SEMINARS
Updated: 2-18-2009
 FEBRUARY 2009 Mathematical Physics Seminar *** Please note special date, time, and location Topic: Universality at the spectrum edge for random matrices with independent entries: Soshnikov's theorems and some extensions Presenter: Alex Sodin, Tel Aviv University Date: Wednesday, February 18, 2009, Time: 2:00 p.m., Location: Jadwin A08 Abstract: We shall discuss the distribution of extreme eigenvalues for several classes of random matrices with independent entries. In particular, we shall discuss the results of Soshnikov and some of their recent extensions, and the combinatorial questions that appear in the proofs. (Based on joint work with Ohad Feldheim). Department Colloqium Topic: Mathematical Questions Arising from Bose-Einstein Condensation Presenter: Israel Michael Sigal, University of Toronto and IAS Date: Wednesday, February 18, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Abstract: Bose-Einstein condensation was predicted by Einstein in 1925 and was experimentally discovered 70 years later. This discovery was followed by a flurry of activity in the physics community with many new experiments and with attempts to construct a theory of the newly discovered state of matter. In this talk I will review some recent rigorous results in the subject and outline open problems. Graduate Student Seminar Topic: Bend and break Presenter: Bhargav Bhatt, Princeton University Date: Thursday, February 19, 2009, Time: 12:30 p.m., Location: Fine Hall 314 Abstract: Our goal is to explain the following theorem due to Mori: Given a compact complex manifold X whose tangent bundle has lots of (holomorphic) determinantal sections (a Fano manifold), any pair of points on it lie in the image of a holomorphic map from the Riemann sphere P^1. Despite being a complex geometric statement, the only known proof of this result is by reduction to characteristic p. In this talk, we'll discuss what Fano manifolds are, explain the techniques that go into Mori's proof (reducing mod p, deformation theory of maps from curves), and the proof itself. Ergodic Theory and Statistical Mechanics Seminar Topic: The decay of Fourier modes of solutions of 2-D Navier-Stokes system Presenter: Dong Li , Institute for Advanced Study Date: Thursday, February 19, 2009, Time: 2:00 p.m., Location: Fine Hall 401 Ergodic Theory and Statistical Mechanics Seminar Topic: Numerical results related to the talk by D. Li Presenter: Nikolai I. Chernov, University of Alabama Date: Thursday, February 19, 2009, Time: 2:00 p.m., Location: Fine Hall 401 Discrete Mathematics Seminar Topic: Randomness extractors - applications and constructions Presenter: Avi Wigderson, Institute for Advanced Study Date: Thursday, February 19, 2009, Time: 2:15 p.m., Location: Fine Hall 224 Abstract: We will investigate the minimal requirements from a random source under which it is potentially useful for generating perfect randomness. The efficient procedures which utilize such sources, "randomness extractors", turn out to have amazing pseudorandomness properties and are useful in numerous contexts. We'll demonstrate applications in complexity theory, error correction and network design. We'll also describe some constructions of near optimal extractors, with tools from expander graphs and the recent proof of the Kakeya conjecture in finite fields. Number Theory Seminar Topic: Potential automorphy for certain Galois representations to GL(n) Presenter: Thomas Barnet-Lamb, Harvard University Date: Thursday, February 19, 2009, Time: 4:30 p.m., Location: Fine Hall 214 Abstract: I will describe recent generalizations of mine to a theorem of Harris, Shepherd-Barron, and Taylor, showing that have certain Galois representations become automorphic after one makes a suitably large totally-real extension to the base field. The main innovation is that the result applies to Galois representations to $\GL_n$, where the previous work dealt with representations to $\Sp_n$; I can also dispense with certain congruence conditions which existed in the earlier work, and work over a CM, rather than a totally-real, field. The main technique is the consideration of the cohomology the Dwork hypersurface, and in particular, of pieces of this cohomology other than the invariants under the natural group action. Topology Seminar Topic: Two generator subgroups of the pure braid group Presenter: Chris Leininger, U. Illinois, Urbana Date: Thursday, February 19, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Abstract: A group satisfies the "Tits alternative" if every subgroup is either virtually solvable or