SEMINARS
Updated: 4-12-2006
 
APRIL 12 - 14, 2006
 
Number Theory Seminar
Topic: Singular moduli
Presenter: Stephen Kudla, Institute for Advanced Study
Date:  Wednesday, April 12, 2006, Time: 2:00 p.m., Location: Fine Hall 314
Abstract: In this lecture, I will describe some results from the thesis of Jarad Schofer, (Maryland, 2005), which provide a generalization of the Gross-Zagier factorization of singular moduli for arbitrary Borcherds forms. After a review of the construction of Borcherds forms in an adelic setting and their general properties, I will explain how the factorization formula can be obtained by applying a seesaw identity, the Siegel-Weil formula, Maass operators and a Stokes theorem calculation.
   
Discrete Mathematics Seminar
Topic: Laplacians, domination numbers, and hypergraph matching
Presenter: Roy Meshulam, Technion and IAS
Date:  Wednesday, April 12, 2006, Time: 2:15 p.m., Location: Fine 224
Abstract: See http://www.math.princeton.edu/~bsudakov/meshulam2005-2006.pdf
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: Alina Marian, Yale University
Date:  Wednesday, April 12, 2006, Time: 3:00 p.m., Location: Fine Hall 214
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Critical exponents for dynamical systems
Presenter: Omri Sarig, Pennsylvania State University
Date:  Thursday, April 13, 2006, Time: 2:00 p.m., Location: Fine Hall 322
Abstract: In statistical physics, high-order phase transitions are often
accompanied by a power law singularity for the free energy (the exponent in this law is the "critical exponent" mentioned in the title). In the theory of dynamical systems free energy is replaced by an object called "topological pressure". I will describe dynamical and stochastic implications of a power law singularity for the topological pressure in the context of (one-dimensional) countable Markov shifts. As in the physical analogue, these include breakdown of the central limit theorem and infinite correlation length for the equilibrium measure of the critical parameter.
   
Topology Seminar
Topic: Geometry of Heegaard Splittings
Presenter: Juan Souto, University of Chicago
Date:  Thursday, April 13, 2006, Time: 4:30 p.m., Location: Fine Hall 314
   
Analysis Seminar ***Please note special date, time, and location
Topic: Red shift and radiation on black hole space-times
Presenter: Igor Rodnianski, Princeton University
Date:  Friday, April 14, 2006, Time: 2:00 p.m., Location: Fine Hall 601
   
Geometric Analysis Seminar
Topic: Negative point mass singularities in general relativity
Presenter: Hubert Bray, Duke University
Date:  Friday, April 14, 2006, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: In this talk we will discuss a geometric inequality which is in the same spirit as the Positive Mass Theorem and the Penrose Inequality for black holes.  Whereas the cases of equality of these first two theorems are respectively Minkowski space (which can be thought of as Schwarzschild with zero mass) and the Schwarzschild spacetime with positive mass, the case of equality for the inequality we will discuss is the Schwarzschild spacetime with negative mass.

Physically speaking, when positive amounts of energy are concentrated as much as possible, black holes results.  However, when negative amounts of energy are "concentrated" as much as possible, it is in fact possible to form point singularities in each spacelike slice (which form a timelike curve of singularities in the spacetime).

As usual we will focus on maximal, spacelike slices of spacetimes as a first step.  The assumption of nonnegative energy density on these slices implies that these Riemannian 3-manifolds have nonnegative scalar curvature. However, we will allow these 3-manifolds to have singularities which contribute negatively to the total mass.  The standard example is the negative Schwarzschild metric on R3 minus a ball of radius m/2, (1 - m/2r)4 \delta_{ij}.  This metric (which has total mass -m) has zero scalar curvature everywhere but has a singularity at r = m/2.  We will propose a definition for the mass of a singularity, and prove a sharp lower bound on the ADM mass in terms of the masses of the singularities in the 3-manifold.
   
