Seminars & Events for 2009-2010

April 22, 2010
2:30pm - 4:30pm
The circumference of color-critical graphs

A graph is k-critical if every proper subgraph is (k-1)-colorable, but the graph itself is not. We prove that every k-critical graph on n vertices has a cycle of length at least log n/(100 log k). Examples show the bound cannot be improved to exceed 2(k-1)log n/log(k-2). This is joint work with A. Shapira.

Speaker: Robin Thomas, Georgia Institute of Technology
Location:
Fine Hall 224
April 23, 2010
3:00pm - 5:00pm
Liouville-type theorem for nonnegative Bakry-Emery Ricci tensor
Speaker: Guofang Wei, University of California, Santa Barbara
Location:
Fine Hall 314
April 23, 2010
4:30pm - 6:30pm
Monodromy factorizations and symplectic fillings

By a fundamental result of Giroux, contact structures on 3-manifolds may be described via their open books decomposition. A contact manifold can arise as a boundary of a Stein domain if and only if it has a compatible open book whose monodromy is a product of positive Dehn twists. In principle, one has to examine all compatible open books to detect Stein fillings.

Speaker: Olga Plamenevskaya, SUNY at Stony Brook
Location:
Fine Hall 322
April 26, 2010
4:30pm - 6:30pm
Toward practical rare event simulation in high dimensions

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.

Speaker: Jonathan Weare, Courant Institute for Mathematics, NYC
Location:
Fine Hall 214
April 27, 2010
12:30pm - 1:30pm
Transcendence

We all know that e and π are transcendental. How about numbers like $e+π$, $e^π$, or $sqrt(2)^[sqrt(2)]$ If $2n$, $3n$, and $5n$ are all integers, must $n$ be an integer as well? What if only $2n$ and $3n$ are integers? In this talk, I will talk about these and related questions. In particular, I hope to prove the well-known fact above: $e$ and $π$ are transcendental.

Speaker: Boris Alexeev,
Location:
Fine Hall 314
April 27, 2010
4:30pm - 6:30pm
Quasi-adiabatic continuation and the Topology of Many-body Quantum Systems

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.

Speaker: Matthew Hastings, Microsoft Research
Location:
Jadwin Hall 343
April 27, 2010
4:30pm - 6:30pm
Cohomology groups of structure sheaves
Speaker: János Kollár, Princeton University
Location:
Fine Hall 322
April 29, 2010
4:30pm - 6:30pm
Deformation rings of group representations

The motivating open question for this talk is to find for a given prime $p$ all local $Z_p$-algebras which can occur as the deformation ring of some linear representation over $F_p$ of some finite group $G$. We will show for every $p$ that not all of them are complete intersections. This is joint work with Ted Chinburg and Frauke Bleher.

Speaker: Bart de Smit, Universiteit Leiden
Location:
Fine Hall 214
April 30, 2010
2:30pm - 4:30pm
Dynamics of bouncing balls

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.

Speaker: Dmitry Dolgopyat, University of Maryland
Location:
Fine Hall 401
April 30, 2010
3:00pm - 5:00pm
Complex Monge-Ampere equations on symplectic and hermitian manifolds

We will discuss a program to generalize the complex Monge-Ampere equation to symplectic and hermitian manifolds. We will explain to which extent the classical theory on Kahler manifolds extends to these two cases, and give some applications. This is joint work with B. Weinkove and partly with S.-T. Yau.

Speaker: Valentino Tosatti, Columbia University
Location:
Fine Hall 314
April 30, 2010
3:30pm - 5:30pm
Large almost monochromatic subsets in hypergraphs

We show that for all $t$ and $\epsilon > 0$ there is a constant $c=c(t,\epsilon)>0$ such that every $t$-coloring of the triples of an $N$-element set contains a subset $S$ of size $c(log N)^{1/2}$ such that at least a $1-\epsilon$ fraction of the triples of $S$ have the same color.

Speaker: Jacob Fox, Princeton University
Location:
Fine Hall 224
May 3, 2010
4:30pm - 6:30pm
Sensor Registration and Synchronisation in Networks

An important problem in distributed and networked sensing is registration of coordinate systems or synchronisation of clocks across the network. The main problem discussed in this talk is as follows. We have a network of sensors each with its own local coordinate system.

Speaker: Stephen Howard, University of Melbourne, Australia
Location:
Fine Hall 214
May 4, 2010
12:30pm - 1:30pm
Regularity of the Hardy Littlewood Function

$Lp$ boundedness of the Hardy-Littlewood function is a classic result in harmonic analysis. But not much is understood about the regularity of it. For instance, if your function $f$ is in the Sobolev W1,1 space, is its maximal function in$L1$? The answer to this question is unknown, but I will discuss our partial understanding.

Speaker: Kevin Hughes,
Location:
Fine Hall 314
May 5, 2010
4:30pm - 6:30pm
Elliptic curves and Hilbert's 10th problem

In this talk I will introduce elliptic curves and discuss recent work with Barry Mazur on ranks of elliptic curves in families of quadratic twists.

Speaker: Karl Rubin, University of California - Irvine
Location:
Fine Hall 314
May 6, 2010
4:30pm - 6:30pm
Selmer ranks of twists of elliptic curves

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.

Speaker: Karl Rubin, University of California - Irvine
Location:
Fine Hall 214
May 7, 2010
3:00pm - 5:00pm
Front propagation and phase transitions for fractional diffusion equations

Long range or anomalous diffusions, such as diffusions given by the fractional powers $(-\Delta)^s$ of the Laplacian, attract lately interest in Physics, Biology, and Finance. From the mathematical point of view, nonlinear analysis for fractional diffusions is being developed actively in the last years.

Speaker: Xavier Cabré, ICREA and Universitat Politècnica de Catalunya
Location:
Fine Hall 314
May 10, 2010
4:00pm - 6:00pm
On the soliton dynamics under a slowly varying medium for generalized KdV equations

We consider the problem of the soliton propagation, in a slowly varying medium, for a generalized Korteweg - de Vries equations (gKdV). We study the effects of inhomogeneities on the dynamics of a standard soliton. We prove that slowly varying media induce on the soliton solution large dispersive effects in large time.

Speaker: Claudio Munoz, University of Versailles
Location:
Fine Hall 110
May 17, 2010
4:30pm - 6:30pm
Hydraulic Fractures: multiscale phenomena, asymptotic and numerical solutions

Hydraulic fractures (HF) are a class of tensile fractures that propagate in brittle materials by the injection of a pressurized viscous fluid. In this talk I provide examples of natural HF and situations in which HF are used in industrial problems. Natural examples of HF include the formation of dykes by the intrusion of pressurized magma from deep chambers.

Speaker: Anthony Peirce, University of British Columbia
Location:
Fine Hall 214
April 17, 2012
11:36am - 11:36am
Stationary Phases and Spherical Averages

In this talk we will give an expository account of the following theorem of Stein about spherical averages, which asserts that if f is a function in Lp on Rn, with n≥3 and p>n/(n-1), then for almost every x in Rn, the average of f over a sphere of radius r centered at x is well-defined, and converges to f(x) as r tends to 0.

Speaker: Po-Lam Yung,
Location:
Fine Hall 314

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