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APRIL 2007 |
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| Sato-Tate Seminar |
| Topic: |
Modularity lifting for unitary groups |
| Presenter: |
Andrew Wiles, Princeton University |
| Date: |
Wednesday, April 25, 2007, Time: 1:30 p.m., Location: Fine 314 |
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| Discrete Mathematics Seminar |
| Topic: |
Dvoretzsky's theorem in metric spaces |
| Presenter: |
Assaf Naor, NYU |
| Date: |
Wednesday, April 25, 2007, Time: 2:15 p.m., Location: Fine 224 |
| Abstract: |
See http://www.math.princeton.edu/~bsudakov/naor2007-spring.pdf |
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| Department Colloquium |
| Topic: |
Knot homologies |
| Presenter: |
Jacob Rasmussen, Princeton University |
| Date: |
Wednesday, April 25, 2007, Time: 4:30 p.m., Location: Fine 314 |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Poincare Lectures II |
| Presenter: |
Aaron Naber, Princeton University |
| Date: |
Thursday, April 26, 2007, Time: 2:00 p.m., Location: Fine 401 |
| Abstract: |
We relate the recent advances made by Perelman in the Ricci Flow and their application to the proof of the Poincare Conjecture. The proof is broken into three parts: The existence and classification of singularity dilations of the Ricci Flow, the definition and long time existence of the Ricci Flow with Surgery, and the finite time extension of such a flow. After an overview of the proof we will focus on the singularity classification in dimension three. |
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| Joint Princeton University and IAS Number Theory Seminar |
| Topic: |
A Product Theorem in (Virtually) Free Groups |
| Presenter: |
A. Razborov, IAS |
| Date: |
Thursday, April 26, 2007, Time: 4:30 p.m., Location: Fine 322 |
| Abstract: |
In inverse problems in arithmetic combinatorics, one is interested in describing internal properties of those finite subsets $A$ of an algebraic structure that ``barely expand'' under its operations. One of the deepest results in the area is Freiman's theorem providing a complete characterization of the sets $A$ in abelian torsion-free groups for which $|A+A|$ is almost linear in $A$. Nothing non-trivial, however, is known already about sets of integers $A$ with $|A+A|\leq A^{1+\delta}$. Surprisingly, these questions have turned out to be easier for more complicated algebraic structures like commutative rings or, very recently, non-abelian groups. In particular, Chang (2006) proved that for some fixed $\delta$, any set $A$ in a free group with $|AAA|\leq A^{1+\delta}$ belongs to a cyclic subgroup. We give a purely combinatorial proof of this result based on the theory of periodic words and their occurrences. Our proof also shows that $\delta$ can be chosen arbitrarily close to 1, and this is optimal. This further generalizes to arbitrary virtually free groups (with the respective change in the conclusion); in particular, our result is applicable to the modular group $PSL_2(Z)$. |
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| Operations Research and Financial Engineering Seminar |
| Topic: |
Nurse-to-Patient Ratios Staffing Legislation: A Queueing Critique |
| Presenter: |
Otis B. Jennings, The Fuqua School of Business |
| Date: |
Thursday, April 26, 2007, Time: 4:30 p.m., Location: E-219, E-Quad |
| Abstract: |
See http://orfe.princeton.edu/papers/jennings-abstract.pdf |
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| Topology Seminar |
| Topic: |
Heegaard Splittings and Hyperbolic Geometry |
| Presenter: |
Hossein Namazi, Princeton University |
| Date: |
Thursday, April 26, 2007, Time: 4:30 p.m., Location: Fine 314 |
| Abstract: |
How does a hyperbolic 3-manifold look like? We speak about an approach to answer this question which uses the combiatorial data provided by a Heegaard splitting. |
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| Symplectic Geometry Seminar |
| Topic: |
Vanishing of the fundamental class of displaceable Lagrangian submanifolds |
| Presenter: |
Peter Albers, NYU |
| Date: |
Friday, April 27, 2007, Time: 2:00 p.m., Location: Fine 214 |
| Abstract: |
In this talk I will sketch a proof of the following theorem. The fundamental class of a displaceable monotone Lagrangian submanifold vanishes. This proof uses an geometric argument and Hamiltonian Floer homology. Afterwards I will put this into a more conceptual context involving Lagrangian and Hamiltonian Floer homology and their interplay. This yields another (slightly more general proof of the aforementioned theorem and some further corollaries concerned with topological properties of Lagrangian submanifolds. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
Curvature flow on S^1 |
| Presenter: |
Meijun Zhu, University of Oklahoma |
| Date: |
Friday, April 27, 2007, Time: 3:00 p.m., Location: Fine 314 |
| Abstract: |
In this talk, I shall report our recent results on the study of curvature problems on S1. The classifications of extremal metrics, the global existence and exponential convergence of curvature flows are obtained. The results on one dimensional affine curvature flow are obtained as special cases under the general setting. |
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| Differential Geometry and Geometric Analysis Seminar *** Please note special time |
| Topic: |
The Riemannian Penrose Inequality in dimensions less than 8 |
| Presenter: |
Dan Lee, Duke University |
| Date: |
Friday, April 27, 2007, Time: 4:00 p.m., Location: Fine 314 |
| Abstract: |
The Riemannian Penrose Inequality was first proved in three dimensions in 1997 by G. Huisken and T. Ilmanen for the case of a single black hole. In 1999, H. Bray extended this result to the general case of multiple black holes using a different technique. I will discuss joint work with H. Bray on extending Bray's technique to dimensions less than 8. |
