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APRIL 2011 |
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| Department Colloquium |
| Topic: |
Limit Theorems for Translation Flows |
| Presenter: |
Alexander Bufetov, Steklov Institute of Mathematics and Rice University |
| Date: |
Wednesday, April 20, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
The talk is devoted to limit theorems for translation flows on flat surfaces. Consider a compact oriented surface of genus at least two endowed with a holomorphic one-form. The real and the imaginary parts of the one-form define two foliations on the surface, and each foliation defines an area-preserving translation flow. By a Theorem of H.Masur and W.Veech, for a generic surface these flows are uniquely ergodic. The first result of the talk, which extends earlier work of A.Zorich and G.Forni, is an asymptotic formula for time integrals of Lipschitz functions. One of the main objects of the talk is the space of finitely-additive Hoelder transverse invariant measures for our foliations. These measures are classified and related to G. Forni's invariant distributions of Sobolev regularity -1 for translation flows. Time integrals of Lipschitz functions are then shown to admit an asymptotic expansion in terms of the finitely-additive measures. Next, given an Lipschitz function of average zero on the surface, we consider its time integrals as random variables and study the limit behaviour of their probability distributions. Informally, the main result states that the probability distributions of time integrals converge to an orbit of an ergodic dynamical system in the space of random variables with compactly supported distributions. The argument relies on a symbolic representation of translation flows as suspension flows over Vershik's automorphisms, a construction developing one proposed by S.Ito. The talk is based on the preprint http://arxiv.org/abs/0804.3970 |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
On the Vershik-Kerov Conjecture Concerning the Shannon-McMillan-Breiman Theorem for the Plancherel Family of Measures on the Space of Young Diagrams |
| Presenter: |
Alexander Bufetov, Steklov Institute of Mathematics and Rice University |
| Date: |
Thursday, April 21, 2011, Time: 2:00 p.m., Location: Fine Hall 801 |
| Abstract: |
Vershik and Kerov conjectured in 1985 that dimensions of irreducible representations of finite symmetric groups, after appropriate normalization, converge to a constant with respect to the Plancherel family of measures on the space of Young diagrams. The statement of the Vershik-Kerov conjecture can be seen as an analogue of the Shannon-McMillan-Breiman Theorem for the non-stationary Markov process of the growth of a Young diagram. The limiting constant is then interpreted as the entropy of the Plancherel measure. The main result of the paper is the proof of the Vershik-Kerov conjecture. The argument is based on the methods of Borodin, Okounkov and Olshanski. The talk is based on the preprint arXiv:1001.4275 |
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| Discrete Mathematics Seminar |
| Topic: |
New Proofs in Graph Minors |
| Presenter: |
Paul Wollan, Sapienza University of Rome and Georgia Tech |
| Date: |
Thursday, April 21, 2011, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: |
The graph minor structure theorem of Robertson and Seymour gives an approximate characterization of graphs which do not contain a fixed graph H as a minor. The theorem has numerous applications including Robertson and Seymour's proof for the disjoint paths algorithm as well as the proof of Wagner's conjecture that graphs are well-quasi-ordered under the minor relation. The original proof of the structure theorem is quite long and technical. We will discuss a new and simpler proof which makes the result more widely accessible. This is joint work with Ken-ichi Kawarabayashi |
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| Algebraic Topology Seminar |
| Topic: |
Unstable operations in etale and motivic cohomology |
| Presenter: |
Chuck Weibel, Rutgers University |
| Date: |
Thursday, April 21, 2011, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
Epstein constructed cohomology operations P^i in etale cohomology, and Voevodsky constructed cohomology operations P^i in motivic cohomology. These differ from the topological operations because of twisting. We modify Henri Cartan's classification of unstable operations to classify all etale operations (they are the expected operations), and classify all weight one motivic operations. Here new operations arise, and we paint a conjectural picture in all weights. This is joint work with Bert Guillou. |
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| Joint Princeton University and IAS Number Theory Seminar |
| Topic: |
Algebraic cycles and Euler systems for real quadratic fields |
| Presenter: |
Henri Darmon, McGill University |
| Date: |
Thursday, April 21, 2011, Time: 4:30 p.m., Location: Fine Hall 214 |
| Abstract: |
I will discuss some possible applications of algebraic cycles and p-adic families of modular forms to the arithmetic of elliptic curves over abelian extensions of real quadratic fields. This is a report on work in progress with Victor Rotger and Ignacio Sols, and on earlier work with Massimo Bertolini and Kartik Prasanna. |
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| Topology Seminar |
| Topic: |
A combinatorial spanning tree model for knot Floer homology |
| Presenter: |
John Baldwin, Princeton University |
| Date: |
Thursday, April 21, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
I'll describe a new combinatorial method for computing the delta-graded knot Floer homology of a link in S3. Our construction comes from iterating an unoriented skein exact triangle discovered by Manolescu, and yields a chain complex for knot Floer homology which is reminiscent of that of Khovanov homology, but is generated (roughly) by spanning trees of the black graph of the link. This is joint work with Adam Levine. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
The Yamabe problem for the conformal fractional Laplacian |
