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FEBRUARY 2010 |
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Department Colloquium |
Topic: |
Pretentiousness in the analytic theory of numbers |
Presenter: |
Andrew Granville, Universite de Montreal |
Date: |
Wednesday, February 24, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
Following the brilliant insight of Riemann, that a good understanding of the distribution of prime numbers is equivalent to a good understanding of the location of zeros of pertinent L-functions, analytic number theory has traditionally centered on developing this point-of-view. The Riemann Hypothesis, that all the zeros "lie on the 1/2-line", remains unproven, so researchers have many theorems bounding some aspect of the zeros close to the 1-line. These yield the proofs of many of the key results in the subject.
Given Riemann's equivalence, and the consequent goal to prove the Riemann Hypothesis, it has long seemed "obvious" that one should approach the subject by gaining a better and better understanding of the distribution of zeros. However is this really the correct way to proceed? Is it so obvious that this is the right way to gain an improved understanding of central issues concerning the distribution of primes? Recently Soundararajan and the speaker have shown that several of the key results in the subject can be proved more succinctly, arguably more easily, without reverting to a study of zeros of L-functions, using the notion of pretentiousness.
In this talk we will explain what "pretentiousness" is, exhibit the depth of ideas we use, and show how various well-known results follow, as well as several new results. |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
Limit theorems for sticky particle systems and positivity of integrated random walks |
Presenter: |
Vlad Vysotsky, University of Delaware |
Date: |
Thursday, February 25, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
Abstract: |
Consider the model of a one-dimensional gas, whose particles have random initial positions and random initial velocities. Particle attract each other due to gravitation, and stick together at collisions. As time goes, the number of particles decreases while their sizes increase until there forms a giant single particle of the total mass.
The results on this process of mass aggregation are given in form of limit theorems as the number of initial particles tends to infinity. For example, the stochastic processes of the total number of particles satisfy a functional central limit theorem. I will show how this problem on the number of particles is related to positivity of integrated random walks. I will discuss the problem of finding one-sided small deviation probabilities of integrated random walks and other stochastic processes, and tell about the progress in this field. |
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Algebraic Topology Seminar |
Topic: |
Pointed torsors and Galois groups |
Presenter: |
Rick Jardine, University of Western Ontario. |
Date: |
Thursday, February 25, 2010, Time: 2:30 p.m., Location: Fine Hall 314 |
Abstract: |
Suppose that H is an algebraic group which is defined over a field k, and let L be the algebraic closure of k. The canonical stalk for the etale topology on k induces a simplicial set map from the classifying space B(H-tors) of the groupoid of H-torsors (aka. principal H-bundles) to the space BH(L). The homotopy fibres of this map are groupoids of pointed torsors. These fibres are analyzed with cocycle techniques, and their path components are categorical representations of the absolute Galois groupoid (suitably defined) in H. Analogous results hold for finite etale sites: pointed torsors in that context are classified by continuous morphisms defined on a Grothendieck fundamental groupoid. |
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Joint Princeton University and Institute for Advanced Study Number Theory Seminar |
Topic: |
On Eisenstein series and the cohomology of arithmetic groups |
Presenter: |
Joachim Schwermer, University of Vienna, ESI |
Date: |
Thursday, February 25, 2010, Time: 4:30 p.m., Location: IAS S-101 |
Abstract: |
The automorphic cohomology of a reductive $\mathbb{Q}$--group $G$, defined in terms of the automorphic spectrum of $G$, captures essential analytic aspects of the arithmetic subgroups of $G$ and their cohomology. We discuss the actual construction of cohomology classes represented by residues or principal values of derivatives of Eisenstein series, We show that non--trivial Eisenstein cohomology classes can only arise if the point of evaluation features a 'half--integral' property. This rises questions concerning the analytic behavior of certain automorphic L--functions at half--integral arguments. |
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Topology Seminar |
Topic: |
Heegaard Floer Homology and Knot Surgeries |
Presenter: |
Margaret Doig, Princeton University |
Date: |
Thursday, February 25, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
Wallace and Lickorish showed that any 3-manifold can be realized as surgery on a link in S3; however, fifty years later, we still have a rather poor understanding of which manifolds can be constructed from surgery on a knot and which knots give these surgeries. For example, the Berge Conjecture attempts to list all knots which can give rise to a lens space. We will ask a slightly easier question, that of which spherical Seifert fibered spaces (aka spherical space forms) arise as knot surgeries. We will use an obstruction from Heegaard Floer theory, the "correction terms" assigned to a manifold and its associated spin^c structures. These terms can be calculated either from a knot surgery description of a manifold or from a description of it as a Seifert fibered space. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
Conformally Warped Manifolds and quasi-Einstein metrics |
Presenter: |
Jeffrey Case, UCSB |
Date: |
Friday, February 26, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
Abstract: |
The concept of a smooth metric measure space has recently arisen as a useful object within Riemannian geometry, for example in Perelman's formulation of Ricci flow as a gradient flow. In this setting, a key objective is to find a suitable generalization of Ricci curvature, and to understand the associated ``quasi-Einstein'' metrics. Taking two different perspectives, Lott, Villani, Sturm and Chang, Gursky and Yang have found two distinct approaches to studying smooth metric measure spaces. While the formulations are different, they both introduce an extra dimensional parameter $m$ which, in the limit $m\to\infty$, recovers the curvatures that arise in Perelman's treatment of the Ricci flow. In this way it becomes interesting to see if the two approaches are related. As the quasi-Einstein metrics of these approaches include conformally Einstein metrics, the bases of Einstein warped products, and gradient Ricci solitons, finding a relation between them might also allow us to find interesting connections between these metrics.