 
APRIL 17 - 21, 2006
 
Special Analysis Seminar ***Please note special date, time, and location
Topic: Lacunary summability, analytic continuation, and universal approximation
Presenter: Tatevik L. Gharibyan, Armenian National Academy of Sciences
Date:  Monday, April 17, 2006, Time: 3:00 p.m., Location: Fine Hall 314
   
PACM Seminar
Topic: Turbulence and Large-scale Circulation in the Ocean and Atmosphere
Presenter: Geoff Vallis, Geosciences / Atmospheric & Oceanic Sciences, Princeton University
Date:  Monday, April 17, 2006, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: The large-scale circulation is not only affected but is essentially effected by turbulent flows. This turbulence is not the small-scale turbulence that is (unfortunately) sometimes connoted by the word turbulence, but is turbulence up to the scale of the large-scale flow itself. This is largely two-dimensional, so-called geostrophic turbulence. We will discuss what is known and what is unknown about such flow, the problems of both simulating it and of understanding it, and whether these two are the same.
   
Graduate Student Seminar
Topic: Discriminant Varieties
Presenter: Lanie Wood, Princeton University
Date:  Tuesday, April 18, 2006, Time: 12:30 p.m., Location: Fine 224
Abstract: Given two curves in the plane, for example, $ax^2y+bx^3y^8 +cx^7=0$ and $exy+fy^9+gx^7y^7=0$ (where $a,b,c,e,f,g$ are coefficients), when do they have a multiple common intersection? This is a condition on $a,b,c,e,f,g$, which defines some variety in 6-dimensional space. What does this variety look like? Another question: Given a continuously varying family of varieties, we might wish to understand which varieties in the family are singular. If, for example, the varieties are defined by the parameters $a, b$, and $c$, we ask for the condition on $a, b$, and $c$ for them to define a singular variety. This condition is a variety (called an $A$-discriminant) in the parameter space--what does it look like? Varieties which are $A$-discriminants (for some family of varieties) turn up in all sorts of places, and include all the classical discriminants and resultants, as well as the first example of this abstract. We can understand $A$-discriminants well when they are smooth varieties, but some in some natural and interesting cases (like the first one given above!) the $A$-discriminant varieties are singular and it seems hard to say much at all about the variety! I will present a simple and combinatorial conjecture for the degree of the variety in the first case given above.
   
Geometric Analysis Seminar ***Please note special time, date, and location
Topic: Evolution of minimal tori in Riemannian manifolds
Presenter: Weiyue Ding, Beijing University
Date:  Tuesday, April 18, 2006, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: In a joint work with Jiayu Li, Qingyue Liu, we propose to study the existence of minimal surfaces of gengus p>=1 in Riemannian manifolds using a L^2 gradient flow of the energy E(u, g), where g denotes conformal structures in the Teichmuller space T_p. The problem is much simpler when p=1, i.e. the surfaces are tori. In this case, we obtain results on the solvability of the Cauchy problem, blow-up of the map u(t) and degeneration of the conformal structure g(t), energy identities when blow-up or degeneration occurs, and convergence at time infinity, etc.
   
Mathematical Physics Seminar
Topic: TBA
Presenter: Y. Peres, University of California, Berkeley
Date:  Tuesday, April 18, 2006, Time: 4:30 p.m., Location: Jadwin 343
 
Discrete Mathematics Seminar
Topic: Shannon capacity and privileged users
Presenter: Noga Alon, Tel Aviv University and IAS
Date:  Wednesday, April 19, 2006, Time: 2:15 p.m., Location: Fine 224
Abstract: See http://www.math.princeton.edu/~bsudakov/alon2005-2006.pdf
   
