SEMINARS
Updated: 3-4-2009
 MARCH 2009 Department Colloqium Topic: Internal aggregation Models: From Diaconis-Fulton addition to a free boundary problem Presenter: Yuval Peres, University of California, Berkeley Date: Wednesday, March 4, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Abstract: Start with n particles at each of k points in the d-dimensional lattice, and let each particle perform simple random walk until it reaches an unoccupied site. The law of the resulting random set of occupied sites does not depend on the order in which the walks are performed, as shown by Diaconis and Fulton. We prove that if the distances between the starting points are suitably scaled, then the set of occupied sites has a deterministic scaling limit. In two dimensions, the boundary of the limiting shape is an algebraic curve of degree 2k. (For k = 1 it is a circle, as proved in 1992 by Lawler, Bramson and Griffeath.) The limiting shape can also be described in terms of a free-boundary problem for the Laplacian and quadrature identities for harmonic functions. I will describe applications to the abelian sandpile, and show simulations that suggest intriguing (yet unproved) connections with conformal mapping. Joint work with Lionel Levine. Graduate Student Seminar Topic: Lie Groups: Decomposition and Exponentiation Presenter: Kevin Wilson, Princeton University Date: Thursday, March 5, 2009, Time: 12:30 p.m., Location: Fine Hall 314 Abstract: A manifold with a smooth group structure is called a Lie group. Most of the information about Lie groups is captured by the tangent space at the identity and its Poisson bracket. The map relating these two structures is the exponential map (which in the compact case is the same as the geodesic exponential map). In this talk I'll start from first principles, give a brief overview of some decompositions of Lie groups based on this algebraic/analytic interplay, and use these facts to prove some interesting theorems about the image of $\exp$, viz., 1) If $\exp$ is a homeomorphism, then the group is solvable; and 2) while $\exp$ need not be surjective, the connected component of the identity is the square of the image of $\exp$. Ergodic Theory and Statistical Mechanics Seminar Topic: Hénon Renormalization Presenter: Marco Martens, State University of New York at Stony Brook Date: Thursday, March 5, 2009, Time: 2:00 p.m., Location: Fine Hall 401 Abstract: The geometry of strongly dissipative infinite renormalizable Hénon maps of period doubling type is surprisingly different from its one-dimensional counterpart. There are universal geometrical properties. However, the Cantor attractor is not geometrically rigid. Typically, it doesn't have bounded geometry. The average Jacobian is a topological invariant of the global attractor. Although the geometry of the Cantor attractor can be deformed by changing the average Jacobian, the geometry is universal in a distributional sense. Discrete Mathematics Seminar Topic: New bounds on the size of Kakeya sets in finite fields Presenter: Zeev Dvir, Institute for Advanced Study Date: Thursday, March 5, 2009, Time: 2:15 p.m., Location: Fine Hall 224 Abstract: A Kakeya set is a set in (F_q)^n (the n dimensional vector space over a field of q elements) which contains a line in every direction. In this talk I will present a recent result which gives a lower bound of (q/2)^n on the size of such sets. This bound is tight to within a multiplicative factor of two from the known upper bounds. The proof extends the polynomial method used in [Dvir 08, Saraf Sudan 08] and uses polynomials of unbounded degree. If time allows I will also discuss the applications to the explicit construction of mergers that follow from our techniques. Joint work with Kopparty, Saraf and Sudan (arxiv paper: "Extensions to the Method of Multiplicities, with applications to Kakeya Sets and Mergers"). Princeton University and IAS Number Theory Seminar Topic: A "Relative" Langlands Program and Periods of Automorhic Forms Presenter: Yiannis Sakellaridis, University of Toronto Date: Thursday, March 5, 2009, Time: 4:30 p.m., Location: Fine Hall 214 Abstract: Motivated by the relative trace formula of Jacquet and experience on period integrals of automorphic forms, we take the first steps towards formulating a "relative" Langlands program, i.e. a set of conjectures on H-distinguished representations of a reductive group G (both locally and globally), where H is a spherical subgroup of G. We prove several results in this direction. Locally, the spectrum of H\G is described with the help of the dual group associated to any spherical variety by Gaitsgory and Nadler. Globally, period integrals are conjectured to be Euler products of explicit local functionals, which we compute at unramified places and show that they are equal to quotients of L-values. If time permits, I will also discuss an approach which shows that different integral techniques for representing L-functions (e.g. Tate integrals, Rankin-Selberg