In this talk, I will introduce what I call ``conformally warped manifolds'' as a way to unite the approaches of Lott-Villani-Sturm and Chang-Gursky-Yang. I will discuss three results which suggest that this notion is indeed the ``best'' approach. First, I will discuss the variational problem associated to quasi-Einstein metrics, which naturally relates the Yamabe constant to Perelman's shrinker entropy. Second, I will discuss a Liouville-type theorem which illustrates the usefulness of studying the limit $m\to\infty$ as a way to overcome difficulties in the $m=\infty$ comparison theory. Third, I will discuss a compactness theorem for compact quasi-Einstein metrics analogous to Anderson's theorem for Einstein metrics, which is independent of the parameter $m$. |
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Special Joint Columbia/Courant/Princeton Algebraic Geometry Seminar |
Topic: |
Normal forms for lattice polarized K3 surfaces and Siegel modular forms |
Presenter: |
Charles Doran, University of Alberta |
Date: |
Friday, February 26, 2010, Time: 3:30 p.m., Location: NYU, WWH 101 |
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Special Joint Columbia/Courant/Princeton Algebraic Geometry Seminar |
Topic: |
Prime exceptional divisors on holomorphic symplectic varieties |
Presenter: |
Eyal Markman, University of Massachusetts, Amherst |
Date: |
Friday, February 26, 2010, Time: 5:00 p.m., Location: NYU, WWH 101 |
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MARCH 2010 |
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PACM Colloquium |
Topic: |
Probabilistic approach to high order assignment problems |
Presenter: |
Yosi Keller, School of Electrical Engineering, Bar-Ilan University (Israel) |
Date: |
Monday, March 1, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
A variety of computer vision and engineering problems can be cast as high order matching problems, where one considers the affinity of two or more assignments simultaneously. The spectral matching approach of Leordeanu and Hebert (2005) was shown to provide an approximate solution of this np-hard problem. It this talk we present a probabilistic interpretation of spectral matching and derive a new probabilistic matching scheme. We show how our approach can be extended to high order matching scheme, via a dual tensor marginalization-decomposition. Last, we present an Integer Least Squares algorithm and apply it to the decoding of MIMO channels and the solution of Suduko puzzles. Joint work with Amir Egozi, Michael Chertok and Amir Leshem |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
Hodge polynomials of moduli spaces of sheaves on K3 surfaces |
Presenter: |
B. Bakker, Princeton University |
Date: |
Monday, March 1, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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Algebraic Geometry Seminar |
Topic: |
Rational simple connectedness and Serre's "Conjecture II" |
Presenter: |
Jason Starr, Stony Brook University |
Date: |
Tuesday, March 2, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
Abstract: |
In the early 1960's Serre formulated two conjectures about Galois cohomology. The first was proved by Steinberg shortly thereafter, but the second remains open. I will discuss the proof of Serre's Conjecture II in the "geometric case": every principal homogeneous space for a bundle of simply connected, semisimple groups over a surface has a rational section. Due to the work of many people -- Merkurjev and Suslin, E. Bayer and Parimala, Chernousov, Gille-- the geometric case further reduces to the "split, geometric case", i.e., the bundle of groups is constant. And this case was proved by de Jong, X. He and myself using "rational simple connectedness". No background in Galois cohomology or rational connectedness will be assumed. |
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Mathematical Physics Seminar |
Topic: |
On the Boltzmann limit of a homogeneous Fermi gas |
Presenter: |
Igor Rodnianski, Princeton University |
Date: |
Tuesday, March 2, 2010, Time: 4:30 p.m., Location: Jadwin 343 |
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Department Colloquium |
Topic: |
Adding a list of numbers (and other determinantal processes)
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Presenter: |
Persi Diaconis, Stanford University |
Date: |
Wednesday, March 3, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
Adding a list of digits produces 'carries along the way. The distribution theory of carries involves the emerging theory of determinantal point processes (explanations provided). Thinking of carries as cocycles, the story extends to central extensions. There are also nice connections to Koszul algebras. This is joint work with Alexei Borodin and Jason Fulman. |
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SPECIAL SEMINAR |
Topic: |
From Magic to Mathematics and Back |
Presenter: |
Persi Diaconis, Stanford University |
Date: |
Thursday, March 4, 2010, Time: 11:00 a.m., Location: McCosh 10 |
Abstract: |
The way that a magic trick works is sometimes as amazing as the trick itself. I will illustrate with a trick that fools magicians. The mathematics behind the trick, which has its origins in Sanskrit poetry, now has applications to cryptography, robot vision (and smart pens), breaking and entering and elsewhere. Varying the trick in natural ways leads to problems beyond modern mathematics. This lecture will be accessible to a general audience. |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Francesco Cellarosi, Princeton University |