Special Seminar
Topic: Huygens' principle and hyperplane configurations
Presenter: A.P. Veselov, Loughborough, UK
Date:  Wednesday, April 19, 2006, Time: 2:15 p.m., Location: Fine Hall 314
Abstract: Huygens' principle (in the narrow Hadamard's sense) for a second-order hyperbolic equation means that its fundamental solution is located on the characteristic conoid. Physically this implies that a localised disturbance will have an effect localised in time at any point. This remarkable property holds in particular for the wave equations in the Euclidean spaces of odd dimension starting from 3. The description of the hyperbolic equations satisfying Huygens' principle is known as Hadamard's problem, which still remains largely open. The development of the theory of quantum integrable systems in the last two decades led to a substantial progress in this old problem, which turned out to be closely related to a new special class of hyperplane configurations, generalizing the Coxeter arrangements. I will discuss what is currently known about these configurations and some related geometric structures, appeared in the theory of Frobenius manifolds and WDVV equation.
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: Martijn Wijnholt, Princeton University
Date:  Wednesday, April 19, 2006, Time: 3:00 p.m., Location: Fine Hall 214
   
Department Colloquium
Topic: Point Processes, Repulsion, and Fair Allocation
Presenter: Yuval Peres, University of California, Berkeley
Date:  Wednesday, April 19, 2006, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: A random collection of points in space is called a "point
process". Recently, there has been increasing interest in processes that exhibit "repulsion", such as zeros of random polynomials, noncolliding particles and Eigenvalues of random matrices. I will describe the class of determinantal point processes, which exhibit perfect repulsion, and discuss the dynamical meaning of repulsion, see the movie at http://stat-www.berkeley.edu/~peres/GAF/dynamics/dynamics.html .
  In the second part of the talk, based on joint work with C. Hoffman and A. Holroyd, I will discuss the problem of "fair allocation": allocating the same area to every point of an isometry-invariant point process. Given such a point process M in the plane, the Voronoi tesselation assigns a polygon (of different area) to each point of M.  Fair allocations, see   http://stat-www.berkeley.edu/~peres/stable/stable.html have a richer
geometry. For any Isometry-invariant point process, we show that there is a unique fair allocation that is "stable" in the sense of the Gale-Shapley stable marriage problem.  It turns out that repelling point processes have allocations that are better localized than the Poisson process.
 
Algebraic Topology Seminar
Topic: Homotopy groups of toric spaces
Presenter: Martin Bendersky, CUNY
Date:  Thursday, April 20, 2006, Time: 3:00 p.m., Location: Fine Hall 401
Abstract: I will lecture on the work of David Allen.   Unstable spectral sequences will be used to determine the homotopy groups of some toric spaces through a range.
   
Analysis Seminar
Topic: Weak-strong uniqueness for the Navier-Stokes equation
Presenter: Pierre Germain, Ecole Polytechnique, Palaiseau
Date:  Thursday, April 20, 2006, Time: 4:00 p.m., Location: Fine Hall 322
Abstract: There exist classes of strong solutions of the Navier-Stokes equation such that: if a weak solution belongs to them, it is unique. We say then that weak-strong uniqueness holds. Serrin criterion is the first example of such a result. We will discuss new results which generalize Serrin criterion.
   
Algebraic Geometry Seminar *** Please note special date and location
Topic: TBA
Presenter: Fedor Bogomolov, New York University
Date:  Thursday, April 20, 2006, Time: 4:30 p.m., Location: Fine 314
   
Topology Seminar
Topic: Mom Technology and Low-Volume Hyperbolic 3- Manifolds
Presenter: Robert Meyerhoff, IAS and Boston College
Date:  Thursday, April 20, 2006, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: In the late 1970's, W. Thurston proved that the set of volumes of complete hyperbolic 3-manifolds (of finite volume) is well-ordered and of order type omega^omega. In particular, there is a smallest volume v(1), a second smallest volume v(2), and so on; and that this sequence v(1) < v(2) < v(3) < ... has a limit point v(omega) which is the smallest volume of a one-cusped hyperbolic 3-manifold. And so on after that.  D. Gabai, P. Milley, and I have developed a new method, the "Mom technology," which holds considerable promise for finding a reasonable collection of parent manifolds from which the low-volume manifolds can be obtained by hyperbolic Dehn surgery.
   
