SEMINARS
Updated: 4-26-2006
 
APRIL 26 - 28, 2006
   
Number Theory Seminar
Topic: Identities in theta correspondence
Presenter: Zhengyu Mao, Rutgers at Newark
Date:  Wednesday, April 26, 2006, Time: 2:00 p.m., Location: Fine Hall 314
Abstract: I will describe some identities of  linear forms and distributions attached to representations in theta correspondence. These identities can be used to prove formula of special values of L-functions.
   
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: Coarse geometry of mapping class groups
Presenter: Yair Minsky, Yale University
Date:  Wednesday, April 26, 2006, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: The mapping class group of a compact surface can be studied from the point of view of geometric group theory, in which coarse or large-scale properties of its Cayley graph can be related to algebraic properties of the group.  I will give a partial picture of this coarse geometry, including a distance formula, a description of some quasi-isometrically embedded subgroups, and a solution of the Brock-Farb rank conjecture. This represents joint work with Masur and with Behrstock.
   
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.
   
PACM Seminar - Distinguished Lecture Series
Topic: Quantum Computers: How physics experiments might solve mathematical problems
Presenter: Peter Shor, Mathematics, Massachusetts Institute of Technology
Date:  Thursday, April 27, 2006, Time: 8:00 p.m., Location: A02 McDonnell Hall
Abstract: Quantum computers are hypothetical devices which use the principles of quantum mechanics to perform computations. For some difficult computational problems, including the cryptographically important problems of prime factorization and finding discrete logarithms, the best algorithms known for classical computers are exponentially slower than the algorithms known for quantum computers. Although they have not yet been built, quantum computers do not appear to violate any fundamental principles of physics. I will explain how quantum mechanics provides this extra computational power. One of the main difficulties in building quantum computers is in manipulating coherent quantum states without introducing errors or losing coherence. This problem can be alleviated by the use of quantum error correcting codes; if a quantum computer can be built with only moderately reliable hardware, then software can be used to make it extremely reliable. I will discuss these results as well.
   
Geometric Analysis Seminar
Topic: Classification of extremal metrics on geometrically ruled surfaces
Presenter: Christina W. Tonnessen-Friedman, Union College
Date:  Friday, April 28, 2006, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: This talk will cover some recent results from joint work with V. Apostolov, D. Calderbank, and P. Gauduchon on extremal K\"ahler metrics on so-called admissible projective bundles. Since it is an excellent motivator and simplifies the presentation significantly, I will focus on the case of a geometrically ruled complex surface, where we now have complete answers to some long-standing questions.
   
MAY 1 - 5, 2006
 
PACM Seminar
Topic: Rare events in complex systems: How to determine their transition pathways and rate?
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
Abstract: The dynamical behavior of many systems arising in physics, chemistry, biology, etc. is dominated by rare but important transition events between long lived states. Important examples include nucleation events during phase transition, conformational changes of macromolecules, or chemical reactions. Understanding the mechanism and computing the rate of these transitions is a topic that has attracted a lot of attention for many years. In this talk, I will discuss the theoretical background and algorithmic details of the finite-temperature string method, which gives a firm theoretical background to the concept of reaction coordinate to describe these transitions, and allows to determine their pathways and rate. The string method will be illustrated via several examples.
   
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.
   
Analysis Seminar
Topic: Hyperbolicity and the stability of the Hamilton system
Presenter: Antonio Bove, University of Bologna
Date:  Thursday, May 4, 2006, Time: 4:00 p.m., Location: Fine Hall 322
Abstract: We prove that the Cauchy Problem for a class of hyperbolic operators with double characteristics and whose simple null bicharacteristics have limit points on the set of double points is not well-posed in the $ C^{\infty} $ category, even though the usual Ivrii-Petkov conditions on the lower order terms are satisfied. According to the standard linear algebra classification these operators, at a double point, have fundamental matrices exhibiting a Jordan block of size 4.
   
Geometric Analysis Seminar
Topic: Bergman kernels, Bergman metrics and Monge-Ampere geodesics
Presenter: Steve Zelditch, Johns Hopkins University
Date:  Friday, May 5, 2006, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: The space of Hermitian metrics of positive curvature on a positive holomorphic line bundle $L \to M$ is an infinite dimensional symmetric space whose geodesics are defined by a Monge-Ampere equation (Mabuchi, Semmes, Donaldson).  Each hermitian metric may be approximated by Bergman metrics of high  level k, i.e. metrics induced by holomorphic embeddings in projective space by sections of L^k (Tian-Yau-Z expansion). Recently, Phong-Sturm have raised the question of how well  the geodesics in the space B_k of Bergman metrics of level k approximate the Monge-Ampere geodesics. My talk is about  joint work in progress with Jian Song, in which we show that on a toric variety, the Bergman geodesics approach the Monge Ampere geodesics in certain norms.
   
Geometric Analysis Seminar ***Please note special time
Topic: Blowup analysis for the Yamabe equation in high dimensions
Presenter: Fernando Marques, Stanford University
Date:  Friday, May 5, 2006, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: In this talk we will address the problem of analyzing the blow-up behavior of a sequence of solutions to the Yamabe equation in high dimensions. We will show how sharp pointwise estimates can be used to prove that the Weyl tensor vanishes up to order $[\frac{n-6}{2}]$ at a blowup point. This gives a proof of the compactness of the set of solutions to the Yamabe problem, a result conjectured by R. Schoen around 15 years ago. This is joint work with Marcus Khuri and Richard Schoen.
   
MAY 8 - 12, 2006
   
Analysis Seminar *** Please note special day and location
Topic: The local equivalence problem and symmetries of Levi degenerate
hypersurfaces
Presenter: Martin Kolar, Masaryk University Brno
Date:  Monday, May 8, 2006, Time: 4:00 p.m., Location: Fine Hall 314
   
MAY 15- 19, 2006
   
Operation Research and Financial Engineering Seminar
Topic: Dynamic risk measures
Presenter: Pauline Barrieu, London School of Economics and Political Science
Date:  Tuesday, May 16, 2006, Time: 4:30 p.m., Location: Room E-219, Engineering Quad
Abstract: We develop a methodology to optimally design financial instruments, written on a non-tradeable underlying risk. The idea is to minimize the risk of the issuer under the participation constraint imposed by the buyer. The problem is reduced to a unique inf-convolution problem involving a transformation of the initial convex risk measures of the agents. Introducing dynamic risk measures defined through their local specifications using Backward Stochastic Differential Equations (BSDEs) enables to achieve some tractability in the risk assessment criterion, but also to solve this inf-convolution problem and obtain an explicit characterization of the optimal transfer in general situations.