Date: |
Thursday, March 4, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Daniel Kral, Charles University |
Date: |
Thursday, March 4, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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Joint Princeton University and Institute for Advanced Study Number Theory Seminar |
Topic: |
Geometric Overconvergent Modular Forms |
Presenter: |
Vincent Pilloni, Columbia University |
Date: |
Thursday, March 4, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
Abstract: |
We will give a geometric definition of the notion of overconvergent modular form of any p-adic weight. As a consequence, we re-obtain Coleman's theory of p-adic families of eigenforms and the eigencurve of Coleman and Mazur without using the Eisenstein family. Similar results have just been obtained independantly by Andreatta, Iovita and Stevens. We will then explain how a similar construction can be applied to construct p-adic families of Hilbert and Siegel eigenforms (over the total weight space). This last part is a work in progress with Andreatta and Iovita. |
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Topology Seminar |
Topic: |
Cosmetic Surgery Conjecture on S^3 |
Presenter: |
Zhongtao Wu, Princeton University |
Date: |
Thursday, March 4, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
It has been known over 40 years that every closed orientable 3-manifold is obtained by surgery on a link in S3. However, a complete classification has remained elusive due to the lack of uniqueness of this surgery description. In this talk, we discuss the following uniqueness theorem for Dehn surgey on a nontrivial knot in S3. Let K be a knot in S3, and let r and r' be two distinct rational numbers of same sign, allowing r to be infinite; then there is no orientation preserving homeomophism between the manifolds obtained by performing Dehn surgery of type r and r', respectively. In particular, this result implies the Knot Complement Theorem of Gordon and Luecke. |
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Ergodic Theory and Statistical Mechanics Seminar ***Please note special day and time |
Topic: |
The dimension of self-affine sets: past, present and future. |
Presenter: |
Pablo Shmerkin, Manchester |
Date: |
Friday, March 5, 2010, Time: 2:30 p.m., Location: Fine Hall 401 |
Abstract: |
Calculating the dimension of sets invariant under non-conformal dynamics is a formidable problem. My talk will be a survey on what is known and expected for self-affine sets, i.e. sets invariant under piece-wise affine expanding maps on Euclidean space. Some emphasis will be given to my joint work with A. Käenmäki on self-affine sets of Kakeya type, and the thermodynamic formalism for the singular value function. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Christina Sormani, CUNY |
Date: |
Friday, March 5, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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Analysis Seminar |
Topic: |
Complex variables are not dead |
Presenter: |
Leon Ehrenpreis, Temple University, Philadelphia |
Date: |
Monday, March 8, 2010, Time: 4:00 p.m., Location: Fine Hall 110 |
Abstract: |
Our lecture will focus on two problems in pde which are solvable by ideas in holomorphic functions of complex variables. The first problem is called the strip theorem. Let f be a function defined in the strip in the complex plane l Im z l <= 1. Suppose f agrees on the boundary of each unit circle centered on the real axis, radius 1, with the solution (depending on the circle) of a suitable elliptic pde, the agreement being to order one greater than the order of the Dirichlet data. Then f satisfies this pde. If the equation is the Cauchy-Riemann equation then equality suffices. The second type of problems we discuss are the Phragmen-Lindelof theorem for pde and a form of the Heisenberg uncertainty for pde. These were introduced in Kenig's lecture at Fefferman's birthday bash. We shall put them in a general framework. |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
D. Gaiotto, IAS |
Date: |
Monday, March 8, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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Group Actions Seminar |
Topic: |
TBA |
Presenter: |
Tomasz Zamojski, University of Chicago |
Date: |
Tuesday, March 9, 2010, Time: 12:30 p.m., Location: Fine Hall 322 |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Aaron Bertram, University of Utah |
Date: |
Tuesday, March 9, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
Random polygons in plane convex sets |
Presenter: |
John Pardon, Princeton University |
Date: |
Thursday, March 11, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
Abstract: |
Consider picking N random points in a convex set K and forming their convex hull K_N. Recently, there have been a number of results concerning the asymptotic behavior of random variables such as the area and number of vertices of K_N. These are, however, all limited to two special cases: 1) K is a polygon and 2) K is "smooth". I will discuss work which obtains uniform bounds over the family of all convex sets K. These results include central limit theorems for the area and number of vertices of K_N. |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Jan Hladky, University of Warwick |
