SEMINARS
Updated: 11-15-2006
   
NOVEMBER 2006
   
Sato-Tate Seminar
Topic: Monodromy of the Dwork family Part II
Presenter: Nicholas Katz, Princeton University
Date:  Wednesday, November 15, 2006, Time: 1:30 p.m., Location: Fine 314
   
Geometry, Representation Theory, and Moduli Seminar
Topic: Quantum cohomology of Hilbert scheme of points of A_n resolutions
Presenter: Alexei Oblomkov, Princeton University
Date:  Wednesday, November 15, 2006, Time: 3:00 p.m., Location: Fine 214
Abstract: The generator of the ring of the equivariant quantum cohomology of the Hilbert scheme of points of complex plane was computed by A. Okounkov and R. Pandharipande. The construction uses the fact that the complex plane is toric and symplectic. Another surface which has the last two properties is the resolution of the A_{n-1} singularity. This case is treated in the joint work with D. Maulik. In my talk I will discuss only the case of the plane and A_1.
   
Department Colloquium
Topic: Invariants of singularities in positive characteristic
Presenter: Mircea Mustaţă, University of Michigan; IAS
Date:  Wednesday, November 15, 2006, Time: 4:30 p.m., Location: Fine 314
Abstract: In characteristic zero one defines invariants of singularities using the order of vanishing along various divisors. In practice, one can compute them using a resolution of singularities. I will discuss some related invariants defined in positive characteristic. While their definition is very elementary, using the Frobenius morphism, they seem to encode subtle arithmetic information. I will discuss rationality properties of these invariants, as well as known and conjectural connections between the invariants in characteristic zero and those in characteristic p.
   
Institute for Advanced Study and Princeton University Number Theory Seminar
Topic: Intersection complex on the Baily-Borel compactification of a Siegel modular variety
Presenter: Sophie Morel, IAS and Clay Math Institute
Date:  Thursday, November 16, 2006, Time: 4:30 p.m., Location: Fine 214
Abstract: In this talk, I will explain how to compute the trace of a power of the Frobenius endomorphism on the intersection cohomology of the Baily-Borel compactification of a Siegel modular variety. The main tools are : - Kottwitz's calculation of the number of points of PEL Shimura varieties over finite fields; - a theorem of Pink about the direct image in the Baily-Borel compactification of a local system on a Shimura variety; - a new construction of the intermediate extension of a pure perverse sheaf as a weight truncation of the full direct image.
   
Topology Seminar
Topic: On triangulations of 3-manifolds
Presenter: William Jaco, IAS and Oklahoma State University
Date:  Thursday, November 16, 2006, Time: 4:30 p.m., Location: Fine 314
Abstract: We shall discuss work (mostly joint with Hyam Rubinstein) on triangulations of 3-manifolds. This includes the construction of minimal-vertex triangulations, including layered and efficient triangulations; and operations on triangulations, including crushing triangulations along normal surfaces and blow-ups of ideal triangulations. We shall also discuss triangulated Heegaard splittings and triangulated Dehn fillings. There are many, many open questions and interesting speculation on connections of these triangulations to the geometry of 3-manifolds.
   
Differential Geometry and Geometric Analysis Seminar
Topic: Determinants of Laplacians as functions on spaces of metrics
Presenter: Young-Heon Kim, University of Toronto
Date:  Friday, November 17, 2006, Time: 3:00 p.m., Location: Fine 314
Abstract: The determinant of the Laplacian is a global Riemannian invariant which is defined formally as the product of all the countably many nonzero eigenvalues of the Laplacian of the given Riemannian metric, and it gives us a continuous function on the space of Riemannian metrics. In this talk we are interested in the case of compact surfaces with boundary and will discuss the properness of the determinant function on the moduli space of hyperbolic surfaces with geodesic boundary, and on the moduli space of flat surfaces with boundary of constant geodesic curvature. We will also discuss an application to the following isospectral compactness problem: On a given compact surface with boundary, consider the set of all smooth flat metrics having the same Dirichlet Laplacian spectrum, is it compact in C^\infty topology?
   
Differential Geometry and Geometric Analysis Seminar ***Please note special time
Topic: The complex Hessian equation on compact Kaehler manifolds
Presenter: Zbigniew Blocki, IM, Krakow Poland
Date:  Friday, November 17, 2006, Time: 4:00 p.m., Location: Fine 314
Abstract: The Hessian operator is an intermediate between the Laplacian and the Monge-Ampere operator. It is a fully nonlinear elliptic operator which is a symmetric function of the eigenvalues of the Levi form. We will analyze the corresponding Dirichlet problem on compact Kaehler manifolds.
   
