SEMINARS
Updated: 4-21-2010

   
APRIL 2010
   
Discrete Mathematics Seminar
Topic: The circumference of color-critical graphs
Presenter: Robin Thomas, Georgia Tech
Date:  Thursday, April 22, 2010, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: 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.
   
Algebraic Topology Seminar
Topic: Equivariant formality and beyond
Presenter: Matthias Franz, University of Western Ontario
Date:  Thursday, April 22, 2010, Time: 2:30 p.m., Location: Fine Hall 314
Abstract: A space with a torus action is called "equivariantly formal" if its equivariant cohomology (say, with rational coefficients) is free over the polynomial ring H^*(BT). Many interesting spaces fall into this class. A nice feature of them is that their equivariant cohomology can be easily computed from the fixed point set and the one-dimensional orbits. It turns out that this last property holds for more spaces than just the equivariant formal ones. We will characterise these spaces and present some examples. We will also discuss equivariant formality for cohomology with integer coefficients.
   
Differential Geometry and Geometric Analysis Seminar
Topic: Liouville-type theorem for nonnegative Bakry-Emery Ricci tensor
Presenter: Guofang Wei, UCSB
Date:  Friday, April 23, 2010, Time: 3:00 p.m., Location: Fine Hall 314
   
Topology Seminar ***Please note special date and location
Topic: Monodromy factorizations and symplectic fillings
Presenter: Olga Plamenevskaya, SUNY Stony Brook
Date:  Friday, April 23, 2010, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: 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 {\em all} compatible open books to detect Stein fillings. However, a theorem of Wendl says that if a compatible open book has planar pages, all Stein fillings are compatible with the {\em given} open books. To apply this theorem, we develop combinatorial techniques to study positive monodromy factorizations in the planar case. As a result, we can classify symplectic fillings for all contact structures on L(p,1), and detect non-fillability of certain contact structures on Seifert fibered spaces. (Joint with Jeremy Van Horn-Morris.)
   
Analysis Seminar
Topic: TBA
Presenter: Justin Holmer, Brown University
Date:  Monday, April 26, 2010, Time: 4:00 p.m., Location: Fine Hall 110
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: D. Maulik, MIT
Date:  Monday, April 26, 2010, Time: 4:30 p.m., Location: Fine Hall 314
   
PACM Colloquium
Topic: Toward practical rare event simulation in high dimensions
Presenter: Jonathan Weare, Courant Institute for Mathematics, NYC
Date:  Monday, April 26, 2010, Time: 4:30 p.m., Location: Fine Hall 214
Abstract: 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. He will introduce an estimator related to a deterministic control problem that not only has an optimal variance decay rate under certain conditions, but that can even have vanishingly small statistical relative error in the small noise limit. The method can be seen as the limit of a well known zero variance importance sampling scheme for diffusions which requires the solution of a second order partial differential equation.
   
Group Actions Seminar
Topic: TBA
Presenter: Andrzej Zuk, Université Paris 7
Date:  Tuesday, April 27, 2010, Time: 12:30 p.m., Location: Fine Hall 322
   
Algebraic Geometry Seminar
Topic: Cohomology groups of structure sheaves
Presenter: János Kollár, Princeton University
Date:  Tuesday, April 27, 2010, Time: 4:30 p.m., Location: Fine Hall 322
   
Mathematical Physics Seminar
Topic: Quasi-adiabatic continuation and the Topology of Many-body Quantum Systems
Presenter: Matthew Hastings, Microsoft Research
Date:  Tuesday, April 27, 2010, Time: 4:30 p.m., Location: Jadwin 343
Abstract: 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. I will explain the technique of quasi-adiabatic continuation, which provides a way to rigourously formulate many of the topological arguments made by physicists for these systems. In particular, I will discuss its application to a higher dimensional Lieb-Schultz-Mattis theorem (a statement about degeneracy of ground states, which can arise for topological reasons), where this technique was introduced in 2004, and its more recent application to proving quantum Hall conductance quantization for interacting systems.
   
Joint Princeton University and Institute for Advanced Study Number Theory Seminar ****RESCHEDULED (from April 22, 2010) ******
Topic: Deformation rings of group representations
Presenter: Bart de Smit, Universiteit Leiden
Date:  Thursday, April 29, 2010, Time: 4:30 p.m., Location: Fine Hall 214
Abstract: 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.
   
Topology Seminar
Topic: TBA
Presenter: Zoltan Szabo, Princeton University
Date:  Thursday, April 29, 2010, Time: 4:30 p.m., Location: Fine Hall 314
   
SPECIAL Ergodic Theory and Statistical Mechanics Seminar ***Please note special day and time
Topic: Dynamics of bouncing balls
Presenter: Dmitry Dolgopyat, University of Maryland
Date:  Friday, April 30, 2010, Time: 2:30 p.m., Location: Fine Hall 401
Abstract: 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.
   
Differential Geometry and Geometric Analysis Seminar
Topic: Complex Monge-Ampere equations on symplectic and hermitian manifolds
Presenter: Valentino Tosatti, Columbia University
Date:  Friday, April 30, 2010, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: 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.
   