Geometric Analysis Seminar
Topic: TBA
Presenter: Mu-Tao Wang, Columbia University
Date:  Friday, April 21, 2006, Time: 3:00 p.m., Location: Fine Hall 314
 
APRIL 24 - 28, 2006
 
PACM Seminar
Topic: Coherence in stochastic dynamical systems
Presenter: Lee Deville, Courant Institute of Mathematical Sciences, New York University
Date:  Monday, April 24, 2006, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: It is known that random perturbations to dynamical systems can be small and irrelevant, or, alternately, so large as to overwhelm the dynamics. More interesting are cases where small random perturbations introduce qualitative changes in a system without introducing significant randomness. In effect, these are generating noise-induced, yet coherent, dynamics. We will show that this phenomenon is present in a large class of dynamical systems and describe several examples in detail. The examples will include stochastically-forced ODEs and PDEs, and Markov chains.
   
Algebraic Topology Seminar ***Please note special date and location
Topic: A Quillen Stratification for Hochschild Cohomology of Blocks
Presenter: Jonathan Pakianathan, University of Rochester
Date:  Tuesday, April 25, 2006, Time: 3:00 p.m., Location: Fine Hall 401
Abstract: (This talk is based on joint work with Sarah Witherspoon.) Let G be a finite group and k an algebraically closed field of characteristic p, then kG can be decomposed into indecomposable ideal direct summands called blocks which are very important in understanding the modular representations of the group G. The Hochschild cohomology of kG and of these blocks is one of the tools that is commonly used to study their structure. The Hochschild cohomology HH^*(kG) also comes up in topology as additively (but not as a ring!) it is isomorphic to H^*(LBG), where LBG is the free loop space of BG. In this talk I will discuss how one can stratify the spectrum of the Hochchild cohomology rings HH^*(kG) and HH^*(B) using a method analogous to that used by Quillen to stratify the spectru of the normal cohomology ring H^*(G,k). We will see that the spectrum is determined by the poset of elementary abelian p-subgroups of G together with the Alperin-Broue correspondence of blocks. In particular we will prove that the spectrum of the Hochschild cohomology of the principal block of a finite group is always homeomorphic to the spectrum of the k-algebra H^*(G;k), even though the rings in general are not isomorphic.
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Martin Olsson, U. Texas
Date:  Tuesday, April 25, 2006, Time: 4:30 p.m., Location: Fine Hall 322
   
Mathematical Physics Seminar
Topic: TBA
Presenter: Peter Hislop, University of Kentucky
Date:  Tuesday, April 25, 2006, Time: 4:30 p.m., Location: Jadwin 343
 
Algebraic Topology Seminar ***Please note special date and location
Topic: Stable Homology of Aut(F_n)
Presenter: Soren Galatius, Stanford University
Date:  Wednesday, April 26, 2006, Time: 3:00 p.m., Location: Fine Hall 801
Abstract: Let Aut(F_n) denote the automorphism group of a free group on n generators.  It is known that H_k(Aut(F_n)) is independent of n as long as n >> k.  There is a natural homomorphism from the symmetric group S_n to Aut(F_n), I will sketch a proof that it induces an isomorphism from H_k(S_n) to H_k(Aut(F_n)) for n >> k.  An important point of view here is that BAut(F_n) can be thought of as a moduli space of metric graphs, i.e. graphs equipped with metrics, considered up to isometry.
   