Analysis Seminar
Topic: TBA
Presenter: Alexander Kiselev, University of Wisconsin
Date:  Monday, November 20, 2006, Time: 4:00 p.m., Location: Fine 110
   
PACM Colloquium
Topic: Faithful recovery of vector valued functions from incomplete data. Recolorization and art restoration
Presenter: Massimo Fornasier, PACM, Princeton University
Date:  Monday, November 20, 2006, Time: 4:00 p.m., Location: Fine 214
Abstract:

On March 11, 1944, the famous Eremitani's Church in Padua (Italy) was destroyed in an Allied bombing together with the inestimable frescoes by Andrea Mantegna et al. contained in the Ovetari Chapel. In the last 60 years, several attempts have been made to restore the fresco fragments by traditional methods, but without much success. We have developed a fast, robust, and efficient pattern recognition algorithm in order to map the original position and orientation of the fragments, based on comparisons with an old gray level image of the fresco prior to the damage. This innovative technique allowed for the partial reconstruction of the frescoes. Unfortunately, the surface covered by the fragments is only 77 m^2, while the original area was of several hundreds. This means that we can currently reconstruct only a fraction (less than 8%) of this inestimable artwork. In particular the original color of the blanks is not known. This begs the question of whether it is possible to estimate mathematically the original colors of the frescoes by making use of the potential information given by the available fragments and the gray level of the pictures taken before the damage. Can one estimate how faithful such restoration is?

In this talk we retrace the development of the recovery of the frescoes as an inspiring and challenging real-life problem for the development of new mathematical methods. We introduce two models for the recovery of vector valued functions from incomplete data, with applications to the fresco recolorization problem. The models are based on the minimization of a functional which is formed by the discrepancy with respect to the data and additional regularization constraints. The latter refer to joint sparsity measures with respect to frame expansions for the first functional and functional total variation for the second. We establish the relations between these two models. As a byproduct we develop the basis of a theory of fidelity in color recovery, which is a crucial issue in art restoration.

   
Special Analysis/Geometry Seminar
Topic: Representations of surface groups
Presenter: Anna Wienhard, University of Chicago
Date:  Tuesday, November 21, 2006, Time: 3:00 p.m., Location: Fine 314
Abstract: For any homomorphism of the fundamental group of a compact connected oriented surface S (with boundary) into the isometry group of a Hermitian symmetric space we can define a numerical invariant. This invariant, called the Toledo invariant, has many interesting properties (additivity under connected sum, congruence properties with respect to rotation numbers, continuity, uniform boundedness). Most importantly, the homomorphisms on which the Toledo invariant realizes its maximal value, have striking geometric properties, e.g. they are all faithful with discrete image. In this talk we focus on this set of "maximal representations" and its relations to higher Teichmueller spaces. When the isometry group of the Hermitian symmetric space is PSL(2,R), maximal representations are precisely the holonomy representations of complete hyperbolic structures on S. We will indicate that a similar geometric interpretation should also be expected for higher Teichmueller spaces and general maximal representations.
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Mircea Mustaţă, University of Michigan; IAS
Date:  Tuesday, November 21, 2006, Time: 4:30 p.m., Location: Fine 322
   
Mathematical Physics Seminar
Topic: Mean-Field and Classical Limit of Many-body Schroedinger Dynamics for Bosons
Presenter: Sandro Graffi, Univ. of Bologna
Date:  Tuesday, November 21, 2006, Time: 4:30 p.m., Location: Jadwin 343
Abstract: A new proof of the convergence of the N-particle Schroedinger dynamics for bosons towards the dynamics generated by the Hartree equation in the mean-field limit. For a restricted class of two-body interactions, we obtain convergence estimates uniform in h- bar, up to an exponentially small remainder. For h-bar = 0, the classical dynamics in the mean-field limit is given by the Vlasov equation. (Joint work with J.Froehlich and S.Schwarz.)
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: Rados Radoicic, CUNY
Date:  Wednesday, November 22, 2006, Time: 2:15 p.m., Location: Fine 224
   