| Presenter: |
Maria del Mar Gonzalez, Universitat Politècnica de Catalunya |
| Date: |
Friday, April 22, 2011, Time: 4:00 p.m., Location: Fine Hall 314 |
| Abstract: |
Based on the relations between scattering operators of asymptotically hyperbolic metrics and Dirichlet-to-Neumann operators of uniformly degenerate elliptic boundary value problems, we formulate fractional Yamabe problems that include the boundary Yamabe problem studied by Escobar. We observe an interesting Hopf type maximum principle together with interplays between analysis of weighted trace Sobolev inequalities and conformal structure of the underlying manifolds, which extend the phenomena displayed in the classic Yamabe problem and boundary Yamabe problem. This is joint work with J. Qing. |
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| PACM Colloquium |
| Topic: |
Learning from Labeled and Unlabeled Data: Global vs. Multiple Approaches |
| Presenter: |
Boaz Nadler, Weizmann Institute - Israel |
| Date: |
Monday, April 25, 2011, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
In recent years there is increasing interest in learning from both labeled and unlabeled data (a.k.a. semi-supervised learning, or SSL). The key assumption in SSL, under which an abundance of unlabeled data may help, is that there is some relation between the unknown response function to be learned and the marginal density of the predictor variables. In the first part of this talk I'll present a statistical analysis of two popular graph based SSL algorithms: Laplacian regularization method and Laplacian eigenmaps. In the second part I'll present a novel multiscale approach for SSL as well as supporting theory. Some intimate connections to harmonic analysis on abstract data sets will be discussed. Joint work with Nati Srebro (TTI), Xueyuan Zhou (Chicago), Matan Gavish (WIS/Stanford) and Ronald Coifman (Yale). |
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| Algebraic Topology Seminar |
| Topic: |
Integral and Rigid Elliptic Genera |
| Presenter: |
Victor Buchstaber, Steklov Mathematical Institute, Russian Academy of Sciences |
| Date: |
Thursday, April 28, 2011, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
Each Hirzebruch genus is de ned by the exponential of the corresponding formal group law. We will describe the formal group law associated with the general Weierstrass model of the elliptic curve with parameters ¹ = (¹1; ¹2; ¹3; ¹4; ¹6) and arithmetic Tate uniformization. We obtain the corresponding general elliptic genus which is Z[¹]-integral. Krichever genus is de ned by the Baker-Akhiezer function of an elliptic curve and has 4 parameters. This genus has the fundamental rigidity property on S1-equivariant SU-manifolds. We will introduce the universal Krichever formal group law and describe the conditions necessary and su cient for the elliptic formal group law to become the Krichever formal group law. We will obtain the list of corresponding integral genera with the rigidity property on S1-equivariant SU-manifolds. Main de nitions will be introduced during the talk. New results presented in the talk were obtained in recent joint works with E. Yu. Bunkova. |
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| Joint Princeton University and IAS Number Theory Seminar **please note special location** |
| Topic: |
Serre´s conjectures on the number of rational points of bounded height |
| Presenter: |
P. Salberger, Chalmers University |
| Date: |
Thursday, April 28, 2011, Time: 4:30 p.m., Location: S-101 at IAS |
| Abstract: |
We give a survey of recent results on conjectures of Heath-Brown and Serre on the asymptotic density of rational points of bounded height. The main tool in the proofs is a new global determinant method inspired by the local real and p-adic determinant methods of Bombieri-Pila and Heath-Brown. |
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| Topology Seminar |
| Topic: |
TBA |
| Presenter: |
Peter Ozsvath, MIT |
| Date: |
Thursday, April 28, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Artem Pulemotov, University of Chicago |
| Date: |
Friday, April 29, 2011, Time: 3:00 p.m., Location: Fine Hall 314 |
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| MAY 2011 |
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| Department Colloquium |
| Topic: |
TBA |
| Presenter: |
Gautam Chinta, The City University of New York |
| Date: |
Wednesday, May 4, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
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| Topology Seminar |
| Topic: |
TBA |
| Presenter: |
Liam Watson, UCLA |
| Date: |
Thursday, May 5, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Yannick Slre, Universite de Aix-Marseille III |
| Date: |
Friday, May 6, 2011, Time: 3:00 p.m., Location: Fine Hall 314 |
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| Department Colloquium |
| Topic: |
TBA |
| Presenter: |
Balazs Szegedy, University of Toronto |
| Date: |
Wednesday, May 11, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
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| Topology Seminar |
| Topic: |
A Heegaard Floer characterization of Borromean knots |
| Presenter: |
Yi Ni, Caltech |
| Date: |
Thursday, May 12, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
If the total rank of the knot Floer homology of a knot is equal to the total rank of the Heegaard Floer (hat) homology of the ambient 3-manifold, we say that the knot has simple knot Floer homology (or the knot is Floer simple). It is known that the unknot is the only Floer simple knot in S3. However, the question of determining all the Floer simple knots in general 3-manifolds is far from being solved. In this talk we will answer this question for the connected sums of S1\times S2: Such knots are essentially the Borromean knots. |
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| Algebraic Geometry Seminar |
| Topic: |
Theta Functions |
| Presenter: |
Hershal Farkas, Hebrew University of Jewish Law |
| Date: |
Tuesday, May 17, 2011, Time: 4:30 p.m., Location: Fine Hall 322 |
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