SEMINARS
Updated: 4-1-2009
 APRIL 2009 Department Colloqium Topic: On a conjecture of De Giorgi Presenter: Ovidiu Savin, Columbia Date: Wednesday, April 1, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Abstract: In 1978 De Giorgi made a conjecture about the symmetry of global solutions to a certain semilinear elliptic equation. He stated that monotone, bounded solutions of $$\triangle u=u^3-u$$ in $\mathbb{R}^n$ are one dimensional (i.e. the level sets of $u$ are hyperplanes) at least in dimension $n \le 8$. This problem is in fact closely related to the theory of minimal surfaces and it is sometimes referred to as "the $\varepsilon$ version of the Bernstein problem for mininimal graphs". In my talk I will explain this relation and I will give an idea about the proof of this conjecture for $n \le 8$. We mention that recently Del Pino, Kowalzyk and Wei provided a counterexample in dimension $n \ge 9$. Graduate Student Seminar Topic: Poisson summation formula Presenter: Ali Altug, Princeton University Date: Thursday, April 2, 2009, Time: 12:30 p.m., Location: Fine Hall 314 Abstract: I will first talk about the classical Poisson summation formula and then about a vast generalization of it, namely the trace formula. Ergodic Theory and Statistical Mechanics Seminar Topic: Large deviations of the current and phase transitions Presenter: Thierry Bodineau, IAS Date: Thursday, April 2, 2009, Time: 2:00 p.m., Location: Fine Hall 401 Abstract: Using the framework of the hydrodynamic limits, we will discuss the large deviations of a particle current through a diffusive system. The deviations can lead to dynamical phase transitions. In the case of asymmetric dynamics we will explain how the large deviation functional of the current provides a physical interpretation to the non-entropic solutions of Burgers equation. Joint Princeton and IAS Number Theory Seminar Topic: A rigid irregular connection on the projective line Presenter: Edward Frenkel, Berkeley Date: Thursday, April 2, 2009, Time: 4:30 p.m., Location: Fine Hall 214 Abstract: From the trace formula and the global Langlands correspondence one can infer the existence of a particular rigid l-adic local system on the projective line with tame ramification at 0 and wild ramification, of the mildest possible kind, at infinity, for any simple algebraic group. These l-adic local systems and their characteristic 0 counterparts have been constructed in some cases by Deligne and Katz. We will explain how to construct such a local system in the characteristic 0 case, uniformly for an arbitrary simple algebraic group, using the formalism of opers introduced by Beilinson and Drinfeld. Among other things, it provides an example of the geometric Langlands correspondence with wild ramification. This is joint work with Dick Gross. Topology Seminar Topic: Bordered Floer homology: bimodules and computations Presenter: Robert Lipshitz, Columbia University Date: Thursday, April 2, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Abstract: We will review the structure of bordered Floer homology, including how it depends on the parametrization of the boundary.  We will then discuss how to compute it, and consequently another algorithm for computing HF-hat. This is work in progress with Peter Ozsvath and Dylan Thurston. Discrete Mathematics Seminar ***Please note special day Topic: The number of 3-SAT functions Presenter: Jeff Kahn, Rutgers University Date: Friday, April 3, 2009, Time: 2:15 p.m., Location: TBA Abstract: We are interested in the number, say G(k,n), of k-SAT functions of n variables (a k-SAT function being a Boolean function representable by a k-SAT formula in, say, conjunctive normal form). We show that G(3,n) is asymptotic to 2^{n + {n \choose 3}}, a strong form of a conjecture of Bollobas, Brightwell and Leader. (The corresponding result for 2-SAT was conjectured by BB&L, and proved by Peter Allen and (independently but later) by the present authors. As usual, the case k=2 doesn't seem to shed much light on larger k, while one expects/hopes that k=3 is about as hard to handle as a general fixed k.) Joint with Liviu Ilinca Differential Geometry and Geometric Analysis Seminar Topic: 11-dimensional supergravity and Dirichlet problem for forms on asymptotically hyperbolic spaces Presenter: Robin Graham, IAS Date: Friday, April 3, 2009, Time: 3:00 