Discrete Mathematics Seminar *** Please note special date and time
Topic: Large almost monochromatic subsets in hypergraphs
Presenter: Jacob Fox, Princeton University
Date:  Friday, April 30, 2010, Time: 3:30 p.m., Location: Fine Hall 224
Abstract: 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. This result is tight up to the constant c and answers an open question of Erdos and Hajnal from 1989 on discrepancy in hypergraphs. For t > 3 colors, it is known that there is a t-coloring of the triples of an N-element set whose largest monochromatic subset has cardinality only on the order of log log N. Thus, our result demonstrates that the maximum almost monochromatic subset that a t-coloring of the triples must contain is much larger than the corresponding monochromatic subset. This is in striking contrast with graphs, where these two quantities have the same order of magnitude. To prove our result, we obtain a new upper bound on the t-color Ramsey numbers of complete multipartite 3-uniform hypergraphs, which answers another open question of Erdos and Hajnal. Joint work with D. Conlon and B. Sudakov.
   
MAY 2010
   
PACM Colloquium
Topic: Sensor Registration and Synchronisation in Networks
Presenter: Stephen Howard, University of Melbourne, Australia
Date:  Monday, May 3, 2010, Time: 4:30 p.m., Location: Fine Hall 214
Abstract: 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. We are given noisy measurements of the transformations connecting the coordinate systems of certain pairs of sensor in the network. The goal is to find local algorithms which will, in a optimal statistical sense, align the coordinate systems across the network. The talk will show how this problem can be formulated as a gauge invariant statistical estimation problem, how it is related to the homology of graphs, and how statistical optimal local estimators can be constructed in a number of cases.
   
Group Actions Seminar
Topic: TBA
Presenter: Yves Cornulier, CNRS, Université de Rennes 1
Date:  Tuesday, May 4, 2010, Time: 12:30 p.m., Location: Fine Hall 322
   
Joint Princeton University and Institute for Advanced Study Number Theory Seminar
Topic: Selmer ranks of twists of elliptic curves
Presenter: Karl Rubin, UC Irvine
Date:  Thursday, May 6, 2010, Time: 4:30 p.m., Location: Fine Hall 214
Abstract: 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. As a consequence, under appropriate hypotheses there are many twists with Mordell-Weil rank zero, and (assuming the Shafarevich-Tate conjecture) many others with Mordell-Weil rank one. The talk will conclude with some speculation about the density of twists with a given Selmer rank.
   
Differential Geometry and Geometric Analysis Seminar
Topic: Front propagation and phase transitions for fractional diffusion equations
Presenter: Xavier Cabré, ICREA and Universitat Politècnica de Catalunya
Date:  Friday, May 7, 2010, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: Long-range or \anomalous" di ffusions, such as di ffusions given by the frac- tional powers (-\Delta)^s of the Laplacian, attract lately interest in Physics, Biol- ogy, and Finance. From the mathematical point of view, nonlinear analysis for fractional di ffusions is being developed actively in the last years. In this talk, I will describe recent results concerning front propagation for the nonlinear fractional KPP heat equation, \partial_t tu+(-\Delta)^su = u(1-u) in (0;1)Rn, 0  u  1, with s 2 (0; 1). In collaboration with J.-M. Roquejo re, we establish that fronts propagate at exponential speed |in contrast with the classical case s = 1 for which there is propagation at a constant KPP speed. I will also describe works in collaboration with Y. Sire and E. Cinti. They concern the fractional elliptic Allen-Cahn equation (-\Delta)^su = f(u) in Rn with s 2 (0; 1), a model being the bistable nonlinearity f(u) = u - u3. Our main results concern the existence and properties of \layer" or heteroclinic solutions, as well as of minimizers of the equation.
   
Analysis Seminar
Topic: On the soliton dynamics under a slowly varying medium for generalized KdV equations
Presenter: Claudio Munoz, University of Versailles
Date:  Monday, May 10, 2010, Time: 4:00 p.m., Location: Fine Hall 110
Abstract: 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. Moreover, unlike gKdV equations, we prove that there is no pure-soliton solution in this regime.
   
PACM Colloquium
Topic: Hydraulic Fractures: multiscale phenomena, asymptotic and numerical solutions
Presenter: Anthony Peirce, University of British Columbia
Date:  Monday, May 17, 2010, Time: 4:30 p.m., Location: Fine Hall 214
Abstract: 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. They are also used in a multiplicity of engineering applications, including: the deliberate formation of fracture surfaces in granite quarries; waste disposal; remediation of contaminated soils; cave inducement in mining; and fracturing of hydrocarbon bearing rocks in order to enhance production of oil and gas wells. Novel and emerging applications of this technology include CO2 sequestration and the enhancement of fracture networks to capture geothermal energy. I describe the governing equations in 1-2D as well as 2-3D models of HF, which involve a coupled system of degenerate nonlinear integro-partial differential equations as well as a free boundary. I demonstrate, via re-scaling the 1-2D model, how the active physical processes manifest themselves in the HF model and show how a balance between the dominant physical processes leads to special solutions. I discuss the challenges for efficient and robust numerical modeling of the 2-3D HF problem and some techniques recently developed to resolve these problems: including robust iterative techniques to solve the extremely stiff coupled equations and a novel Implicit Level Set Algorithm (ILSA) to resolve the free boundary problem. The efficacy of these techniques is demonstrated with numerical results. Relevant papers can be found at: http://www.math.ubc.ca/~peirce