Special Analysis Seminar
Topic: TBA
Presenter: Fabrice Planchon, Paris 13
Date:  Wednesday, November 22, 2006, Time: 3:00 p.m., Location: Jadwin A07
   
Analysis Seminar
Topic: TBA
Presenter: Hongjie Dong, IAS
Date:  Monday, November 27, 2006, Time: 4:00 p.m., Location: Fine 110
   
PACM Colloquium
Topic: Inverse scattering in nuclear magnetic resonance
Presenter: Charles Epstein, Mathematics, University of Pennsylvania
Date:  Monday, November 27, 2006, Time: 4:00 p.m., Location: Fine 214
Abstract: Selective excitation is an essential ingredient of any application of nuclear magnetic resonance, e.g. MR-imaging or spectroscopy. I will explain how the problem of selective excitation of 2-level quantum systems leads directly to the classical inverse scattering problem for the 2x2 AKNS system. We discuss the analysis of the inverse scattering transform and the role of non-linearity. I then show how a viable numerical algorithm, based on the hard pulse approximation, allows for the practical and accurate solution of this problem.
   
Special Analysis Seminar
Topic: Szegö kernels on tubular domains near points of infinite type
Presenter: Alexander Nagel, University of Wisconsin, Madison
Date:  Tuesday, November 28, 2006, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: See http://www.math.princeton.edu/~seminar/2006-07-sem/NagelAbstract11-28-2006.pdf
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Brent Doran, Oxford University and IAS
Date:  Tuesday, November 28, 2006, Time: 4:30 p.m., Location: Fine 322
   
Mathematical Physics Seminar
Topic: The analytic structure of Bloch functions
Presenter: Emil Prodan, Princeton University
Date:  Tuesday, November 28, 2006, Time: 4:30 p.m., Location: Jadwin 343
Abstract: In 1959, Walter Kohn descovered that the band energies of periodic Schroedinger operators in 1 dimension have a beautiful structure when one lets the k-wavevector be complex. He found that the energies of different bands are nothing but the same function evaluated on different sheets of a certain Riemann surface. This Riemann surface is generic in 1 dimension, in the sense that its shape does not depend on the particular form of the periodic potential. The exact asymptotic behavior of most of the correlation functions can be easily computed if the Riemann surface is known. In this talk I will discuss recent results that generalize all the above to linear molecular chains in 3D. The new approach is quite different from the original one and it relies on topological arguments (plus elementary functional analysis). I will discuss the generic structure of the Riemann surface for periodic molecular chains and, if time allows, I will present some explicitly calculated surfaces and go over several applications.
   
Topology Seminar *** Please note special date
Topic: On The Homeomorphism Problem: Classification of 3-manifolds
Presenter: William Jaco, IAS
Date:  Tuesday, November 28, 2006, Time: 4:30 p.m., Location: Fine 314
Abstract: While it may not be widely known, the Thurston Geometrization Conjecture gives a theoretical proof of the Homeomorphism Problem and, consequentially, that 3-manifolds can be classified. In the announcement of G. Perelman (and subsequent work by others), the Thurston Geometrization Conjecture has been claimed to be true. We shall give the steps to an algorithm that determines if two given 3-manifolds are homeomorphic (The Homeomorphism Problem). For 3-manifolds this is equivalent to the existence of a classification. Namely, a list of 3-manifolds can be constructed so that each 3-manifold appears on the list precisely once and given a 3-manifold it can be decided where it is placed on the list (Classification of 3-manifolds).
   
Operations Research and Financial Engineering Seminar
Topic:

Dynamic asset allocation: A portfolio decomposition formula and applications

Presenter: Marcel Rindisbacher, University of Toronto
Date:  Tuesday, November 28, 2006, Time: 4:30 p.m., Location: E-219, E-Quad
Abstract: This paper establishes a new decomposition of the optimal portfolio policy in dynamic asset allocation models with arbitrary vNM preferences and Ito prices. The formula rests on a change of num\'{e}raire which consists in taking pure discount bonds as units of account. When expressed in this new num\'{e}raire the dynamic hedging demand is shown to have two components. If the individual cares solely about terminal wealth, the first hedge insures against fluctuations in a long term bond with maturity date matching the investor's horizon and face value determined by bequest preferences. The second hedge immunizes against fluctuations in future bond return volatilities and market prices of risk. When the individual also cares about intermediate consumption the first hedging component becomes a coupon-paying bond with coupon payments tailored to the consumption needs. The decomposition formula is used to examine the existence of preferred habitats, the investment behavior of extremely risk averse individuals, the demand for long term bonds, the optimal international asset allocation rule, the preference for I-bonds in inflationary environments and the integration of fixed income management and asset allocation.
   