integrals, period integrals) are, in fact, the same. This is in part joint work with Akshay Venkatesh. Topology Seminar Topic: Subgroup classification in Out(F_n) Presenter: Lee Mosher, Rutgers, Newark Date: Thursday, March 5, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Abstract: We prove that for every subgroup G of Out(F_n), one of two alternatives holds: either there is a finite index subgroup H < G and a nontrivial proper free factor A of F_n such that each element of H fixes the conjugacy class of A; or there is an element g \in G such that no nontrivial power of g fixes the conjugacy class of any nontrivial proper free factor of F_n. This theorem is an analogue of Ivanov's classification of subgroups of surface mapping class groups. It has application to bounded 2nd cohomology of Out(F_n), by combining with results of Bestvina-Feighn and of Hamenstadt. This work is joint with Michael Handel. Applied Mathematics Seminar Topic: A generalization of compact operators and its application to the existence of local minima without convexity Presenter: Pablo Pedregal, Professor of Applied Mathematics, UCLM Date: Friday, March 6, 2009, Time: 1:00 p.m., Location: Fine Hall 224 Abstract: We will introduce a certain property for a continuous (non-linear) operator that allows for the existence of local minima for functionals when the derivative complies with such a condition, without the need to check either weak lower semicontinuity or convexity. It turns out that this property is a generalization of the standard compactness for a continuous, non-linear operator. We illustrate the relevance of this condition by applying it to several problems in one space dimension. Differential Geometry and Geometric Analysis Seminar Topic: Greatest lower bounds on the Ricci curvature of Fano manifolds Presenter: Gabor Szekelyhidi, Columbia Date: Friday, March 6, 2009, Time: 3:00 p.m., Location: Fine Hall 314 Abstract: On Fano manifolds we study the supremum of the possible t such that there exists a metric in the first Chern class with Ricci curvature bounded below by t. For the projective plane blown up in one point we show that this supremum is 6/7. Group Actions Seminar Topic: A solution to an open problem of Cassels and Diophantine properties of cubic numbers Presenter: Uri Shapira, Hebrew University Date: Friday, March 6, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Abstract: We prove existence of real numbers x,y, possessing the following property: For any real a,b, liminf |n| ||nx - a|| ||ny - b|| = 0, where ||c|| denotes the distance of c to the nearest integer. This answers a 50 years old question of Cassels. The most interesting part of the result is that there are algebraic numbers with the above property! Analysis Seminar Topic: TBA Presenter: Mihai Tohaneanu, Berkeley Date: Monday, March 9, 2009, Time: 4:00 p.m., Location: Fine Hall 110 PACM Colloquium Topic: Compressive Optical Imaging Presenter: Rebecca Willett, Electrical Engineering, Duke University Date: Monday, March 9, 2009, Time: 4:00 p.m., Location: Fine Hall 214 Abstract: Recent work in the emerging field of compressed sensing indicates that, when feasible, judicious selection of the type of image transformation induced by imaging systems may dramatically improve our ability to perform reconstruction, even when the number of measurements is small relative to the size and resolution of the final image. The basic idea of compressed sensing is that when an image is very sparse (i.e. zero-valued at most locations) or highly compressible in some basis, relatively few incoherent observations suffice to reconstruct the most significant non-zero basis coefficients. These theoretical results have profound implications for the design of new imaging systems, particularly when physical and economical limitations require that these systems be as small, mechanically robust, and inexpensive as possible. In this talk I will describe the primary theory underlying compressed sensing and discuss some of the key mathematical challenges associated with its application to practical imaging systems. In particular, I will explore several novel imaging system designs based on compressed sensing, including compressive coded aperture and hyperspectral imagers, and examine the interplay between compressed sensing theory and the practical physical constraints which must be considered to effectively exploit this theory. Algebraic Geometry Seminar Topic: Compactified Jacobians and Abel maps for singular curves Presenter: Eduardo Esteves, IMPA Date: Tuesday, March 10, 2009, Time: 4:30 p.m., Location: Fine Hall 322 Abstract: We will discuss the problem of extending the construction of the classical Abel maps for smooth curves to the case of singular curves. The construction of degree-1 Abel maps will be shown, together with an approach for constructing higher degree Abel maps. Department Colloqium Topic: TBA Presenter: K. Soundararajan, Stanford Date: Wednesday, March 11, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Ergodic Theory and Statistical Mechanics Seminar Topic: Random walks with memory and statistical mechanics Presenter: Thomas Spencer, Institute for Advanced Study Date: Thursday, March 12, 2009, Time: 2:00 p.m., Location: Fine Hall 401 Abstract: This talk will review some results and conjectures about history dependent random walks. For example, edge reinforced random walk (ERRW) is a random walk which prefers to visit edges it has visited in the past. Diaconis showed that ERRW can be expressed as a random walk in a random environment. This environment is highly correlated and is described in terms of statistical mechanics. Phase transitions for closely related models are believed to occur in three dimensions. One phase corresponds to diffusion and the other phase to localization. This talk is based work of Merkl and Rolles on ERRW and my recent preprint with Disertori and Zirnbauer on a hyperbolic sigma model. Discrete Mathematics Seminar Topic: Inverse Littlewood-Offord theory, Smooth Analysis and the Circular Law Presenter: Van Vu, Rutgers University Date: Thursday, March 12, 2009, Time: 2:15 p.m., Location: Fine Hall 224 Abstract: A corner stone of the theory of random matrices is Wigner's semi-circle law, obtained in the 1950s, which asserts that (after a proper normalization) the limiting distribution of the spectra of a random hermitian matrix with iid (upper diagonal) entries follows the semi-circle law. The non-hermitian case is the famous Circular Law Conjecture, which asserts that (after a proper normalization) the limiting distribution of the spectra of a random matrix with iid entries is uniform in the unit circle. Despite several important partial results (Ginibre-Mehta, Girko, Bai, Edelman, Gotze-Tykhomirov, Pan-Zhu etc) the conjecture remained open for more than 50 years. Last year, T. Tao and I confirmed the conjecture in full generality. I am going to give an overview of this proof, which relies on rather surprising connections between various fields: combinatorics, probability, number theory and theoretical computer science. In particular, ideas from ADDITIVE COMBINATORICS play crucial roles. Number Theory Seminar Topic: The Rudnick-Sarnak Conjectures Presenter: Roman Holowinsky, University of Toronto Date: Thursday, March 12, 2009, Time: 4:30 p.m., Location: IAS S-101 Abstract: We'll discuss the quantum unique ergodicity conjecture of Rudnick and Sarnak and its holomorphic analogue. Highlighting the key ideas in recent joint with with K. Soundararajan, we'll demonstrate how one may use number theoretic techniques to solve this problem. Topology Seminar Topic: Congruence subgroup problem for mapping class groups Presenter: Ben McReynolds, University of Chicago Date: Thursday, March 12, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Abstract: I will discuss the congruence subgroup problem for mapping class groups, a problem that generalizes the classical one for arithmetic groups. I will discuss an unpublished proof by W. Thurston for an affirmative answer to this problem for genus zero mapping class groups. Time permitting, I will discuss the current state of this problem. Differential Geometry and Geometric Analysis Seminar Topic: TBA Presenter: Claude LeBrun, SUNY Stony Brook Date: Friday, March 13, 2009, Time: 3:00 p.m., Location: Fine Hall 314 Number Theory Seminar Topic: p-adically completed cohomology and the p-adic Langlands program Presenter: Matthew Emerton, Northwestern University Date: Thursday, March 19, 2009, Time: 4:30 p.m., Location: IAS S-101 Abstract: Speaking at a general level, a major goal of the p-adic Langlands program (from a global, rather than local, perspective) is to find a p-adic generalization of the notion of automorphic eigenform, the hope being that every p-adic global Galois representation will correspond to such an object. (Recall that only those Galois representations that are motivic, i.e. that come from geometry, are expected to correspond to classical automorphic eigenforms). In certain contexts (namely, when one has Shimura varieties at hand), one can begin with a geometric definition of automorphic forms, and generalize it to obtain a geometric definition of p-adic automorphic forms. However, in the non-Shimura variety context, such an approach is not available. Furthermore, this approach is somewhat remote from the representation-theoretic point of view on automorphic forms, which plays such an important role in the classical Langlands program. In this talk I will explain a different, and very general, approach to the problem of p-adic interpolation, via the theory of p-adically completed cohomology. This approach has close ties to the p-adic and mod p representation theory of p-adic groups, and to non-commutative Iwasawa theory. After introducing the basic objects (namely, the p-adically completed cohomology spaces attached to a given reductive group), I will explain several key conjectures that we expect to hold, including the