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MAY 2007 |
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| Algebraic Geometry Seminar |
| Topic: |
Gerby localization and GW invariants of [C^N/Z_r] |
| Presenter: |
Charles Cadman, University of Michigan |
| Date: |
Tuesday, May 1, 2007, Time: 4:30 p.m., Location: Fine 322 |
| Abstract: |
An important conjecture in Gromov-Witten theory relates the quantum potential of an orbifold with that of a crepant resolution of its coarse moduli space. Recent work has focused on orbifolds of the form [C^N/G], where G is a finite group acting linearly on C^N. I will discuss two approaches to computing the orbifold Gromov-Witten invariants, one of which is joint work with Arend Bayer and the other with Renzo Cavalieri. |
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| Operations Research and Financial Engineering Seminar |
| Topic: |
Hedging variance options on continuous seminartingales |
| Presenter: |
Roger Lee, University of Chicago |
| Date: |
Tuesday, May 1, 2007, Time: 4:30 p.m., Location: E-219, E-Quad |
| Abstract: |
Variance swaps, which pay the realized variance of [the returns on] an underlying price process, have become a leading tool for managing exposure to volatility risk. Variance options -- calls and puts on realized variance -- allow portfolio managers greater control over volatility risk exposure, but present greater hedging difficulties to the dealer. Assuming only that the underlier is a positive continuous semimartingale, we model-independently superreplicate and also (extending Dupire 2005) subreplicate variance options and forward-starting variance options, by dynamically trading the underlier, and statically holding European options. (Joint with Peter Carr) |
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| Department Colloquium |
| Topic: |
TBA |
| Presenter: |
Tamar Ziegler, University of Michigan |
| Date: |
Wednesday, May 2, 2007, Time: 4:30 p.m., Location: Fine 314 |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Bulk Universality and Related Properties of Hermitian Matrix Models |
| Presenter: |
L.Pastur, Institute for Low Temperatures, Kharkiv, Ukraine |
| Date: |
Thursday, May 3, 2007, Time: 2:00 p.m., Location: Fine 401 |
| Abstract: |
We give a new proof of universality properties in the bulk of spectrum of the hermitian matrix models, assuming that the potential that determines the model is globally $C^{2}$ and locally $C^{3}$ function. The proof is based on the orthogonal polynomial techniques but does not use asymptotics of orthogonal polynomials. Rather, we obtain the $sin$-kernel as a unique solution of a certain non-linear integro-differential equation that follows from the determinant formulas for the correlation functions. We also present a simplified and strengthened version of the proof of existence and properties of the limiting Normalized Counting Measure of eigenvalues. |
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| Joint Princeton University and IAS Number Theory Seminar |
| Topic: |
Primes and orbits |
| Presenter: |
Peter Sarnak, Princeton University |
| Date: |
Thursday, May 3, 2007, Time: 4:30 p.m., Location: Fine 322 |
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| Topology Seminar |
| Topic: |
Exotic smooth structures on small 4-manifolds |
| Presenter: |
Doug Park, University of Waterloo |
| Date: |
Thursday, May 3, 2007, Time: 4:30 p.m., Location: Fine 314 |
| Abstract: |
Over the last decade, there has been steady progress in the construction of exotic smooth structures on closed oriented simply-connected 4-manifolds with small Euler characteristics. In this talk, I will survey some recent results. In particular, I will show how one can obtain infinitely many exotic smooth structures on (2n-1)CP2 # (2n+1)(-CP2) for any positive integer n. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Guozheng Lu, Wayne State University |
| Date: |
Friday, May 4, 2007, Time: 3:00 p.m., Location: Fine 314 |
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| Operations Research and Financial Engineering Seminar |
| Topic: |
Portfolio theory with convex risk measures |
| Presenter: |
Frank Heyde, MLU Halle-Wittenberg |
| Date: |
Tuesday, May 8, 2007, Time: 4:30 p.m., Location: E-219, E-Quad |
| Abstract: |
We consider a Markowitz type portfolio selection problem where the risk is measured by a convex risk meausure. We derive necessary and sufficient conditions for the resulting parametric optimization problem and in the coherent case we construct a solution of the dual problem using the density of a risk neutral probability measure. Moreover we analyze the connection to utility maximization problems. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Circle rotations and the shrinking target properties |
| Presenter: |
Jim Tseng, Brandeis University |
| Date: |
Thursday, May 10, 2007, Time: 2:00 p.m., Location: Fine 401 |
| Abstract: |
The shrinking target properties are related to recurrence. We will motivate and present definitions of these properties. We will also give a necessary and sufficient condition for a circle rotation to have the s-exponent monotone shrinking target property (sMSTP), and, thereby we generalize a result for s = 1 that was established by J. Kurzweil and rediscovered by B. Fayad. We will give a detailed sketch of the proof. Finally, we will apply our technique to give a new, very short, proof of the logarithm law for irrational rotations. |
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| Symplectic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Robert Lipshitz, Columbia University |
| Date: |
Friday, May 11, 2007, Time: 2:00 p.m., Location: Fine 214 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Jih-Hsin, Academica Sinica |
| Date: |
Friday, May 11, 2007, Time: 3:00 p.m., Location: Fine 314 |
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