

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 BoseEinstein 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: 
BoseEinstein 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 2D NavierStokes 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 BarnetLamb, 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, ShepherdBarron, and Taylor, showing that have certain Galois representations become automorphic after one makes a suitably large totallyreal 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 totallyreal, 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 BigelowKrammer). 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 3manifold 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 RicciDeTurck 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 HardyLittlewoodSobolev 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 Nparticle 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 FeynmanKac 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 supnorms of cusp forms 
Presenter: 
V. Blomer, University of Toronto 
Date: 
Thursday, February 26, 2009, Time: 4:30 p.m., Location: IAS SH101 
Abstract: 
Given an L^2normalized 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 nontrivial 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 nontrivial 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 manybody 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 GrossPitaevskii hierarchy. This is joint work with S. Klainerman and is a simplification, based on spacetime 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 nonlinear 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 nspace. 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 MorrisonKawamata cone conjecture holds for klt CalabiYau 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 onedimensional 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. zerovalued at most locations) or highly compressible in some basis, relatively few incoherent observations suffice to reconstruct the most significant nonzero 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 degree1 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 OceanAtmospheric 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 onedimensional 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 noiseassisted data analysis method, and the multidimensional 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: 
Sumproduct estimates via combinatorial geometry 
Presenter: 
PoShen Loh, Princeton University and UCLA 
Date: 
Thursday, March 26, 2009, Time: 12:30 p.m., Location: Fine Hall 314 
Abstract: 
Every twodimensional 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 A5/4. What could these two theorems possibly have in common, besides the fact that Endre Szemerédi coauthored 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: 
PoShen 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  UrbanaChampaign 
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 datavectors based on a small number of linear measurements. In its most basic form, robust CS can be viewed as a specialized errorcontrol coding scheme in which the data alphabet does not necessarily have the structure of a finite field and where the notion of a “paritycheck” is replaced by a more general functionality. It is therefore possible to combine and extend classical CS and codingtheoretic 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 lowcomplexity correlationmaximization algorithms that operate based on belief propagation iterations. Our problem analysis is motivated by a myriad of applications ranging from compressed sensing microarray designs, reliabilityreordering decoding of linear blockcodes, identification in multiuser 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 reactiondiffusion 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 reactiondiffusion 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 coagulationfragmentation 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 ddimensional "chessboard" can be completely covered by nonoverlapping 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 epsilonnet problem). I will present a new class of constructions that yield the first nontrivial lower bound on the weak epsilonnet 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: 
Stateoftheart 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 nonlinear, 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 stateoftheart 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 highdensity, hightemperature, highspeed 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 exascale 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, multiphysics 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: 
LeeYang 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 LeeYang 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 



