov.

   
Joint Princeton University and IAS Number Theory Seminar
Topic: Expanding the scope of Hilbert irreducibility
Presenter: Chris Hall, University of Wyoming
Date:  Thursday, October 21, 2010, Time: 4:30 p.m., Location: Fine Hall 214
Abstract:

If K is the rational function field K=Q(t), then a polynomial f in K[x] can be regarded as a one-parameter family of polynomials. If f is irreducible, then a basic form of Hilbert's irreducibility theorem states that there are infinitely many parameters in Q for which the corresponding polynomial is also irreducible. Moreover, if one exploits conjectures of Mordell and Lang (proved by Faltings) one can frequently prove stronger statements, e.g. that there are only finitely many reducible specializations where the parameter lies in a quadratic extension of Q.

In this talk we will introduce an analogous theorem for an abelian variety A/K regarded as a one-parameter family of abelian varieties. More precisely, if A is (geometrically) simple and non-isotrivial over K, we will sketch an argument which shows that there are only finitely many parameters defined over a number field of bounded degree for which the corresponding abelian variety is not simple. Faltings' theorems again play a key role, but as we will explain, recent advances in expander graphs play a significant role as well.

   
Topology Seminar
Topic: On local combinatorial formulae for Pontryagin classes
Presenter: Alexander Gaifullin, Moscow State, Steklov Institute
Date:  Thursday, October 21, 2010, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: The talk will be devoted to the problem of combinatorial computation of the rational Pontryagin classes of a triangulated manifold. This problem goes back to the famous work by A. M. Gabrielov, I. M. Gelfand, and M. V. Losik (1975). Since then several different approaches to combinatorial computation of the Pontryagin classes have been suggested. However, these approaches require a combinatorial manifold to be endowed with some additional structure such as smoothing or certain its discrete analogue. We suggest a new approach based on the concept of a universal local formula. This approach allows us to construct an explicit combinatorial formula for the first Pontryagin class that can be applied to any combinatorial manifold without any additional structure.
   
Differential Geometry and Geometric Analysis Seminar
Topic: Lower Ricci Curvature, Convexity and Applications
Presenter: Aaron Naber, MIT
Date:  Friday, October 22, 2010, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: We prove new estimates for tangent cones along minimizing geodesics in GH limits of manifolds with lower Ricci curvature bounds. We use these estimates to show convexity results for the regular set of such limits. Applications include the proofs of several conjectures dating back to the work of Cheeger/Colding and the ruling out of certain limit spaces, including the so called generalized trumpet spaces. We construct new examples which exhibit various new behaviors and show sharpness of the new theorems. This work is joint with Toby Colding.
   
Analysis Seminar ***Please note special time
Topic: Well-posedness theory for compressible Euler equations in a physical vacuum
Presenter: Juhi Jang, University of California, Riverside
Date: Monday, October 25, 2010, Time: 2:30 p.m., Location: Fine Hall 314
Abstract: An interesting problem in gas and fluid dynamics is to understand the behavior of vacuum states, namely the behavior of the system in the presence of vacuum. A particular interest is so called physical vacuum which naturally arises in physical problems. The main difficulty lies in the fact that the physical systems become degenerate along the boundary. I'll present the well-posedness result of 3D compressible Euler equations for polytropic gases. This is a joint work with Nader Masmoudi.
   
PACM Colloquium
Topic: Feedback, Lineages and Cancer
Presenter: John Lowengrub, University of California - Irvine
Date: Monday, October 25, 2010, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: A multispecies continuum model is developed to simulate the dynamics of cell lineages in solid tumors. The model accounts for spatiotemporally varying cell proliferation and death mediated by the heterogeneous distribution of oxygen and soluble chemical factors. Together, these regulate the rates of self-renewal and differentiation of the different cells within the lineages. As demonstrated in the talk, the feedback processes are found to play a critical role in tumor progression and the development of morphological instability.
   
Mathematical Physics Seminar
Topic: Trace Formulas for Large Random d-Regular Graphs
Presenter: Idan Oren, The Weizmann Institute
Date:  Tuesday, October 26, 2010, Time: 4:30 p.m., Location: Jadwin 343
Abstract: Trace formulas for d-regular graphs are derived and used to express the spectral density in terms of the periodic walks on the graphs under consideration. The trace formulas depend on a parameter (w) which can be tuned continuously to assign different weights to different periodic orbit contributions. At the special value w = 1, the only periodic orbits which contribute are the non back- scattering orbits, and the smooth part in the trace formula coincides with the Kesten-McKay expression. As (w) deviates from unity, non vanishing weights are assigned to the periodic walks with back-scatter, and the smooth part is modified in a consistent way. The trace formulas presented in this talk can be used as tools for showing the connection between the spectral properties of d-regular graphs and the theory of random matrices.
   
