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APRIL 2010 |
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Discrete Mathematics Seminar *** Please note special day |
Topic: |
Eigenvalues, connectivity and matchings in regular graphs |
Presenter: |
Sebastian Cioaba, University of Delaware |
Date: |
Wednesday, April 14, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
Abstract: |
The spectrum of a graph contains a lot of relevant information regarding its structure. In this talk, I will describe some relationships between the eigenvalues of a regular graph, its matching number and connectivity. |
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SPECIAL LECTURE |
Topic: |
Cybersecurity, Mathematics, and Limits on Technology |
Presenter: |
Andrew Odlyzko, University of Minnesota |
Date: |
Wednesday, April 14, 2010, Time: 4:00 p.m., Location: IAS S-101 |
Abstract: |
Mathematics has contributed immensely to the development of secure cryptosystems and protocols. Yet our networks are terribly insecure, and we are constantly threatened with the prospect of imminent doom. Furthermore, even though such warnings have been common for the last two decades, the situation has not gotten any better. On the other hand, there have not been any great disasters either. To understand this paradox, we need to consider not just the technology, but also the economics, sociology, and psychology of security. Any technology that requires care from millions of people, most very unsophisticated in technical issues, will be limited in its effectiveness by what those people are willing and able to do. This imposes strong limits on what formal mathematical methods can accomplish, and suggests that we will have to put up with the equivalent of baling wire and chewing gum, and to live on the edge of intolerable frustration. |
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Department Collquium |
Topic: |
Random Schrodinger Operators and Random Matrices |
Presenter: |
Balint Virag, University of Toronto |
Date: |
Wednesday, April 14, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
It has been conjectured that the eigenvalues of the adjacency matrix of a large box in Z^d, d>=3, perturbed by the right amount of randomness, behave like the eigenvalues of a random matrix. I will discuss this and related conjectures, explain what happens in one dimension, and present a very special provable case of long boxes. Based on joint work with E. Kritchevski and B. Valko. |
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SPECIAL Symplectic Geometry Seminar |
Topic: |
Symplectic measurements and convex geometry |
Presenter: |
Yaron Ostrover, IAS |
Date: |
Thursday, April 15, 2010, Time: 12:30 p.m., Location: Fine Hall 1001 |
Abstract: |
In this talk we discuss some interrelations between symplectic and convex geometry, and show how tools from one field can be used to tackle questions in the other field. In particular, we will discuss a symplectic isoperimetric inequality and its relation to billiard dynamics. No previous knowledge is assumed. |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
Applications of Expansion and Equidistribution to Number Theory |
Presenter: |
Alex Kontorovich, Brown University and IAS |
Date: |
Thursday, April 15, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
Abstract: |
We will discuss recent applications of Expander Graphs to various problems in Equidistribution and Sieving. |
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Joint Princeton University and Institute for Advanced Study Number Theory Seminar |
Topic: |
Split reductions of simple abelian varieties |
Presenter: |
David Zywina, University of Pennsylvania |
Date: |
Thursday, April 15, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
Abstract: |
To an abelian variety over a number field one can associate an abelian variety to each prime ideal p of good reduction by reducing the variety modulo p. The geometry of these reductions need not resemble the geometry of the original abelian variety; for example, there are absolutely simple abelian varieties of dimension 2 whose reductions modulo p always split as a product of elliptic curves. In this talk, we shall describe progress on a conjecture of Murty and Patankar which predicts exactly which absolutely simple abelian varieties have reductions modulo p that are also absolutely simple. |
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Topology Seminar |
Topic: |
A combinatorial approach to Heegaard Floer invariants |
Presenter: |
Ciprian Manolescu, UCLA |
Date: |
Thursday, April 15, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
I will present a combinatorial description of the Heegaard Floer invariants of three- and four-manifolds (mod 2). The idea is to represent the manifolds in terms of links in S3, and then to use grid diagrams to represent the links. Counting holomorphic polygons in symmetric products boils down to counting certain domains on the grids. This is based on joint work with P. Ozsvath and D. Thurston. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