Discrete Mathematics Seminar
Topic: Global connectivity from local conditions
Presenter: David Galvin, University of Pennsylvania
Date:  Wednesday, November 29, 2006, Time: 2:15 p.m., Location: Fine 224
  See http://www.math.princeton.edu/~bsudakov/galvin2006-fall.pdf
   
Department Colloquium
Topic: TBA
Presenter: Chris Skinner, Princeton University
Date:  Wednesday, November 29, 2006, Time: 4:30 p.m., Location: Fine 314
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: On stochastic properties of billiards and on tagged particle diffusion in the 1d Rayleigh gas
Presenter: Peter Balint, Budapest University of Technology and Economics
Date:  Thursday, November 30, 2006, Time: 2:00 p.m., Location: Fine 401
Abstract: In this talk I would like to consider stochastic phenomena arising in various classical mechanical systems. The first part of the talk is meant to give an overview on some recent progress related to ergodic and statistical properties of hyperbolic billiards (joint works with Sebastien Gouezel, Pavel Bachurin and Imre Peter Toth). The second part describes some new observations on tagged particle diffusion in the 1d Rayleigh gas (joint result with Balint Toth and Imre Peter Toth).
   
Institute for Advanced Study and Princeton University Number Theory Seminar
Topic: Sieve methods for Quantum Unique Ergodicity and general shifted sums
Presenter: Roman Holowinsky, IAS
Date:  Thursday, November 30, 2006, Time: 4:30 p.m., Location: Fine 214
Abstract: In this talk, I shall introduce a sieve method for bounding the average size of shifted convolution summation terms related to the Quantum Unique Ergodicity Conjecture for a fixed Hecke-Maass cusp form. This bound will be uniform in the spectral parameter provided that standard bounds hold for the symmetric square and symmetric fourth power L-functions at the point s=1. We shall see that the sieve method can be applied to a wide variety of shifted sums, including sums with multiple shifts.
 
Topology Seminar
Topic: TBA
Presenter: Dillan Thurston, Columbia University and Barnard College
Date:  Thursday, November 30, 2006, Time: 4:30 p.m., Location: Fine 314
   
DECEMBER 2006
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Mario Bonk, University of Michigan
Date:  Friday, December 1, 2006, Time: 3:00 p.m., Location: Fine 314
   
PACM Colloquium - Distinguished Lecture Series
Topic: Genomic Information: Biology and Medicine in the 21st Century
Presenter: Eric S. Lander, Broad Institute, Massachusetts Institute of Technology
Date:  Friday, December 1, 2006, Time: 8:00 p.m., Location:A02 McDonnell Hall
Abstract: The Human Genome Project was just an early step in a decades-long scientific program aimed at achieving a systematic and comprehensive view of biology and medicine. This program involves deep collaboration among biologists, chemists, physicians, engineers and -- importantly -- mathematicians and computer scientists. The lecture will describe current projects in genomic medicine, including comparative genomics, human genetics, cancer genetics and chemical biology. Along the way, it will highlight analytical issues that arise from the massive amounts of genomic information that are rapidly becoming available.
   
Analysis Seminar
Topic: TBA
Presenter: Natasa Pavlovic, Princeton University
Date:  Monday, December 4, 2006, Time: 4:00 p.m., Location: Fine 110
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Günter Harder, Max Planck Institut für Mathematik; IAS
Date:  Tuesday, December 5, 2006, Time: 4:30 p.m., Location: Fine 322
   
Operations Research and Financial Engineering Seminar
Topic: TBA
Presenter: Gordan Zitkovic, University of Texas
Date:  Tuesday, December 5, 2006, Time: 4:30 p.m., Location: E-219, E-Quad
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: Tom Bohman, Carnegie Mellon University
Date:  Wednesday, December 6, 2006, Time: 2:15 p.m., Location: Fine 224
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: M. Mirzakhani, Princeton University
Date:  Wednesday, December 6, 2006, Time: 3:00 p.m., Location: Fine 214
   
