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MAY 2007 |
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| Sato-Tate Seminar |
| Topic: |
Potential Modularity and the Sato-Tate conjecture |
| Presenter: |
Andrew Wiles, Princeton University |
| Date: |
Wednesday, May 2, 2007, Time: 1:30 p.m., Location: Fine 314 |
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| Discrete Mathematics Seminar |
| Topic: |
On the minimal number of convex quadruples on the plane |
| Presenter: |
Jozsef Balogh, University of Illinois, Urbana |
| Date: |
Wednesday, May 2, 2007, Time: 2:15 p.m., Location: Fine 224 |
| Abstract: |
See http://www.math.princeton.edu/~bsudakov/balogh2007-spring.pdf |
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| Department Colloquium |
| Topic: |
Polynomial progressions in primes |
| Presenter: |
Tamar Ziegler, University of Michigan |
| Date: |
Wednesday, May 2, 2007, Time: 4:30 p.m., Location: Fine 314 |
| Abstract: |
In 1977 Szemeredi proved that any subset of the integers of positive density contains arbitrarily long arithmetic progression. A couple of years later Furstenberg gave an ergodic theoretic proof of Szemeredi's theorem. At around the same time Furstenberg and Sarkozy independently proved that any subset of the integers of positive density contains a perfect square difference, namely elements x, y with x–y=n2 for some positive integer n. In 1995, Bergelson and Leibman proved, using ergodic theoretic methods, a vast generalization of both Szemeredi's theorem and the Furstenberg-Sarkozy theorem, establishing the existence of arbitrarily long polynomial progression in subsets of the integers of positive density. The ergodic theoretic methods are limited, to this day, to handling sets of positive density. However, in 2004 Green and Tao proved that the question of finding arithmetic progressions in some special subsets of the integers of zero density - for example the prime numbers - can be reduced to that of finding arithmetic progressions in subsets of positive density. In recent work with T. Tao we show that one can make a similar reduction for polynomial progressions, thus establishing, through the Bergelson-Leibman theorem, the existence of arbitrarily long polynomial progressions in the prime numbers. |
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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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| Mathematical Physics Seminar *** Please note special date |
| Topic: |
Universality of Ageing in Mean Field Spin Glasses |
| Presenter: |
Anton Bovier, TU-Berlin and WIAS |
| Date: |
Thursday, May 3, 2007, Time: 4:30 p.m., Location: Jadwin 343 |
| Abstract: |
``Ageing'' has become a commonly used concept to characterize the slow-down of long-term dynamics in many complex systems, notably glasses and spin-glasses. It is manifest in scaling properties of time-time correlation functions.
A simple exactly solvable toy model which exhibits ageing is the so-called REM-like trap modes, a simple Markov chain with random transition rates with a heavy-tailed distribution. It is believed that this simple model describes correctly the ageing in a large class of more realistic models. In this talk I will present results, obtained in collaboration with G. Ben Arous and J. Cerny, confirming this expectation for a class of Glauber dynamics of p-spin interaction mean-field spin-glass models. |
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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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| Mathematical Physics Seminar *** Please note special date and time |
| Topic: |
Anderson localization for random Schroedinger operators |
| Presenter: |
Francois Germinet, Univ. Cergy-Pontoise |
| Date: |
Friday, May 4, 2007, Time: 1:30 p.m., Location: Jadwin 343 |
| Abstract: |
We shall review some recent developments on localization exhibited by large classes of random operators. In particular, localization in presence of an Anderson potential with an arbitrary non degenerate underlying probability law is proved. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
Sharp constant and extremal function for a modified Moser-Trudinger inequality in two dimension |
| 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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| Joint Princeton University and IAS Number Theory Seminar |
| Topic: |
The existence of Bessel functionals |
| Presenter: |
Ramin Takloo-Bighash, Princeton University |
| Date: |
Thursday, May 10, 2007, Time: 4:30 p.m., Location: Fine 322 |
| Abstract: |
In this talk I will discuss some recent results on the existence of certain unique models related to the Gross-Prasad conjecture. This is joint with Dipendra Prasad. |
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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 Cheng, Academica Sinica |
| Date: |
Friday, May 11, 2007, Time: 3:00 p.m., Location: Fine 314 |
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