p.m., Location: Fine Hall 314 Analysis Seminar Topic: Entire functions and gap theorems Presenter: Alexei Poltoratski, Texas A&M University Date: Monday, April 6, 2009, Time: 4:00 p.m., Location: Fine Hall 110 Abstract: Several classical problems of Analysis can be translated into a universal language based on Hilbert spaces of entire functions and kernels of Toeplitz operators. Problems that can be treated this way include completeness/minimality problems for systems of exponentials or special functions in L^2 and spectral problems for second order differential operators. This approach was used to solve some of such problems in our recent papers with Nikolai Makarov. In this talk I will show how the Toeplitz approach can be used to extend the so-called Beurling's Gap Theorem on the existence of gaps in the Fourier transform of a measure and to solve the Polya-Levinson problem on sampling sets for entire functions of exponential type zero. Algebraic Geometry Seminar Topic: Constructing moduli spaces of objects with infinite automorphisms Presenter: Jarod Alper, Columbia University Date: Tuesday, April 7, 2009, Time: 4:30 p.m., Location: Fine Hall 322 Abstract: Moduli problems parameterizing objects with infinite automorphisms (eg. semi-stable vector bundles) often do not admit coarse moduli schemes but may admit moduli schemes identifying certain non-isomorphic objects. I will introduce techniques to study such moduli stacks and address the question of how such moduli schemes can be intrinsically constructed. The crucial ingredient is the notion of a good moduli space for an Artin stack, which generalizes Mumford's geometric invariant theory and characterizes the desired geometric properties of a moduli scheme parameterizing objects with infinite automorphisms. Mathematical Physics Seminar Topic: Coupling Einstein's equations to Dirac spinors can prevent the big bang/crunch singularity in the Friedmann model. Presenter: Christian Hainzl, University of Alabama at Birmingham Date: Tuesday, April 7, 2009, Time: 4:30 p.m., Location: Jadwin 343 Abstract: We consider a spatially homogeneous and isotropic system of Dirac particles coupled to classical gravity. We recover, on the one hand, the dust and radiation dominated closed Friedmann-Robertson-Walker space-times. On the other hand, we find particular solutions where the oscillations of the Dirac spinors prevent the formation of the big bang or big crunch singularity. This is joint work with F. Finster. Department Colloqium Topic: TBA Presenter: Igor Rodnianski, Princeton University Date: Wednesday, April 8, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Ergodic Theory and Statistical Mechanics Seminar Topic: TBA. Presenter: Corinna Ulcigrai, University of Bristol Date: Thursday, April 9, 2009, Time: 2:00 p.m., Location: Fine Hall 401 Discrete Mathematics Seminar Topic: TBA Presenter: William Cook, Georgia Tech. Date: Thursday, April 9, 2009, Time: 2:15 p.m., Location: Fine Hall 224 Topology Seminar ***Please note special time and location Topic: Existence and rigidity of pseudo-Anosov flows transverse to R-covered foliations Presenter: Sergio Fenley, Princeton University and Florida StateUniversity Date: Thursday, April 9, 2009, Time: 4:00 p.m., Location: Fine Hall 401 Abstract: Pseudo-Anosov flows are extremely common in three manifolds and they are very useful. How many pseudo-Anosov flows are there in a manifold up to topological conjugacy? We analyse this question in the context of flows transverse to a given foliation F. We prove that if F is R-covered (leaf space in the universal cover is the real numbers) then there are at most two pseudo-Anosov flows transverse to F. In addition if there are two, then the manifold is hyperbolic and the the foliation F blows down to a foliation topologically conjugate to the stable foliation of a particular type of an Anosov flow. The results use the topological theory of pseudo-Anosov flows, the universal circle for foliations and the geometric theory of R-covered foliations. We also discuss the existence of transverse pseudo-Anosov flows in this setting. Joint Princeton University and Institute for Advanced Study Analysis Seminar Topic: $h$--Principle and fluid dynamics Presenter: Camillo De Lellis, Universitaet Zuerich Date: Monday, April 13, 2009, Time: 4:00 p.m., Location: Fine Hall 110 Abstract: In