conjectural relationship to Galois deformation spaces. Although these conjectures seem out of reach at present in general, some progress has been made towards them in particular cases. I will describe some of this progress, and along the way will introduce some of the tools that we have developed for studying p-adically completed cohomology, the most important of these being the Poincare duality spectral sequence. This is joint work with Frank Calegari. Analysis Seminar Topic: TBA Presenter: Robert Strain, Princeton University Date: Monday, March 23, 2009, Time: 4:00 p.m., Location: Fine Hall 110 PACM Colloquium Topic: The Empirical Mode Decomposition: the method, its progress, and open questions Presenter: Zhaohua Wu, Department of Meteorology & Center for Ocean-Atmospheric Prediction Studies, Florida State University Date: Monday, March 23, 2009, Time: 4:00 p.m., Location: Fine Hall 214 Abstract: The Empirical Mode Decomposition (EMD) was an empirical one-dimensional data decomposition method invented by Dr. Norden Huang about ten years ago and has been used with great success in many fields of science and engineering. In this talk, I will introduce, from the perspective of a physical scientist, the thinking behind and the algorithm of EMD; and its most recent developments, especially the Ensemble EMD (EEMD), a noise-assisted data analysis method, and the multi-dimensional EMD based on EEMD. I will also outline some open questions that we currently do not have answers, or even clues to the answers, such as how to optimize EMD algorithm, what is the mathematical nature of EMD. To a significant degree, this is a talk intended for obtaining helps from mathematicians. Analysis Seminar *** Rescheduled from March 2, 2009 - Please note special time Topic: On the evolution of solutions to a many-body Schrödinger equation Presenter: Matei Machedon, University of Maryland Date: Monday, March 23, 2009, Time: 5:00 p.m., Location: Fine Hall 110 Abstract: In part I, I will describe background material and a new proof for the uniqueness of solutions to the Gross-Pitaevskii hierarchy. This is joint work with S. Klainerman and is a simplification, based on space-time estimates, of an older proof of Erdös, Schlein and Yau. In Part II (joint work with M. Grillakis and D. Margetis) I will discuss a new, highly non-linear but explicit NLS in two space variables, whose solutions, if they exist, provide a second order correction to the usual tensor product approximation, which works in the Fock space norm. This is inspired by recent work of Rodnianski and Schlein, as well as older work of Wu. Algebraic Geometry Seminar Topic: TBA Presenter: Junecue Suh, MIT Date: Tuesday, March 24, 2009, Time: 4:30 p.m., Location: Fine Hall 322 Mathematical Physics Seminar Topic: TBA Presenter: Cedric Villani, ENS Lyon and IAS Date: Tuesday, March 24, 2009, Time: 4:30 p.m., Location: Jadwin 343 Department Colloqium Topic: TBA Presenter: Cedric Villani, ENS Lyon and IAS Date: Wednesday, March 25, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Graduate Student Seminar Topic: Sum-product estimates via combinatorial geometry Presenter: Po-Shen Loh, Princeton University and UCLA Date: Thursday, March 26, 2009, Time: 12:30 p.m., Location: Fine Hall 314 Abstract: Every two-dimensional drawing of any graph with V vertices and E ≥ 4V edges necessarily has at least E3/V2 pairs of crossing edges. Also, for every set A of real numbers, one of A+A (the set of all pairwise sums of elements of A) or A·A (the set of all pairwise products) has size at least |A|5/4. What could these two theorems possibly have in common, besides the fact that Endre Szemerédi co-authored both? Surprisingly, quite a lot. We will see the proof of the first result, followed by a series of fascinating consequences which culminate in the second result. Of course, the Probablistic Method will make a crucial appearance. Ergodic Theory and Statistical Mechanics Seminar Topic: TBA Presenter: Manfred Denker, Penn State University Date: Thursday, March 26, 2009, Time: 2:00 p.m., Location: Fine Hall 401 Discrete Mathematics Seminar Topic: Avoiding small subgraphs in Achlioptas processes Presenter: Po-Shen Loh, Princeton University and UCLA Date: Thursday, March 26, 2009, Time: 2:15 p.m., Location: Fine Hall 224 Abstract: Consider the following random process. At each round, one is presented with two random edges from the edge set of the complete graph on n vertices, and is asked to choose one of them. The selected edges are collected into a graph, which thus grows at the rate of one edge per round. This is known in the literature as an Achlioptas process, and has been studied by many researchers, mainly in the context of delaying or accelerating the appearance of the giant component. In our work, we investigate the classical small subgraph problem for Achlioptas processes. That is, given a fixed graph H, we study whether there is a deterministic online algorithm that substantially delays or accelerates a