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REVISED WITH ADDED SEMINARS |
APRIL 2011 |
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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 Geometry Seminar |
Topic: |
Kernels for categories of graded singularities |
Presenter: |
Matthew Ballard, University of Pennsylvania |
Date: |
Tuesday, April 26, 2011, Time: 4:30 p.m., Location: Fine Hall 322 |
Abstract: |
Due to work of D. Orlov, there is a strong relationship between the derived category of coherent sheaves on a hypersurface in projective space and the category of singularities of the Z-graded affine cone over the hypersurface. For a pair of graded hypersurfaces, I will describe another category of graded singularities which is equivalent to the category of functors between the pair. Combining our construction with Orlov's result and a result of B. To\"en provides interesting relationships between the derived categories of some projective varieties. This is joint work with D. Favero and L. Katzarkov. |
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Discrete Mathematics Seminar |
Topic: |
Tournament pathwidth and topological containment |
Presenter: |
Alexandra Fradkin, Princeton University |
Date: |
Thursday, April 28, 2011, Time: 2:15 p.m., Location: Fine Hall 224 |
Abstract: |
In this talk we will prove that for a set S of tournaments the following three statements are equivalent: - there exists k such that all members of S have pathwidth less than k; - there exists k such that no member of S contains k vertices that are pairwise k-connected; - there exists a digraph H such that no member of S contains a subdivision of H. As a consequence, we obtain a polynomial time algorithm to test whether a tournament contains a subdivision of a fixed digraph H. We note that the equivalent problem in general digraphs is NP-complete. Joint work with Paul Seymour. |
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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: |
see http://www.math.princeton.edu/~seminar/2010-11-sem/BuchstaberAbstract4-28-2011.pdf
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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: |
Parabolic equations and the Ricci flow on manifolds with boundary |
Presenter: |
Artem Pulemotov, University of Chicago |
Date: |
Friday, April 29, 2011, Time: 3:00 p.m., Location: Fine Hall 314 |
Abstract: |
In the first part of the talk, we will focus on a second-order quasilinear parabolic equation in a vector bundle over a compact manifold~$M$ with boundary. Our goal is to explore the short-time existence of solutions to this equation. In the second part, we will discuss the Ricci flow on~$M$. The objective is to propose a new boundary condition for the flow and state two short-time existence results. |
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MAY 2011 |
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Department Colloquium ***CANCELLED*** |
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: |
Higher order Fourier analysis |
Presenter: |
Balazs Szegedy, University of Toronto |
Date: |
Wednesday, May 11, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
In a famous paper Timothy Gowers introduced a sequence of norms U(k) defined for functions on abelian groups. He used these norms to give quantitative bounds for Szemeredi's theorem on arithmetic progressions. The behavior of the U(2) norm is closely tied to Fourier analysis. In this talk we present a generalization of Fourier analysis (called k-th order Fourier analysis) that is related in a similar way to the U(k+1) norm. Ordinary Fourier analysis deals with homomorphisms of abelian groups into the circle group. We view k-th order Fourier analysis as a theory which deals with morphisms of abelian groups into algebraic structures that we call "k-step nilspaces". These structeres are variants of structures introduced by Host and Kra (called parallelepiped structures) and they are close relatives of nil-manifolds. Our approach has two components. One is an uderlying algebraic theory of nilspaces and the other is a variant of ergodic theory on ultra product groups. Using this theory, we obtain inverse theorems for the U(k) norms on arbitrary abelian groups that generalize results by Green, Tao and Ziegler. As a byproduct we also obtain an interesting limit theory for functions on abelian groups in the spirit of the recently developed graph limit theory. |
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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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