contains a nonabelian free group. This is named after J. Tits who proved that all finitely generated linear groups enjoy this property. The Tits alternative was established for braid groups by Ivanov and McCarthy, but now also follows from linearity (due to Bigelow-Krammer). I'll discuss joint work with D. Margalit, in which we prove a strong version of the Tits alternative for the pure braid groups: every two elements of the pure braid group either commute or generate a free group. The proof uses 3-manifold topology and actions on trees. Differential Geometry and Geometric Analysis Seminar Topic: Geometric flows with rough initial data Presenter: Tobias Lamm, University of British Columbia Date: Friday, February 20, 2009, Time: 3:00 p.m., Location: Fine Hall 314 Abstract: In a recent joint work with Herbert Koch (University of Bonn) we showed the existence of a global unique and analytic solution for the mean curvature flow (in arbitrary codimensions) and the Willmore flow of entire graphs for Lipschitz initial data with small Lipschitz norm. In this talk I will explain our construction and, if time permits, I will show how similar constructions can be used to obtain the existence of a global unique and analytic solution of the Ricci-DeTurck flow on euclidean space for bounded initial metrics which are close to the euclidean metric in $L^\infty$ and of the harmonic map flow for initial maps whose image is contained in a small geodesic ball. Analysis Seminar Topic: Classical convolution inequalities and Boltzmann equations for integrable angular section Presenter: Irene Gamba, University of Texas at Austin Date: Monday, February 23, 2009, Time: 4:00 p.m., Location: Fine Hall 110 Abstract: We study the integrability properties of the gain part of the Boltzmann collision operator using radial symmetrization techniques from harmonic analysis to show Young's inequality in the case of hard potentials and Hardy-Littlewood-Sobolev inequality for soft potentials. The contacts are given by exact formulas depending on the angular cross section. By applying these estimates we can revisit and obtain new results for existence and uniqueness to the corresponding space inhomogeneous equations with special initial data. This is work partly in collaboration with E. Carneiro and R. Alonso Algebraic Geometry Seminar Topic: TBA Presenter: Yichao Tian, IAS Date: Tuesday, February 24, 2009, Time: 4:30 p.m., Location: Fine Hall 322 Mathematical Physics Seminar Topic: Localization bounds for multiparticle systems Presenter: Simone Warzel, Tech. Univ. Munich Date: Tuesday, February 24, 2009, Time: 4:30 p.m., Location: Jadwin 343 Abstract: We discuss the spectral and dynamical properties of quantum systems of N particles on the lattice of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with parameters of the model are the strength of the disorder and the strength of the interparticle interaction. We present a proof that for all N there are regimes of high disorder, and/or weak enough interactions, for which the system exhibits spectral and dynamical localization. The localization bounds are expressed in terms of exponential decay in the Hausdorff distance in the configuration space. The results are derived through the analysis of fractional moments of the N-particle Green function, and related bounds on the eigenfunction correlators. (Joint work with Michael Aizenman). Department Colloqium Topic: Large N limit of random matrices, free probability and the graded algebra of a planar algebra Presenter: Vaugha Jones, Berkeley Date: Wednesday, February 25, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Discrete Mathematics Seminar Topic: TBA Presenter: Joel Spencer, New York University Date: Thursday, February 26, 2009, Time: 2:15 p.m., Location: Fine Hall 224 Ergodic Theory and Statistical Mechanics Seminar ***Please note special time Topic: Limit lognormal process, Selberg integral as Mellin transform, and intermittency differentiation. Presenter: Dmitry Ostrovsky Date: Thursday, February 26, 2009, Time: 4:00 p.m., Location: Fine Hall 401 Abstract: The limit lognormal process is a multifractal stochastic process with the remarkable property that its positive integral moments are given by the celebrated Selberg integral. We will give an overview of the limit lognormal construction followed by a summary of our results on functional Feynman-Kac equations and resulting intermittency expansions that govern its distribution. The talk will focus on the intermittency expansion for the Mellin transform. This expansion recovers Selberg’s formula for the positive