Statistical Mechanics Seminar
Topic: Characterization of Lee-Yang polynomials
Presenter: David Ruelle, IHES, France
Date:  Wednesday, October 27, 2010, Time: 2:00 p.m., Location: Jadwin Hall 343
Abstract: I shall give a characterization of the multi-affine polynomials in n variables that occur in the proof of the Lee-Yang Circle Theorem. In particular, it will be seen that the spin interactions for which the Circle Theorem holds at all temperatures must be the ferromagnetic pair interactions originally considered by Lee and Yang (i.e., for non-pair interactions, the theorem fails at some temperature!).
   
Joint Princeton University and IAS Number Theory Seminar
Topic: Constructing Abelian varieties over Qbar not isogenous to a Jacobian
Presenter: Jacob Tsimerman, Princeton University
Date:  Thursday, October 28, 2010, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: We discuss the following question of Nick Katz and Frans Oort: Given an Algebraically closed field K, is there an Abelian variety over K of dimension g which is not isogenous to a Jacobian? For K the complex numbers its easy to see that the answer is yes for g>3 using measure theory, but over a countable field like Qbar new methods are required. Building on work of Chai-Oort, we show that, as expected, such Abelian varieties exist for K=Qbar and g>3. We will explain the proof as well as its connection to the Andre Oort conjecture.
   
Topology Seminar
Topic: TBA
Presenter: Kei Nakamura, Temple University
Date:  Thursday, October 28, 2010, Time: 4:30 p.m., Location: Fine Hall 314
   
Ergodic Theory and Statistical Mechanics Seminar *** Please note special date and time***
Topic:

Diffusive or superdiffusive asymtotics for periodic and non-periodic Lorentz processes

Presenter: Domokos Szasz, Budapest University of Technology and Economics
Date:  Friday, October 29, 2010, Time: 3:00 p.m., Location: Fine Hall 401
Abstract: After the first success in establishing the diffusive, Brownian limit of planar, finite-horizon, periodic Lorentz processes, in 1981 Sinai turned the interest toward studying models when periodicity is hurt, in particular, to locally perturbed Lorentz processes. The 1981 solution for a random-walk-model - by Telcs and the speaker - only led in 2009 to that for the locally perturbed, finite-horizon Lorentz process (by Dolgopyat, Varju and the present author). Beside reporting on these results we also analyze the first steps in extending the limits obtained for the periodic Lorentz process to locally perturbed periodic or quasi-periodic ones (results by Nandori, Paulin, Varju and the speaker).
   
NOVEMBER 2010
   
Analysis Seminar
Topic: TBA
Presenter: Natasa Pavlovic, University of Texas at Austin
Date: Monday, November 8, 2010, Time: 4:00 p.m., Location: Fine Hall 314
   
PACM Colloquium
Topic: Novel Phenomena and Models of Active Fluids
Presenter: Michael Shelley, Courant Institute
Date: Monday, November 8, 2010, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: Fluids with suspended microstructure - complex fluids - are common actors in micro- and biofluidics applications and can have fascinating dynamical behaviors. A new area of complex fluid dynamics concerns "active fluids" which are internally driven by having dynamic microstructure such as swimming bacteria. Such motile suspensions are important to biology, and are candidate systems for tasks such as microfluidic mixing and pumping. To understand these systems, we have developed both first-principles particle and continuum kinetic models for studying the collective dynamics of hydrodynamically interacting microswimmers. The kinetic model couples together the dynamics of a Stokesian fluid with that of an evolving "active" stress field. It has a very interesting analytical and dynamical structure, and predicts critical conditions for the emergence of hydrodynamic instabilities and fluid mixing. These predictions are verified in our detailed particle simulations, and are consistent with current experimental observation.
   
Algebraic Geometry Seminar
Topic: 4-dimensional symplectic holomorphic contractions
Presenter: Marco Andreatta, Trento
Date:  Tuesday, November 9, 2010, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: In the talk I will consider birational projective morphisms from smooth holomorphic symplectic fourfolds into affine normal varieties. The ultimate goal will be to classify such maps. For the moment I can present special features of them and discuss some important examples.
   