A prime orbit theorem, trace formulae, and interactions between quantum and classical mechanics on asymptotically hyperbolic manifolds |
Presenter: |
Julie Rowlett, Bonn |
Date: |
Friday, April 16, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
Abstract: |
Asymptotically hyperbolic manifolds are a natural generalization of infinite volume hyperbolic manifolds and enjoy similar features. They are of particular interest in physics because all Poincar\'e-Einstein manifolds, which arise in adS-CFT correspondence, are asymptotically hyperbolic. In this talk, we'll recall the definition of these spaces and see some examples. After a brief discussion of their spectral theory and dynamics, I will present a prime orbit theorem and two ``dynamical wave trace formulae.'' Based on the prime orbit theorem and the trace formulae, we will determine a relationship between the existence of pure point spectrum and the topological entropy of the geodesic flow. We can interpret this physically as an interaction between the quantum and classical mechanics. |
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Differential Geometry and Geometric Analysis Seminar *** Please note special time |
Topic: |
regularity of solutions to the complex Monge-Ampere equation |
Presenter: |
Slawomir Dinew, Uniwersystet Jagiollonski w Krakowie |
Date: |
Friday, April 16, 2010, Time: 4:00 p.m., Location: Fine Hall 314 |
Abstract: |
In geometric analysis many arguments rely on a suitable regularity theory for the analyzed differential equations. Similarly to the solution of the Calabi conjecture often derving suitable a priori estimates is in fact the heart of the matter. In the talk a regularity result for the complex Monge-Ampe`re equation will be presented. We will prove that any C1,1 smooth plurisubharmonic solution u to the problem det(uij) = f with f strictly positive and H¨older continuous has in fact H¨older continuous second derivatives. For smoother f this follows form the classical Evans-Krylov theory yet in our case it cannot be applied directly. Instead we shall follow closely an idea of Xu-Jia Wang. Finally we shall discus how this particular regularity result can be used to justify an argument in the proof of uniqueness of metrics of constant scalar curvature by Chen and Tian. |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
G. Bellamy, Edinburgh |
Date: |
Monday, April 19, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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Group Actions Seminar |
Topic: |
Counting Representations of Arithmetic Lattices |
Presenter: |
Nir Avni, Harvard University |
Date: |
Tuesday, April 20, 2010, Time: 12:30 p.m., Location: Fine Hall 322 |
Abstract: |
I will talk about the the number of representations of dimension d of an arithmetic lattice when d tends to infinity. For higher rank lattices, this sequence grows polynomially, with some mysterious exponent. I will talk about some known values of this exponent, and the conjectural relations between the representation growths of different lattices. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Dragos Oprea, UCSD |
Date: |
Tuesday, April 20, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Robin Thomas, Georgia Tech |
Date: |
Thursday, April 22, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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Algebraic Topology Seminar |
Topic: |
Equivariant formality and beyond |
Presenter: |
Matthias Franz, University of Western Ontario |
Date: |
Thursday, April 22, 2010, Time: 2:30 p.m., Location: Fine Hall 314 |
Abstract: |
A space with a torus action is called "equivariantly formal" if its equivariant cohomology (say, with rational coefficients) is free over the polynomial ring H^*(BT). Many interesting spaces fall into this class. A nice feature of them is that their equivariant cohomology can be easily computed from the fixed point set and the one-dimensional orbits. It turns out that this last property holds for more spaces than just the equivariant formal ones. We will characterise these spaces and present some examples. We will also discuss equivariant formality for cohomology with integer coefficients. |
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Joint Princeton University and Institute for Advanced Study Number Theory Seminar |
Topic: |
Deformation rings of group representations |
Presenter: |
Bart de Smit, Universiteit Leiden |
Date: |
Thursday, April 22, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
Liouville-type theorem for nonnegative Bakry-Emery Ricci tensor |
Presenter: |
Guofang Wei, UCSB |
Date: |
Friday, April 23, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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Topology Seminar ***Please note special date and location |
Topic: |
TBA |
Presenter: |
Olga Plamenevskaya, SUNY Stony Brook |
Date: |
Friday, April 23, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Justin Holmer, Brown University |
Date: |
Monday, April 26, 2010, Time: 4:00 p.m., Location: Fine Hall 110 |