the early nineties Scheffer produced a complicated example of a nontrivial weak solution to the incompressible Euler equations, having compact support in space and time. Subsequent papers by Shnirelman produced other examples of quite irregular solutions by different, yet complicated, methods. In a recent joint work with L\'aszl\'o Sz\'ekelyhidi we have used a suitable $h$--principle'' to produce solutions with the same behavior in a relatively simple way. Our approach answers to further questions left open by the works of Scheffer and Shnirelman and might be relevant in understanding a long--standing conjecture of Onsager. The same kind of analysis has relevant applications also to the theory of hyperbolic systems of conservation laws and shares some surprising similarities with aspects of the theory of fully developed turbulence. ***Please note that there will be an additional talk by the speaker at IAS Analysis Seminar ***Please note special time Topic: New results for reaction-diffusion equations arising from reversible chemistry Presenter: Laurent Desvillettes, ENS Cachan Date: Monday, April 13, 2009, Time: 5:00 p.m., Location: Fine Hall 110 Abstract: Entropy/entropy dissipation methods have been used with success lately in the study of the large time behavior of kinetic equations, nonlinear diffusions, etc., and have led to the development of the concept of hypocoercivity. They are also very useful in the context of reaction-diffusion equations (especially when they are derived from reversible chemistry), where they lead to new results of convergence to equilibrium as well as new results of existence of weak and strongs solutions. We shall detail some of those results, together with their links with recent works on coagulation-fragmentation models, and the use of results of regularity for singular parabolic problems. Algebraic Geometry Seminar Topic: Vector bundles with sections Presenter: Brian Osserman, UC Davis Date: Tuesday, April 14, 2009, Time: 4:30 p.m., Location: Fine Hall 322 Abstract: Classical Brill-Noether theory studies, for given g, r, d, the space of line bundles of degree d with r+1 global sections on a curve of genus g. We will review the main results in this theory, and the role of degeneration techniques in proving them, and then we will discuss the situation for higher-rank vector bundles, where even the most basic questions remain wide open. Mathematical Physics Seminar Topic: An Asymptotic Expansion for the Dimer Lambda_d Presenter: Paul Federbush, University of Michigan Date: Tuesday, April 14, 2009, Time: 4:30 p.m., Location: Jadwin 343 Abstract: The dimer problem is to count the number of ways a d-dimensional "chessboard" can be completely covered by non-overlapping dimers (dominoes), each dimer covering two nearest neighbor boxes. The number is ~exp(Lambda_d*V) as the volume V goes to infinity. It has been long known Lambda_d ~ (1/2)ln(d) +(1/2)(ln(2)-1) We derive an asymptotic expansion whose first few terms are Lambda_d ~ (1/2)ln(d) +(1/2)(ln(2)-1) +(1/8)(1/d) + (5/96)(1/d2) + (5/64)(1/d3) The last term here was calculated by computer, and we conjecture the next term will never be explicitly computed ( just by reason of required computer time ). The expansion is not yet rigorously established. Department Colloqium Topic: TBA Presenter: Giovanni Forni, University of Maryland Date: Wednesday, April 15, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Ergodic Theory and Statistical Mechanics Seminar Topic: TBA. Presenter: Giovanni Forni, University of Maryland Date: Thursday, April 16, 2009, Time: 2:00 p.m., Location: Fine Hall 401 Discrete Mathematics Seminar Topic: Geometric selection theorems Presenter: Boris Bukh, Princeton University and UCLA Date: Thursday, April 16, 2009, Time: 2:15 p.m., Location: Fine Hall 224 Abstract: In combinatorial geometry one frequently wants to select a point or a set of points that meets many simplices of a given family. The two examples are choosing a point in many simplices spanned by points of some P in R^d, and choosing a small set of points which meets the convex hull of every large subset of P (the weak epsilon-net problem). I will present a new class of constructions that yield the first nontrivial lower bound on the weak epsilon-net problem, and improve the best bounds for several other selection problems. Joint work