Mathematical Physics Seminar
Topic: TBA
Presenter: Clément Hongler, Columbia University
Date:  Tuesday, November 9, 2010, Time: 4:30 p.m., Location: Jadwin 343
   
Department Colloquium
Topic: Metaphors in systolic geometry
Presenter: Larry Guth, Toronto University
Date:  Wednesday, November 10, 2010, Time: 4:30 p.m., Location: Fine Hall 314
Abstract:

The systolic inequality says that any Riemannian metric on an n-dimensional torus with volume 1 contains a non-contractible closed curve with length at most C(n) - a constant depending only on n. One remarkable feature of the inequality is it holds for such a wide class of metrics. It's much more general than an inequality that holds for all metrics obeying a certain curvature condition.

The systolic inequality is a difficult theorem, and each proof is guided by a metaphor that connects the systolic inequality to a different area of geometry or topology. In this talk, I will explain three metaphors. They connect the systolic inequality to minimal surface theory, topological dimension theory, and scalar curvature.

   
Ergodic Theory and Statistical Mechanics Seminar
Topic: TBA
Presenter: Percy Wong, Princeton University
Date:  Thursday, November 11, 2010, Time: 2:00 p.m., Location: Fine Hall 401
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: Oleg Pikhurko, Carnegie Mellon
Date:  Thursday, November 11, 2010, Time: 2:15 p.m., Location: Fine Hall 224
   
Princeton University and IAS Number Theory Seminar
Topic: Periods of special cycles and derivatives of L-series
Presenter: Shou-Wu Zhang, Columbia University
Date:  Thursday, November 11, 2010, Time: 4:30 p.m., Location: Fine Hall 214
Abstract: In this talk, I will state some conjectures and examples concerning the central derivatives of automorphic L-series in terms of heights of special cycles on Shimura varieties.
   
Topology Seminar
Topic: Transverse homology
Presenter: Lenny Ng, Duke University
Date:  Thursday, November 11, 2010, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Knot contact homology is a combinatorial Floer-theoretic knot invariant derived from Symplectic Field Theory. I'll discuss the geometry behind this invariant and a new filtered version, transverse homology, which turns out to be a fairly effective invariant of transverse knots
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Olivaine De Queiroz, Universidade Estadual De Campinas
Date:  Friday, November 12, 2010, Time: 3:00 p.m., Location: Fine Hall 314
   
PACM Colloquium
Topic: A New Formalism for Electromagnetic Scattering in Complex Geometry
Presenter: Leslie Greengard, Courant Institute
Date: Monday, November 15, 2010, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: We will describe some recent, elementary results in the theory of electromagnetic scattering in R3. There are two classical approaches that we will review - one based on the vector and scalar potential and applicable in arbitrary geometry, and one based on two scalar potentials, due to Lorenz, Debye and Mie, valid only in the exterior (or interior) of a sphere. In extending the Lorenz-Debye-Mie approach to arbitrary geometry, we have encountered some new mathematical questions involving differential geometry, partial differential equations and numerical analysis. This is joint work with Charlie Epstein.
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Tamás Szamuely, Hungarian Academy and University of Pennsylvania
Date:  Tuesday, November 16, 2010, Time: 4:30 p.m., Location: Fine Hall 322
   
Department Colloquium
Topic: Acoustical spacetime geometry and shock formation
Presenter: Demetri Christodoulou, ETH
Date:  Wednesday, November 17, 2010, Time: 4:30 p.m., Location: Fine Hall 314
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: TBA
Presenter: Percy Wong, Princeton University
Date:  Thursday, November 18, 2010, Time: 2:00 p.m., Location: Fine Hall 401
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: Noga Alon, Tel-Aviv University and IAS
Date:  Thursday, November 18, 2010, Time: 2:15 p.m., Location: Fine Hall 224
   
Topology Seminar
Topic: TBA
Presenter: Igor Rivin, Temple University
Date:  Thursday, November 18, 2010, Time: 4:30 p.m., Location: Fine Hall 314
   
Differential Geometry and Geometric Analysis Seminar
Topic: Laplace eigenvalues via asymptotic separation of variables
Presenter: Chris Judge, Indiana University
Date:  Friday, November 19, 2010, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: We study the behavior of eigenvalues under geometric perturbations using a method that might be called asymptotic separation of variables. In this method, we use quasi-mode approximations to compare the eigenvalues of a warped product and another metric that is asymptotically close to a warped product. As one application, we shoe that the generic Euclidean triangle has simple Laplace spectrum. This is joint work with Luc Hillairet.
   