Date: |
Thursday, March 11, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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Topology Seminar |
Topic: |
The structure of groups with a quasiconvex hierarchy |
Presenter: |
Daniel Wise, McGill |
Date: |
Thursday, March 11, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
We prove that hyperbolic groups with a quasiconvex hierarchy are virtually subgroups of graph groups. Our focus is on "special cube complexes" which are nonpositively curved cube complexes that behave like "high dimensional graphs" and are closely related to graph groups. The main result illuminates the structure of a group by showing that it is "virtually special", and this yields the separability of the quasiconvex subgroups of the groups we study.
As an application, we resolve Baumslag's conjecture on the residual finiteness of one-relator groups with torsion. Another application shows that generic haken hyperbolic 3-manifolds have "virtually special" fundamental group. Since graph groups are residually finite rational solvable, combined with Agol's virtual fibering criterion, this proves that finite volume haken hyperbolic 3-manifolds are virtually fibered. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
A Codazzi-like equation and the singular set for surfaces in the Heisenberg group |
Presenter: |
Jih-Hsin Cheng, Academia Sinica, Taiwan |
Date: |
Friday, March 12, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Michael Weinstein, Columbia University |
Date: |
Monday, March 22, 2010, Time: 4:00 p.m., Location: Fine Hall 110 |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
Y. Berest, Cornell University |
Date: |
Monday, March 22, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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Group Actions Seminar |
Topic: |
Non-nonpositive curvature of some non-cocompact arithmetic groups |
Presenter: |
Kevin Wortman, University of Utah |
Date: |
Tuesday, March 23, 2010, Time: 12:30 p.m., Location: Fine Hall 322 |
Abstract: |
I'll explain why arithmetic subgroups of semisimple groups of relative Q-type A_n, B_n, C_n, D_n, E_6, or E_7 have an exponential lower bound to their isoperimetric inequality in the dimension that is 1 less than the real rank of the semisimple group. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Sándor Kovács, University of Washington |
Date: |
Tuesday, March 23, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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Mathematical Physics Seminar |
Topic: |
On the formation of black holes |
Presenter: |
Sergiu Klainerman, Princeton University |
Date: |
Tuesday, March 23, 2010, Time: 4:30 p.m., Location: Jadwin 343 |
Abstract: |
I will discuss some recent results obtained in collaboration with I. Rodnianski on the dynamic formation of black holes for the Vacuum Einstein equations. These results simplify and extend considerably the recent well known result of D. Christodoulou. |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Ilya Vinogrodov, Princeton University |
Date: |
Thursday, March 25, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Jason Morton, Penn State |
Date: |
Thursday, March 25, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Mario Bonk, Michigan |
Date: |
Friday, March 26, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Mingmin Shen, Columbia University |
Date: |
Tuesday, March 30, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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APRIL 2010 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Vitaly Bergelson, Ohio State University |
Date: |
Thursday, April 1, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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Discrete Mathematics Seminar *** Please note special day |
Topic: |
TBA |
Presenter: |
Assaf Naor, Courant Institute, NYU |
Date: |
Friday, April 2, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
CJ Anna Sung, Tsing-Hwa University, Taiwan |
Date: |
Friday, April 2, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
Y. Ruan, Michigan |
Date: |
Monday, April 5, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
TBA |
Presenter: |
Peter Winkler, AT&T Labs Research, Florham Park NJ |
Date: |
Monday, April 5, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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Group Actions Seminar |
Topic: |
Compact forms of homogeneous spaces and group actions |
Presenter: |
David Constantine, University of Chicago |
Date: |
Tuesday, April 6, 2010, Time: 12:30 p.m., Location: Fine Hall 322 |
Abstract: |
Given a homogeneous space J\H, does there exist a discrete subgroup \Gamma in H such that J\H/Gamma is a compact manifold? These compact forms of homogeneous spaces turn out to be rare outside of a few natural cases. Their existence has been studied by a very wide range of techniques, one of which is via the action of the centralizer of J in H. In this talk I'll show that no compact form exists when H is a simple Lie group, J is reductive and the acting group is higher-rank and semisimple. The proof uses cocycle superrigidity, Ratner's theorem and techniques from partially hyperbolic dynamics. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
James McKernan, MIT |
