SEMINARS
Updated: 10-6-2010

   
OCTOBER 2010
   
Statistical Mechanics Seminar
Topic: Phase transition in kinetically constrained models
Presenter: Thierry Bodineau, Ecole Normale Superieur, Paris
Date:  Wednesday, October 6, 2010, Time: 2:00 p.m., Location: Jadwin Hall 343
Abstract: Kinetically constrained models are simple lattice models of glasses with a dynamical frustration: a move can be performed only if some local constraints are satisfied, for example if the local density is low enough. These models have been introduced to explain on a purely dynamical ground the glass forming phenomenology. The local constraints give rise to collective dynamics leading to hierarchical and cooperative relaxation. An important issue is to understand the structure of the dynamical heterogeneity, i.e. the regions which are mobile (active) vs the regions which are blocked (inactive). The activity of the system measures the microscopic number of moves per unit time and it has been proposed as a relevant parameter to characterize glassiness. In the first part of the talk, we will review the rich dynamical behaviour displayed by the kinetically constrained models. In the second part, we will focus on the large deviations of the activity and show that it leads to a first order phase transition.
   
Department Colloquium
Topic: Blow-up phenomena for the Yamabe equation
Presenter: Simon Brendle, Stanford University
Date:  Wednesday, October 6, 2010, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: The Yamabe problem asserts that any Riemannian metric on a compact
manifold can be conformally deformed to one of constant scalar curvature.
However, this metric is not, in general, unique, and there are examples of
manifolds that admit many metrics of constant scalar curvature in a given
conformal class.

It was conjectured by R. Schoen in the 1980s (and, independently, by Aubin) that the set of all metrics of constant scalar curvature 1 in a given conformal class is compact, except if the underlying manifold is conformally equivalent to the sphere $S^n$ equipped with its standard metric. The significance of Schoen's conjecture is that it would imply Morse inequalities for the total scalar curvature functional.

I will discuss counterexamples to this conjecture in dimension 52 and higher. I will also describe joint work with F. Marques, which extends these counterexamples to dimension 25 and higher. The condition $n \geq 25$ turns out to be optimal.
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Shortest Curves Associated to a Degenerate Jacobi Metric on the two Torus
Presenter: John Mather, Princeton University
Date:  Thursday, October 7, 2010, Time: 2:00 p.m., Location: Fine Hall 401
Abstract: Let P be a potential on the two torus that takes its minimum value at a unique point m. Set E_0 := P(m). For a real number E, let g_E be the Jacobi metric associated to P and E. For E > E_0, g_E is a Riemannian metric. An ancient theorem of Morse and Hedlund says that a g_E-shortest curve in an indivisible homology class is simple. For E = E_0, g_E is no longer a Riemannian metric because it vanishes at m. (It is a Riemannian metric in the complement of m.) For a suitable potential P, and a suitable indivisible homology class h, a g_E_0-shortest curve in h crosses itself at m, so the theorem of Hedlund and Morse does not generalize to the case E = E_0. In this talk, I will describe examples of such shortest curves that cross themselves and give a few ideas of how to prove that each such shortest curve does not cross itself except at m and is a bouquet of simple curves in at most three homology classes.
   
Discrete Mathematics Seminar
Topic: Random Graphs and the Parity Quantifier
Presenter: Swastik Kopparty, IAS
Date:  Thursday, October 7, 2010, Time: 2:15 p.m., Location: Fine Hall 224
Abstract:

The classical zero-one law for first-order logic on random graphs says that for any first-order sentence F in the theory of graphs, the probability that the random graph G(n, p) satisfies F approaches either 0 or 1 as n grows. It is well known that this law fails to hold for properties involving parity phenomena (oddness/evenness): for certain properties, the probability that G(n, p) satisfies the property need not converge, and for others the limit may be strictly between 0 and 1.

In this talk, I will discuss the behavior of FO[parity], first order logic equipped with the parity quantifier, on random graphs. Our main result is a "modular convergence law" which precisely captures the behavior of FO[parity] properties on large random graphs.

I will give an overview of this result and its proof. Along the way, we will ask (and answer) some basic, natural questions about the distribution of subgraph counts *mod 2* in random graphs (what is the probability that G(n,p) has: an odd number of triangles? an even number of 4-cycles? an odd number of triangles and an even number of 4-cycles? etc.). Our approach is based on multivariate polynomials over finite fields, in particular, on a variation on the Gowers norm. The proof generalizes the original quantifier elimination approach to the zero-one law, and has analogies with the Razborov-Smolensky method from circuit complexity.

Joint work with Phokion Kolaitis.

   
Joint Princeton University and IAS Number Theory Seminar
Topic: An integral Eisenstein-Sczech cocycle on GL_n(Z) and p-adic L-functions of totally real fields
Presenter: Samit Dasgupta, University of California, Santa Cruz
Date:  Thursday, October 7, 2010, Time: 4:30 p.m., Location: Fine Hall 214
Abstract: In 1993, Sczech defined an n-1 cocycle on GL_n(Z) valued in a certain space of distributions. He showed that specializations of this cocyle yield the values of the partial zeta functions of totally real fields of degree n at nonpositive integers. In this talk, I will describe an integral refinement of Sczech's cocycle. By introducing a "smoothing" prime l, we define an n-1 cocycle on a congruence subgroup of GL_n(Z) valued in a space of p-adic measures. We prove that the specializations analogous to those considered by Sczech produce the p-adic L-functions of totally real fields. We also consider certain other specializations that conjecturally yield the Gross--Stark units defined over abelian extensions of these fields. This is joint work with Pierre Charollois.
   