with Jiří Matoušek and Gabriel Nivasch. Joint Princeton and IAS Number Theory Seminar Topic: Stable topology of Hurwitz spaces and arithmetic counting problems Presenter: Jordan Ellenberg, University of Wisconsin - Madison Date: Thursday, April 16, 2009, Time: 4:30 p.m., Location: Fine Hall 214 Abstract: We will discuss some arithmetic counting problems, ranging from the antique (how many squarefree integers are there in [0..N]?) to the au courant (conjectures of Bhargava and Cohen-Lenstra about the distributions of discriminants and of class groups.) When considered over function fields, these conjectures reveal themselves as having to do with stabilization of cohomology of moduli spaces of covers of curves, or Hurwitz spaces. We will report on progress on the topological study of Hurwitz spaces, which leads to information about arithmetic counting problems over function fields over finite fields; for instance, a version of Cohen-Lenstra "correct up to the constant" for F_q(t). If time permits I will try to give a picture of the rather general ensemble of arithmetic counting conjectures suggested by the method (e.g. -- for how many squarefree integers in [0..N] is there a totally real quintic extension of Q with discriminant N?) and explain how to prove versions of these conjectures in the much easier regime where "q goes to infinity first." (joint work with Akshay Venkatesh and Craig Westerland) Topology Seminar Topic: TBA Presenter: Zoltan Szabo, Princeton University Date: Thursday, April 16, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Analysis Seminar Topic: TBA Presenter: Diogo Arsenio, Courant Institute Date: Monday, April 20, 2009, Time: 4:00 p.m., Location: Fine Hall 110 PACM Colloquium Topic: Interdisciplinarity in the Age of Networks Presenter: Jennifer Chayes, Microsoft Corporation Date: Monday, April 20, 2009, Time: 4:00 p.m., Location: Fine Hall 214 Abstract: Everywhere we turn these days, we find that networks have become increasing appropriate descriptions of relevant interactions. In the high tech world, we see the Internet, the World Wide Web, mobile phone networks, and a variety of online social networks. In economics, we are increasingly experiencing both the positive and negative effects of a global networked economy. In epidemiology, we find disease spreading over our ever growing social networks, complicated by mutation of the disease agents. In problems of world health, distribution of limited resources, such as water resources, quickly becomes a problem of finding the optimal network for resource allocation. In biomedical research, we are beginning to understand the structure of gene regulatory networks, with the prospect of using this understanding to manage the many diseases caused by gene mis-regulation. In this talk, I look quite generally at some of the models we are using to describe these networks, processes we are studying on the networks, algorithms we have devised for the networks, and finally, methods we are developing to indirectly infer network structure from measured data. In particular, I will discuss models and techniques which cut across many disciplinary boundaries. Ergodic Theory and Statistical Mechanics Seminar***Pleaset note special date Topic: An explicit approach to the control of Lyapunov exponents Presenter: Ilya Goldsheid, Queen Mary, University of London Date: Tuesday, April 21, 2009, Time: 2:00 p.m., Location: Fine Hall 401 Abstract: I shall discuss a new approach to the proof the exponential growth of products of random matrices. The classical Furstenberg's analysis relies on properties of infinite-dimensional unitary representations. The method I am going to discuss uses finite-dimensional representations and allows one to have a more explicit control over Lyapunov exponents. Algebraic Geometry Seminar Topic: Automorphisms mapping a point into a subvariety Presenter: Bjorn Poonen, MIT Date: Tuesday, April 21, 2009, Time: 4:30 p.m., Location: Fine Hall 322 Abstract: Given a variety X, a point x in X, and a subvariety Z of X, is there an automorphism of X mapping x into Z? We prove that this problem is undecidable. Department Colloqium Topic: TBA Presenter: J. M. Bismut Date: Wednesday, April 22, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Ergodic Theory and Statistical Mechanics Seminar Topic: TBA Presenter: Michael