typical appearance of H, compared to its threshold of appearance in the random graph G(n,M). It is easy to see that one cannot accelerate the appearance of any fixed graph by more than a factor of 2, so we concentrate on the task of avoiding H. We determine thresholds for the avoidance of all cycles C_t, cliques K_t, and complete bipartite graphs K_{t,t}. Joint work with Michael Krivelevich and Benny Sudakov. Analysis Seminar Topic: TBA Presenter: Cedric Villani, Ecole Normale Supérieure de Lyon Date: Monday, March 30, 2009, Time: 4:00 p.m., Location: Fine Hall 110 PACM Colloquium Topic: On the interplay between coding theory and compressed sensing Presenter: Olgica Milenkovic, Electrical & Computer Engrg, University of Illinois - Urbana-Champaign Date: Monday, March 30, 2009, Time: 4:00 p.m., Location: Fine Hall 214 Abstract: Compressed sensing (CS) is a signal processing technique that allows for accurate, polynomial time recovery of sparse data-vectors based on a small number of linear measurements. In its most basic form, robust CS can be viewed as a specialized error-control coding scheme in which the data alphabet does not necessarily have the structure of a finite field and where the notion of a “parity-check” is replaced by a more general functionality. It is therefore possible to combine and extend classical CS and coding-theoretic paradigms in terms of introducing new minimum distance, reconstructions complexity, and quantization precision constraints. In this setting, we derive fundamental lower and upper bounds on the achievable compression rate for such constrained compressed sensing (CCS) schemes, and also demonstrate that sparse reconstruction in the presence of noise can be performed via low-complexity correlation-maximization algorithms that operate based on belief propagation iterations. Our problem analysis is motivated by a myriad of applications ranging from compressed sensing microarray designs, reliability-reordering decoding of linear block-codes, identification in multi-user communication systems, and fault tolerant computing. This is a joint work with Wei Dai and Vin Pham Hoa from the ECE Department at UIUC. Algebraic Geometry Seminar Topic: TBA Presenter: Nicolas Templier, IAS Date: Tuesday, March 31, 2009, Time: 4:30 p.m., Location: Fine Hall 322 Mathematical Physics Seminar Topic: UC Berkeley Presenter: Detlev Buchholz , Univ of Goettingen Date: Tuesday, March 31, 2009, Time: 4:30 p.m., Location: Jadwin 343 Abstract: Recently, Grosse and Lechner introduced a deformation procedure for non-interacting quantum field theories, giving rise to interesting examples of theories with non-trivial scattering matrix in any number of spacetime dimensions. In this talk we outline an extension of this procedure to the general framework of quantum field theory by introducing the concept of "warped" convolutions of operator functions. These convolutions have some intriguing properties which permit the deformation of arbitrary nets of algebras based on wedge-shaped regions of Minkowski space to nets which still satisfy Einstein's principles of relativistic covariance and causality. The deformed nets still admit a scattering theory and give rise to a deformed scattering matrix. 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 $n \ge 9$. Ergodic Theory and Statistical Mechanics Seminar Topic: TBA Presenter: Thierry Bodineau, Rutgers University Date: Thursday, April 2, 2009, Time: 2:00 p.m., Location: Fine Hall 401 Analysis Seminar Topic: TBA Presenter: Alexei Poltoratski, Texas A&M University Date: Monday, April 6, 2009, Time: 4:00 p.m., Location: Fine Hall 110 PACM Colloquium Topic: TBA Presenter: Shannon Hughes, PACM, Princeton University Date: Monday, April 6, 2009, Time: 4:00 p.m., Location: Fine Hall 214 Algebraic Geometry Seminar Topic: TBA Presenter: Jarod Alper, Columbia University Date: Tuesday, April 7, 2009, Time: 4:30 p.m., Location: Fine Hall 322 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 Analysis Seminar Topic: TBA Presenter: Camillo De Lellis, Universitaet Zuerich Date: Monday, April 13, 2009, Time: 4:00 p.m., Location: Fine Hall 110 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: TBA Presenter: Brian Osserman, UC Davis Date: Tuesday, April 14, 2009, Time: 4:30 p.m., Location: Fine Hall 322 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. 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: TBA Presenter: Jennifer Chayes, Microsoft Corporation Date: Monday, April 20, 2009, Time: 4:00 p.m., Location: Fine Hall 214 Algebraic Geometry Seminar Topic: TBA Presenter: Bjorn Poonen, MIT Date: Tuesday, April 21, 2009, Time: 4:30 p.m., Location: Fine Hall 322 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 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: TBA Presenter: Mihai Stoiciu, Williams College Date: Tuesday, April 28, 2009, Time: 4:30 p.m., Location: Jadwin 343 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 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