Topology Seminar
Topic: Homology of the curve complex and the Steinberg module of the mapping class group
Presenter: Nathan Broaddus, Ohio State University
Date:  Thursday, October 7, 2010, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: The homology of the curve complex is of fundamental importance for the homology of the mapping class group. It was previously known to be an infinitely generated free abelian group, but to date, its structure as a mapping class group module has gone unexplored. I will give a resolution for the homology of the curve complex as a mapping class group module. > From the presentation coming from the last two terms of this resolution I will show that this module is cyclic and give an explicit single generator. As a corollary, this generator is a homologically nontrivial sphere in the curve complex.
   
Differential Geometry and Geometric Analysis Seminar
Topic: Regularity of absolutely minimizing Lipschitz extensions
Presenter: Charles Smart, Courant Institute
Date:  Friday, October 8, 2010, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: I will present joint work with Lawrence C. Evans on the everywhere differentiability of absolutely minimizing Lipschitz extensions.
   
Analysis Seminar
Topic: A limiting interaction energy for Ginzburg-Landau vortices
Presenter: Sylvia Serfaty, Courant Institute
Date: Monday, October 11, 2010, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: This is a joint work with Etienne Sandier where we study minimizers of the two-dimensional Ginzburg-Landau energy with applied magnetic field, between the first and second critical fields H_{c1} and H_{c2}. In that regime, minimizing configurations exhibit densely packed hexagonal vortex lattices, called Abrikosov lattices. We derive, in some asymptotic regime, a limiting interaction energy between points in the plane, W, which we prove has to be minimized by limits of energy-minimizing configurations, once blown-up at a suitable scale. Among lattice configurations the hexagonal lattice is the unique minimizer of W, thus providing a first rigorous hint at the Abrikosov lattice. I will describe briefly how W also appears in the study of the statistical mechanics of Coulomb gases/random matrices.
   
Analysis Seminar *** Please note special time ***
Topic: Charge screening in quantum crystals
Presenter: Eric Cances, Cermics, ENPC, Paris
Date: Monday, October 11, 2010, Time: 5:00 p.m., Location: Fine Hall 314
Abstract: Density Functional Theory (DFT) has become a major tool in chemistry, materials science, molecular biology and nanotechnology. It is also an inexhaustible source of exciting mathematical and numerical issues. In this talk, I will present some of the variational models derived from DFT, and discuss their mathematical properties. I will focus in particular on the modeling of crystals with local defects. I will show that local defects are always neutral in the Thomas-Fermi-von Weis?cker (TFW) theory of crystals. In this respect, all crystals therefore behave as metals. The situation is more complex for the Hartree model, which is able to describe not only metals, but also insulators and semi-conductors. In the latter cases, two different values for the charge of a local defect are obtained, depending on the viewpoint adopted. The first value corresponds to the bare charge, the second one to the screened (or renormalized) charge. The fact that these two values differ is a consequence of the long-range of the Coulomb potential.
   
PACM Colloquium
Topic: Extrapolation Models
Presenter: David Levin, Tel Aviv University
Date: Monday, October 11, 2010, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: http://www.math.princeton.edu/~seminar/2010-11-sem/LevinAbstract10-11-2010.pdf
   
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
   
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.
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: TBA
Presenter: Amit Singer and Xiuyuan Cheng, Princeton University
Date:  Thursday, October 14, 2010, Time: 2:00 p.m., Location: Fine Hall 401
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: Ofer Neiman, Courant Institute, NYU
Date:  Thursday, October 14, 2010, Time: 2:15 p.m., Location: Fine Hall 224
   
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 triangle 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 $n \geq 3$
   
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

   
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.
   
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: TBA
Presenter: Aaron Naber, MIT
Date:  Friday, October 22, 2010, Time: 3:00 p.m., Location: Fine Hall 314
   
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: TBA
Presenter: John Lowengrub, University of California - Irvine
Date: Monday, October 25, 2010, Time: 4:00 p.m., Location: Fine Hall 214
   
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 ***Please note special time ***
Topic: Constructing Abelian varieties over Qbar not isogenous to a Jacobian
Presenter: Jacob Tsimerman, Princeton University
Date:  Thursday, October 28, 2010, Time: 2:15 p.m., Location: IAS S-101
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: TBA
Presenter: Marco Andreatta, Trento
Date:  Tuesday, November 9, 2010, Time: 4:30 p.m., Location: Fine Hall 322
   
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: TBA
Presenter: Shou-Wu Zhang, Columbia University
Date:  Thursday, November 11, 2010, Time: 4:30 p.m., Location: Fine Hall 214
   
Topology Seminar
Topic: TBA
Presenter: Lenny Ng, Duke University
Date:  Thursday, November 11, 2010, Time: 4:30 p.m., Location: Fine Hall 314
   
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
   
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
   
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
   
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