Hochman, Princeton University Date: Thursday, April 23, 2009, Time: 2:00 p.m., Location: Fine Hall 401 Discrete Mathematics Seminar Topic: TBA Presenter: Maria Chudnovsky, Columbia University Date: Thursday, April 23, 2009, Time: 2:15 p.m., Location: Fine Hall 224 Topology Seminar Topic: TBA Presenter: Kekiko Kawamuro, IAS Date: Thursday, April 23, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Analysis Seminar Topic: Stefan Problem with Surface Tension Presenter: Yan Guo, Brown University Date: Monday, April 27, 2009, Time: 4:00 p.m., Location: Fine Hall 110 PACM Colloquium Topic: State-of-the-art Computer Simulations of Supernova Explosions Presenter: Adam Burrows, Astrophysics, Princeton University Date: Monday, April 27, 2009, Time: 4:00 p.m., Location: Fine Hall 214 Abstract: To simulate supernova explosions, one must solve simultaneously the non-linear, coupled partial differential equations of radiation hydrodynamics. What's more, due to a variety of instabilities and asymmetries, this must eventually be accomplished in 3D. The current state-of-the-art is 2D, plus rotation and magnetic fields (assuming axisymmetry). Nevertheless, with the current suite of codes, we have been able to explore the evolution of the high-density, high-temperature, high-speed environment at the core of a massive star at death. It is in this core that the supernova explosion is launched. However, the complexity of the problem has to date obscured the essential physics and mechanisms of the phenomenon, making it indeed one of the "Grand Challenges" of 21st century astrophysics. Requiring forefront numerical algorithms and massive computational resources, the resolution of this puzzle awaits the advent of peta- and exa-scale architectures and the software to efficiently use them. In this talk, I will review the current state of the science and simulations as we plan for the fully 3D, multi-physics capabilities that promise credibly to crack open this obdurate astrophysical nut. Algebraic Geometry Seminar Topic: TBA Presenter: Chad Schoen, Duke University Date: Tuesday, April 28, 2009, Time: 4:30 p.m., Location: Fine Hall 322 Mathematical Physics Seminar Topic: Eigenvalue Statistics for Random CMV Matrices Presenter: Mihai Stoiciu, Williams College Date: Tuesday, April 28, 2009, Time: 4:30 p.m., Location: Jadwin 343 Abstract: CMV matrices are the unitary analogues of one dimensional discrete Schrodinger operators. We consider CMV matrices with random coefficients and we study the statistical distribution of their eigenvalues. For slowly decreasing random coefficients, we show that the eigenvalues are distributed according to a Poisson process. For rapidly decreasing coefficients, the eigenvalues have rigid spacing (clock distribution). For a certain critical rate of decay we obtain the circular beta distribution. This is a joint work with Rowan Killip. Ergodic Theory and Statistical Mechanics Seminar Topic: Lee-Yang zeros for the Diamond Hierarchical Lattice and 2D rational dynamics Presenter: Mikhail Lyubich, State University of New York at Stony Brook Date: Thursday, April 30, 2009, Time: 2:00 p.m., Location: Fine Hall 401 Abstract: In a classical work of 1950's, Lee and Yang proved that zeros of the partition functions of the Ising models on graphs always lie on the unit circle. Distribution of these zeros is physically important as it controls phase transitions in the model. We study this distribution for a special Diamond Hierarchical Lattice". In this case, it can be described in terms of the dynamics of an explicit rational map in two variables. We prove partial hyperbolicity of this map on an invariant cylinder, and derive from it that the Lee-Yang zeros are organized asymptotically in a transverse measure for the central foliation. From the global complex point of view, the zero distributions get interpreted as slices of the Green (1,1)-current on the projective space. It is a joint work with Pavel Bleher and Roland Roeder. MAY 2009 Analysis Seminar ***Please note special date and time Topic: TBA Presenter: Lydia Bieri, Harvard University Date: Wednesday, May 6, 2009, Time: 5:00 p.m., Location: Fine Hall 110 Ergodic Theory and Statistical Mechanics Seminar Topic: TBA Presenter: Ilya Vinogradov and Francesco Cellarosi, Princeton University Date: Thursday, May 7, 2009, Time: 2:00 p.m., Location: Fine Hall 401