Department Colloquium
Topic: TBA
Presenter: Yair Minsky, Yale University
Date:  Wednesday, April 26, 2006, Time: 4:30 p.m., Location: Fine Hall 314
 
Ergodic Theory and Statistical Mechanics Seminar
Topic: Geometric Coincidence Conjecture for Pisot Substitutions
Presenter: Jaroslaw Kwapisz, Montana State University
Date:  Thursday, April 27, 2006, Time: 2:00 p.m., Location: Fine Hall 322
Abstract: The talk will focus on the central conjecture in the theory of Pisot substitutions (i.e. substitutions over a finite alphabet with the spectral   radius of the abelianization that is a P.V. number) asserting that the translation   action on the tiling spaces (or substitutive systems) of unimodular Pisot   substitutions has pure discrete spectrum.  I will identify the discrete spectrum,   recast the conjecture as a problem about injectivity of a natural geometric   realization map, and further boil it down to an algorithmically verifiable   Geometric Coincidence Condition (GCC). I will indicate how the GCC can be   verified for some families of substitutions (including a broad class of beta shifts).
   
Algebraic Topology Seminar
Topic: Moduli Space of Nodal curves and Homotopy Theory
Presenter: Soren Galatius, Stanford University
Date:  Thursday, April 27, 2006, Time: 3:00 p.m., Location: Fine Hall 401
Abstract: Riemann's moduli space M_g classifies isomorphism classes of genus g Riemann surfaces (or algebraic curves). M_g is a non-compact algebraic variety and has a natural compactification due to Deligne, Mumford and Knudsen. A point in the compactification is an isomorphism class of a nodal curve, ie. a Riemann surface with a certain mild kind of singularities. Madsen and Weiss' proof of Mumford's conjecture tells much about M_g. I will describe an attempt to understand the compactification from a similar point of view. This is joint work with Y. Eliashberg.
   
Analysis Seminar
Topic: Optimal transportation and Ricci curvature for metric measure spaces
Presenter: Karl-Theodor Sturm, University of Bonn
Date:  Thursday, April 27, 2006, Time: 4:00 p.m., Location: Fine Hall 322
Abstract: We introduce and analyze generalized Ricci curvature bounds for
metric measure spaces (M,d,m), based on convexity properties of the relative entropy Ent(. | m). For Riemannian manifolds, Curv(M,d,m) \ge K if and only if Ric_M\ge K on M. For the Wiener space, Curv(M,d,m)=1. One of the main results is that these lower curvature bounds are stable under (e.g. measured Gromov-Hausdorff) convergence. Moreover, we introduce a curvature-dimension condition CD(K,N) being more restrictive than the curvature bound Curv(M,d,m)\ge K. For Riemannian manifolds, CD(K,N) is equivalent to Ric_M(\xi,\xi)\ge K\cdot |\xi|^2 and dim}(M)\le N. Condition CD(K,N) implies sharp version of the Brunn-Minkowski inequality, of the Bishop-Gromov volume comparison theorem and of the Bonnet-Myers theorem. Moreover, it allows to construct canonical Dirichlet forms with {Gaussian upper and lower bounds} for the corresponding heat kernels.
   
Topology Seminar
Topic: Contact structures, Giroux torsion  and contact invariants
Presenter: Andras Stipsicz, Renyi Institute of Mathematics
Date:  Thursday, April 27, 2006, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Contact structures with positive Giroux torsion are expected to behave quite differently than the ones with vanishing torsion. For example it is conjectured that the positivity of the Giroux torsion of a contact structure is an obstruction for fillability. We give some evidence for this conjecture through verifying a vanishing result for the contact Ozsvath-Szabo invariants of contact structures with large enough torsion on certain 3-manifolds.
   
Geometric Analysis Seminar
Topic: TBA
Presenter: Christina W. Tonnessen-Friedman, Union College
Date:  Friday, April 28, 2006, Time: 3:00 p.m., Location: Fine Hall 314
 
MAY 1 - 5, 2006
 
PACM Seminar
Topic: TBA
Presenter: Eric Vanden-Eijnden, Courant Institute of Mathematical Sciences, New York University
Date:  Monday, May 1, 2006, Time: 4:00 p.m., Location: Fine Hall 214
   
Algebraic Geometry Seminar
Topic: Filtrations on cohomology arising from geometry
Presenter: Mark Andrea de Cataldo, Stony Brook, State University of New York
Date:  Tuesday, May 2, 2006, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: I will report on work in progress with Luca Migliorini at Bologna. Given a map of complex algebraic varieties, the Leray spectral sequence and the perverse Leray spectral sequence induce filtrations on the (intersection) cohomology (with compact supports) of the domain. We describe these filtrations geometrically in terms of hyperplane sections and deduce various new Hodge-theoretic consequences for the homology of complex varieties. A very interesting precursor of this new point of view, concerning the Leray spectral sequence for cohomology, is due to Donu Arapura.
   