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PACM Colloquium |
Topic: |
Toward practical rare event simulation in high dimensions |
Presenter: |
Jonathan Weare, Courant Institute for Mathematics, NYC |
Date: |
Monday, April 26, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
Abstract: |
Prof. Weare will discuss an importance sampling method for certain rare event problems involving small noise diffusions. Standard Monte Carlo schemes for these problems behave exponentially poorly in the small noise limit. Previous work in rare event simulation has focused on developing, in specific situations, estimators with optimal exponential variance decay rates. He will introduce an estimator related to a deterministic control problem that not only has an optimal variance decay rate under certain conditions, but that can even have vanishingly small statistical relative error in the small noise limit. The method can be seen as the limit of a well known zero variance importance sampling scheme for diffusions which requires the solution of a second order partial differential equation. |
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Mathematical Physics Seminar |
Topic: |
Quasi-adiabatic continuation and the Topology of Many-body Quantum Systems |
Presenter: |
Matthew Hastings, Microsoft Research |
Date: |
Tuesday, April 27, 2010, Time: 4:30 p.m., Location: Jadwin 343 |
Abstract: |
Topological arguments play a key role in understanding quantum systems. For example, recently it has been shown that K-theory provides a tool for classifying different phases of non-interacting, or single-particle, systems. However, topological arguments have also been applied to interacting systems. I will explain the technique of quasi-adiabatic continuation, which provides a way to rigourously formulate many of the topological arguments made by physicists for these systems. In particular, I will discuss its application to a higher dimensional Lieb-Schultz-Mattis theorem (a statement about degeneracy of ground states, which can arise for topological reasons), where this technique was introduced in 2004, and its more recent application to proving quantum Hall conductance quantization for interacting systems. |
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Topology Seminar |
Topic: |
TBA |
Presenter: |
Zoltan Szabo, Princeton University |
Date: |
Thursday, April 29, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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SPECIAL Ergodic Theory and Statistical Mechanics Seminar ***Please note special day and time |
Topic: |
Dynamics of bouncing balls |
Presenter: |
Dmitry Dolgopyat, University of Maryland |
Date: |
Friday, April 30, 2010, Time: 2:30 p.m., Location: Fine Hall 401 |
Abstract: |
We consider a ball bouncing off infinitely heavy periodically moving wall in the presence of a potential force. We are interested in the question how large is the set of orbits whose energy tends to infinity. Both smooth and piecewise smooth motions of wall will be considered. We also present some related questions about small piecewise smooth perturbations of nearly integrable systems. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Valentino Tosatti, Columbia University |
Date: |
Friday, April 30, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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MAY 2010 |
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PACM Colloquium |
Topic: |
TBA |
Presenter: |
Stephen Howard, University of Melbourne, Australia |
Date: |
Monday, May 3, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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Group Actions Seminar |
Topic: |
TBA |
Presenter: |
Yves Cornulier, CNRS, Université de Rennes 1 |
Date: |
Tuesday, May 4, 2010, Time: 12:30 p.m., Location: Fine Hall 322 |
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Joint Princeton University and Institute for Advanced Study Number Theory Seminar |
Topic: |
Selmer ranks of twists of elliptic curves |
Presenter: |
Karl Rubin, UC Irvine |
Date: |
Thursday, May 6, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
Abstract: |
In joint work with Barry Mazur, we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions for an elliptic curve to have twists of arbitrary 2-Selmer rank, and we give lower bounds for the number of twists (with bounded conductor) that have a given 2-Selmer rank. As a consequence, under appropriate hypotheses there are many twists with Mordell-Weil rank zero, and (assuming the Shafarevich-Tate conjecture) many others with Mordell-Weil rank one. The talk will conclude with some speculation about the density of twists with a given Selmer rank. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Xavier Cabre, Universitat Politècnica de Catalunya |
Date: |
Friday, May 7, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
TBA |
Presenter: |
Anthony Peirce, University of British Columbia |
Date: |
Monday, May 17, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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