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NOVEMBER 2006 |
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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 |
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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. |
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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. |
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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. |
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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. |
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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? |
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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. |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Alexander Kiselev, University of Wisconsin |
Date: |
Monday, November 20, 2006, Time: 4:00 p.m., Location: Fine 110 |
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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. |
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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. |
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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 |
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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.) |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Rados Radoicic, CUNY |
Date: |
Wednesday, November 22, 2006, Time: 2:15 p.m., Location: Fine 224 |
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Special Analysis Seminar |
Topic: |
TBA |
Presenter: |
Fabrice Planchon, Paris 13 |
Date: |
Wednesday, November 22, 2006, Time: 3:00 p.m., Location: Jadwin A07 |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Hongjie Dong, IAS |
Date: |
Monday, November 27, 2006, Time: 4:00 p.m., Location: Fine 110 |
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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. |
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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 |
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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 |
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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. |
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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). |
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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. |
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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 |
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See http://www.math.princeton.edu/~bsudakov/galvin2006-fall.pdf |
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Department Colloquium |
Topic: |
TBA |
Presenter: |
Chris Skinner, Princeton University |
Date: |
Wednesday, November 29, 2006, Time: 4:30 p.m., Location: Fine 314 |
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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). |
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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. |
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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 |
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DECEMBER 2006 |
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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 |
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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. |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Natasa Pavlovic, Princeton University |
Date: |
Monday, December 4, 2006, Time: 4:00 p.m., Location: Fine 110 |
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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 |
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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 |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Tom Bohman, Carnegie Mellon University |
Date: |
Wednesday, December 6, 2006, Time: 2:15 p.m., Location: Fine 224 |
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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 |
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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. |
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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 |
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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 |
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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. |
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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 |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Enno Lenzman, MIT |
Date: |
Monday, December 11, 2006, Time: 4:00 p.m., Location: Fine 110 |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Brendan Hassett, Rice University |
Date: |
Tuesday, December 12, 2006, Time: 4:30 p.m., Location: Fine 322 |
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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 |
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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. |
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Topology Seminar |
Topic: |
TBA |
Presenter: |
Saul Schleimer, Rutgers University |
Date: |
Thursday, December 14, 2006, Time: 4:30 p.m., Location: Fine 314 |
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