Operation Research and Financial Engineering Seminar
Topic: Climate Risk, Securitization, and Equilibrium Bond Pricing
Presenter: Ulrich Horst, University of BC Vancouver
Date:  Tuesday, May 2, 2006, Time: 4:30 p.m., Location: Friend Center Bowl 008
Abstract: We propose a method of pricing financial securities written on non-tradable underlyings such as temperature or precipitation levels. To this end, we analyze a financial market where agents are exposed to financial and non-financial risk factors. The agents hedge their financial risk in the stock market and trade a risk bond issued by an insurance company. From the issuer's point of view the bond's primary purpose is to shift insurance risks related to non-catastrophic weather events to financial markets. As such its terminal payoff and yield curve depend on an underlying climate or temperature process whose dynamics is independent of the randomness driving stock prices. We prove that if the bond's payoff function is monotone in the external risk process, it can be priced by an equilibrium approach. The equilibrium market price of climate risk and the equilibrium price process are characterized as solution of non-linear backward stochastic differential equations. Transferring the BSDEs into PDEs, we represent the bond prices as smooth functions of the underlying risk factors. The talk is based on joint work with Matthias Muller.
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: Alexander Braverman, Brown University
Date:  Wednesday, May 3, 2006, Time: 3:00 p.m., Location: Fine Hall 214
   
Department Colloquium
Topic: Asymptotics for prime specialization over finite fields
Presenter: Brian Conrad, University of Michigan
Date:  Wednesday, May 3, 2006, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: It is a classical and extremely difficult problem to prove theorems about prime values of irreducible polynomials over the integers. For example, it is still not known if there are infinitely many primes of the form n2 + 1. There is a long history of analogies between the integers and polynomials (in one variable) over a finite field, and so one can formulate an analogous problem in this other setting. It was discovered several years ago (joint work with K. Conrad and R. Gross) that there are some surprises. We illustrate the unexpected behavior by means of some explicit examples, and discuss theorems that predict these phenomena.  The main goal of the talk is to motivate (by examples) and (briefly!) discuss the proofs of recent asymptotic results as the finite field and polynomial being specialized are allowed to vary; these asymptotics accord well with a general philosophy of Katz concerning limiting behavior over large finite fields and behavior over number fields. The case of characteristic 2 is not suitable for a general audience, but anyone interested can ask me about it at the colloquium dinner.
   
Geometric Analysis Seminar
Topic: TBA
Presenter: Steve Zelditch, Johns Hopkins University
Date:  Friday, May 5, 2006, Time: 3:00 p.m., Location: Fine Hall 314
   
Geometric Analysis Seminar ***Please note special time
Topic: TBA
Presenter: Fernando Marques, Stanford University
Date:  Friday, May 5, 2006, Time: 4:00 p.m., Location: Fine Hall 314
   
MAY 8 - 12, 2006
   
Operation Research and Financial Engineering Seminar
Topic: TBA
Presenter: Jan Vecer, Columbia University
Date:  Tuesday, May 9, 2006, Time: 4:30 p.m., Location: Room E-219, Engineering Quad
   
MAY 15- 19, 2006
   
Operation Research and Financial Engineering Seminar
Topic: TBA
Presenter: Pauline Barrieu
Date:  Tuesday, May 16, 2006, Time: 4:30 p.m., Location: Room E-219, Engineering Quad