Analysis Seminar
Topic: TBA
Presenter: Vincent Moncrief, Yale University
Date: Monday, November 22, 2010, Time: 4:00 p.m., Location: Fine Hall 314
   
PACM Colloquium
Topic: Wavelet Frames and Applications
Presenter: Zuowei Shen, National University of Singapore
Date: Monday, November 22, 2010, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: This talk focuses on the tight wavelet frames derived from multiresolution analysis and their applications in imaging sciences. One of the major driven forces in the area of applied and computational harmonic analysis over the last two decades is to develop and understand redundant systems that have sparse approximations of different classes of functions. Such redundant systems include wavelet frame, ridgelet, curvelet, shearlet and so on. In this talk, we will first give a brief survey on the development of the unitary extension principle and its generalizations. The unitary extension principle and its extensions give systematical constructions of wavelet frames from multiresolution analysis that can be used in various problems in imaging science. Then we will focus on applications of wavelet frames. Especially, we will discuss frame based image analysis and restorations, which includes image inpainting, image denosing, image deblurring and blind deblurring, image decomposition, and image segmentation.
   
Analysis Seminar
Topic: TBA
Presenter: Colin Guillarmou, Universite de Nice Sophia-Antipolis
Date: Monday, November 29, 2010, Time: 4:00 p.m., Location: Fine Hall 314
   
DECEMBER 2010
   
Department Colloquium
Topic: Natural maps old and new
Presenter: Gerard Besson, Grenoble
Date:  Wednesday, December 1, 2010, Time: 4:30 p.m., Location: Fine Hall 314
Abstract:

In 1995, G. Courtois, S. Gallot and myself constructed a family of maps with very good properties regarding volume elements between certain manifolds. We used it to give an alternative proof of Mostow's rigidity for rank one closed symmetric spaces as well as a rigidity result for their geodesic flow, conjectured by A. Katok. Various modifications of the original construction have been made since yielding new results in different settings. We shall describe the basic construction, the modifications, some applications and open questions.

   
Ergodic Theory and Statistical Mechanics Seminar
Topic: TBA
Presenter: Zhiren Wang , Princeton University
Date:  Thursday, December 2, 2010, Time: 2:00 p.m., Location: Fine Hall 401
   
Topology Seminar
Topic: TBA
Presenter: Sa'ar Hersonsky, University of Georgia
Date:  Thursday, December 2, 2010, Time: 4:30 p.m., Location: Fine Hall 314
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Gilles Courtois, École/ Polytechnique/
Date:  Friday, December 3, 2010, Time: 3:00 p.m., Location: Fine Hall 314
   
PACM Colloquium
Topic: Diffusions Interacting Through Their Ranks, and the Stability of Large Equity Markets
Presenter: Ioannis Karatzas, Columbia University
Date: Monday, December 6, 2010, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: We introduce and study ergodic multidimensional di usion processes interacting through their ranks. These interactions give rise to invariant measures which are in broad agreement with stability properties observed in large equity markets over long time-periods. The models we develop assign growth rates and variances that depend on both the name (identity) and the rank (according to capitalization) of each individual asset. Such models are able realistically to capture critical features of the observed stability of capital distribution over the past century, all the while being simple enough to allow for rather detailed analytical study. The methodologies used in this study touch upon the question of triple points for systems of interacting di usions; in particular, some choices of parameters may permit triple (or higher-order) collisions to occur. We show, however, that such multiple collisions have no e ect on any of the stability properties of the resulting system. This is accomplished through a detailed analysis of intersection local times. The theory we develop has connections with the analysis of Queueing Networks in heavy traffic, as well as with models of competing particle systems in Statistical Mechanics, such as the Sherrington-Kirkpatrick model for spin-glasses.
   
Princeton University and IAS Number Theory Seminar
Topic: TBA
Presenter: Benedict Gross, Harvard University
Date:  Thursday, December 9, 2010, Time: 4:30 p.m., Location: TBA
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Izzet Coskun, UIC
Date:  Tuesday, December 14, 2010, Time: 4:30 p.m., Location: Fine Hall 322
   
Joint Princeton University and IAS Number Theory Seminar
Topic: TBA
Presenter: Henryk Iwaniec, Rutgers University
Date:  Thursday, December 16, 2010, Time: 4:30 p.m., Location: TBA
   
Topology Seminar
Topic: TBA
Presenter: Andy Cotton-Clay, Harvard University
Date:  Thursday, December 16, 2010, Time: 4:30 p.m., Location: Fine Hall 314