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APRIL 2011 |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Polynomials in the Poisson scaling regime and gaps in n^(1/3) mod 1 |
| Presenter: |
Ilya Vinogradov, Princeton University |
| Date: |
Thursday, April 28, 2011, Time: 2:00 p.m., Location: Fine Hall 801 |
| Abstract: |
I will show that a quadratic polynomial exhibits "random" behavior on the circle in the Poisson scaling regime. Specifically I will prove that second moments are Poissonian and motivate why other moments could be Poissonian. An essential feature of the polynomial under consideration is that it has a sufficiently "random" constant term. In the corresponding exponential sum the main term will not come from "major arcs" but from other points. Finally, I will relate this problem to gaps in n^(1/3) mod 1 and show that Poisson moments (only two moments known at this time) for a specific quadratic polynomial imply exponential distribution for gaps. |
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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: |
Computational aspects of bordered Floer homology |
| Presenter: |
Peter Ozsvath, MIT |
| Date: |
Thursday, April 28, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
I will give a brief outline of bordered Floer homology, and explain how it can be used to describe aspects of Heegaard Floer homology. I will pay special emphasis on the branched double-covers of links in $S3$. This is joint work with Robert Lipshitz and Dylan Thurston. |
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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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| Algebraic Geometry Seminar |
| Topic: |
On the three compactifications of Siegel space |
| Presenter: |
Valery Alexeev, University of Georgia |
| Date: |
Tuesday, May 3, 2011, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
The moduli space of $A_g$ of abelian varieties has three classical toroidal compactifications: (1) perfect, (2) 2nd Voronoi, and (3) Igusa blowup, each with its own distinct geometric meaning. It is an interesting problem to understand exactly how these compactifications are related. I will show that (1) and (2) are isomorphic in a neighborhood of the image of a regular map from the Deligne-Mumford's moduli space $\bar M_g$, and that the rational map $\bar M_g \to \bar A_g$ for (3) is not regular for $g>8$. This is a joint work with Adrian Brunyate. |
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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 |
| Abstract: |
In this talk we consider Weierstrass points for the linear space of meromorphic functions on a compact Riemann surface whose divisors are multiples of $\frac{1}{P_0^{\alpha}P_1..P_{g-1}} where the points $P_i$ are points on the surface and $\alpha$ is a positive integer for which there is no holomorphic differential whose divisor is a multiple of $P_0^{\alpha)P_1..P_{g-1}$. Thus by the Riemann Roch theorem the dimension of the space is precisely $\alpha$. It develops that here are two different ways to define the Weierstrass points for this space. One way is to consider the Wronskian determinant of a basis for the space and to define the Weierstrass points as the zeros of the Wronskian and the weight of the Weierstrass point as the order of the zero. Another way is to consider, for a suitably chosen $ e \in C^g$, the Riemann theta function $ \theta(\alpha \Phi_{P_0}(P)-e)$ as a multivalued function on the surface, to define the Weierstrass points as its zeros and the weight of the Weierstrass point as the order of the zero. In this talk we deal with the question of whether to two definitions agree. We show that the sets of zeros are indeed the same and the problem is to detrmine whether the weights are the same. We give a partial solution to this problem. |
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