Date: |
Tuesday, April 6, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
Concentration inequalities for dynamical systems |
Presenter: |
Jean-René Chazottes, CNRS and École-Polytechnique |
Date: |
Thursday, April 8, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
Abstract: |
Concentration inequalities are a powerful tool to estimate the fluctuations of observables more general than ergodic sums: one can consider any observable F(x,...,T^n x) provided it is separately Lipschitz. Such inequalities can be established for non-uniformly hyperbolic systems and we shall present some applications. |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Alexandra Kolla, IAS |
Date: |
Thursday, April 8, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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Joint Princeton University and Institute for Advanced Study Number Theory Seminar |
Topic: |
Proof, via smooth homology, of the existence of rational families of H-invariant linear forms on G-induced representations, when G/H is a symetric, reductive, p-adic space, via smooth homology |
Presenter: |
Philippe Blanc, Institut de Mathématiques de Luminy |
Date: |
Thursday, April 8, 2010, Time: 4:30 p.m., Location: IAS S-101 |
Abstract: |
We fix F a local non archmedean field of characteristic zero, G the points over F of an algebraic reductive group defined over F and s a rational involution of G defined over F. We note H the group of fixed points of G under the action of s and X(G,s) the connected component on the neutral element of the set of complex characters of G antiinvariant under the action of s. Let P be a s-parabolic subgroup of G, id est the intersection M of P with s(P) is a s-stable Levi subgroup, we construct from a irreducible, smooth representation r of M, a rational family of distributions above the algebraic variety X(G,s), which are H-invariant linear forms on tne smooth induced representation ind(P,G; r ). Our main trick is the use of homology of groups. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Pierre Albin, Courant |
Date: |
Friday, April 9, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
Internet Traffic Matrices and Compressive Sensing |
Presenter: |
Walter Willinger, Mathematics and Computer Science, Darthmouth College |
Date: |
Monday, April 12, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
Abstract: |
Internet traffic matrices (TMs) specify the traffic volumes between origins and destinations in a network over some time period. For example, origins and destinations can be individual IP addresses, prefixes, routers, points-of-presence (PoPs), or entire networks or Autonomous Systems (ASes). Past work on TMs has almost exclusively focused on large ASes such as AS7018 (AT&T) and their router- or PoP-level TMs, mainly because the latter are critical inputs to many basic network engineering tasks, and the thrust of much of this work has been on measurement and inference of TMs. A key remaining challenge in this area is how to cope with missing values that frequently arise in real-world TMs. This problem brings TM research into the realm of compressive sensing, a generic technique for dealing with missing observations that exploits the presence of structure or redundancy in data from many real-world systems. In particular, since real-world TMs have been found to be of low rank, the concept of compressive sensing is directly applicable, at least in theory. In this talk, I will report on novel applications of compressive sensing to TM interpolation and inference and discuss how the resulting techniques work in practice. I will end by describing some challenging open problems concerning measuring and inferring the completely unknown Internet-wide AS-level TM. (This is joint work with Y. Zhang and L. Qiu (Univ. of Texas) and M. Roughan (Univ. od Adelaide).) |
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Group Actions Seminar |
Topic: |
TBA |
Presenter: |
Daryl Cooper, University of California, Santa Barbara |
Date: |
Tuesday, April 13, 2010, Time: 12:30 p.m., Location: Fine Hall 322 |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Shin-Yao Jow, University of Pennsylvania |
Date: |
Tuesday, April 13, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Alex Kontorovich, Brown University and IAS |
Date: |
Thursday, April 15, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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Topology Seminar |
Topic: |
TBA |
Presenter: |
Ciprian Manolescu, UCLA |
Date: |
Thursday, April 15, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Julie Rowlett, Bonn |
Date: |
Friday, April 16, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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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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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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PACM Colloquium |
Topic: |
TBA |
Presenter: |
Jonathan Weare, Courant Institute for Mathematics, NYC |
Date: |
Monday, April 26, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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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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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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