Department Colloquium
Topic: Blow ups of complex solutions of 3D-Navier-Stokes system and Renormalization Group Method.
Presenter: Yakov Sinai, Princeton University
Date:  Wednesday, December 6, 2006, Time: 4:30 p.m., Location: Fine 314
Abstract: In this talk I shall explain the following result of Dong Li and mine:there exists an open set in the space of 10-parameter families of initial conditions such that for each family from this set there are values of parameters such that the corresponding solution develops blow up in finite time.
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Concentration Inequalities for Dependent Random Variables via the Martingale Method
Presenter: Leonid Kontorovich, School of Computer Science, Carniegie Mellon
Date:  Thursday, December 7, 2006, Time: 2:00 p.m., Location: Fine 401
Abstract:

We use the martingale method to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the way, we obtain bounds on certain martingale differences associated with the random sequences, which may be of independent interest. As an application of our result, we also derive a concentration inequality for inhomogeneous Markov chains, and establish an extremal property associated with their martingale difference bounds. This work complements certain concentration inequalities obtained by Marton and Samson, while also providing a different proof of some known results. Paper written with Kavita Ramanan. http://arxiv.org/abs/math.PR/0609835

   
Institute for Advanced Study and Princeton University Number Theory Seminar
Topic: Periods and relative trace formulas for GL(2) in the local setting
Presenter: Brooke Feigon, IAS
Date:  Thursday, December 7, 2006, Time: 4:30 p.m., Location: Fine Hall 214
   
Topology Seminar
Topic: On the contact class in Heegaard Floer homology
Presenter: William H. Kazez, University of Georgia
Date:  Thursday, December 7, 2006, Time: 4:30 p.m., Location: Fine 314
Abstract: In joint work with Ko Honda and Gordana Matic, we present an alternate description of the Ozsv\'ath-Szab\'o contact class in Heegaard Floer homology. Using this description, we prove that if a contact structure $(M,\xi)$ has an adapted open book decomposition whose page $S$ is a once-punctured torus, then the monodromy is right-veering if and only if the contact structure is tight.
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Bruce Kleiner, Yale University
Date:  Friday, December 8, 2006, Time: 3:00 p.m., Location: Fine 314
   
Analysis Seminar
Topic: TBA
Presenter: Enno Lenzman, MIT
Date:  Monday, December 11, 2006, Time: 4:00 p.m., Location: Fine 110
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Brendan Hassett, Rice University
Date:  Tuesday, December 12, 2006, Time: 4:30 p.m., Location: Fine 322
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: M. Aganagic, Berkeley
Date:  Wednesday, December 13, 2006, Time: 3:00 p.m., Location: Fine 214
   
Department Colloquium
Topic: Trees, elliptic operators, and K-theory for group C*-algebra
Presenter: Paul Baum, Penn State University
Date:  Wednesday, December 13, 2006, Time: 4:30 p.m., Location: Fine 314
Abstract: Let G be a locally compact Hausdorff second countable topological group. Examples are Lie groups, discrete groups, p-adic groups and adelic groups. The regular representation of G gives rise to a C* algebra known as the reduced C* algebra of G. Twenty five years ago P.Baum and A.Connes conjectured an answer to the problem of calculating the K-theory of this C* algebra. When true, this conjecture has corollaries in various branches of mathematics. Among these corollaries are the Novikov conjecture (topology) and the stable Gromov-Lawson-Rosenberg conjecture (differential geometry). In essence, the conjecture asserts that every element in the K-theory of the reduced C* algebra of G is the index of some G-equivariant elliptic operator, and that the only relations on these indices are the "obvious" index preserving relations. This is made precise by using the universal example for proper actions of G. In low dimensions this universal example is a tree. Due to the work of a number of mathematicians, the conjecture is now known to be true for certain classes of groups (e.g. connected Lie groups, discrete hyperbolic groups, discrete a-t-menable groups, algebraic p-adic groups, algebraic adelic groups). The search for a counter-example (to a somewhat generalized version of the conjecture) has led to some intriguing questions involving the expander graphs of Lubotzky-Sarnak and a random group (which probably exists) of Gromov. The talk is intended for a general mathematical audience. The basic definitions (C* algebra, K-theory etc) will be carefully stated in the talk.
   
Topology Seminar
Topic: TBA
Presenter: Saul Schleimer, Rutgers University
Date:  Thursday, December 14, 2006, Time: 4:30 p.m., Location: Fine 314