integral moments and gives a novel product formula for the negative ones. By summing it in general using a moment constant method, we obtain an extension of Selberg’s finite product to the Mellin transform of a probability distribution in the form of an infinite product of ratios of gamma functions in the complex plane. This distribution is conjectured to be the limit lognormal distribution. Number Theory Seminar Topic: Bounding sup-norms of cusp forms Presenter: V. Blomer, University of Toronto Date: Thursday, February 26, 2009, Time: 4:30 p.m., Location: IAS SH-101 Abstract: Given an L^2-normalized cusp form f on a modular curve X_0(N), what can be said about pointwise bounds for f? For Hecke eigenforms, we will prove the first non-trivial bound in terms of the level N as well as hybrid bounds in terms of the level and the Laplacian eigenvalue. Similar techniques work for functions on other spaces, e.g. quotients of quaternion algebras. This is joint work with R. Holowinsky. Topology Seminar Topic: Topologically invariant Chern numbers of projective varieties Presenter: Dieter Kotschick, Munchen, IAS Date: Thursday, February 26, 2009, Time: 4:30 p.m., Location: Fine Hall 314 Abstract: In 1954 Hirzebruch asked which linear combinations of Chern numbers are topological invariants of smooth complex projective varieties. Until recently, this problem was wide open, with few non-trivial results. We give a complete solution in arbitrary dimensions. An interesting feature of this solution is how it is derived from the well known case of complex dimension two, which at first sight looks rather special and exceptional. Differential Geometry and Geometric Analysis Seminar Topic: TBA Presenter: Xianzhe Dai, UCSB Date: Friday, February 27, 2009, Time: 3:00 p.m., Location: Fine Hall 314 MARCH 2009 Analysis Seminar Topic: On the evolution of solutions to a many-body Schr\"odinger equation Presenter: Matei Machedon, University of Maryland Date: Monday, March 2, 2009, Time: 4:00 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 Erd\"os, 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: Algebraic surfaces and hyperbolic geometry Presenter: Burt Totaro, Cambridge University Date: Tuesday, March 3, 2009, Time: 4:30 p.m., Location: Fine Hall 322 Abstract: The intersection form on the group of line bundles on a complex algebraic surface always has signature (1,n) for some n. So the automorphism group of an algebraic surface always acts on hyperbolic n-space. For a class of surfaces including K3 surfaces and many rational surfaces, there is a close connection between the properties of the variety and the corresponding group acting on hyperbolic space. (In fancier terms: the Morrison-Kawamata cone conjecture holds for klt Calabi-Yau pairs in dimension 2.) Mathematical Physics Seminar Topic: TBA Presenter: Yuval Peres, UC Berkeley Date: Tuesday, March 3, 2009, Time: 4:30 p.m., Location: Jadwin 343 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: TBA Presenter: Zeev Dvir, Institute for Advanced Study Date: Thursday, March 5, 2009, Time: 2:15 p.m., Location: Fine Hall 224 Differential Geometry and Geometric Analysis Seminar Topic: TBA Presenter: Gabor Szekelyhidi, Columbia Date: Friday, March 6, 2009, Time: 3:00 p.m., Location: Fine Hall 314 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. Ergodic Theory and Statistical Mechanics Seminar Topic: TBA Presenter: Thomas Spencer, Institute for Advanced Study Date: Thursday, March 12, 2009, Time: 2:00 p.m., Location: Fine Hall 401 Discrete Mathematics Seminar Topic: TBA Presenter: Van Vu, Rutgers University Date: Thursday, March 12, 2009, Time: 2:15 p.m., Location: Fine Hall 224 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 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. 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 Date: Tuesday, March 24, 2009, Time: 4:30 p.m., Location: Jadwin 343 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: TBA Presenter: Detlev Buchholz , Univ of Goettingen Date: Tuesday, March 31, 2009, Time: 4:30 p.m., Location: Jadwin 343 APRIL 2009 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 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. 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 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 9, 2009, Time: 2:15 p.m., Location: Fine Hall 224 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 Analysis Seminar Topic: Stefan Problem with Surface Tension Presenter: Yan Guo, Brown University Date: Monday, May 4, 2009, Time: 4:00 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