SEMINARS
Updated: 2-11-2009
   
FEBRUARY 2009
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Limiting Distribution of Large Frobenius Numbers.
Presenter: Yakov Sinai and Ilya Vinogradov, Princeton University
Date:  Thursday, February 12, 2009, Time: 2:00 p.m., Location: Fine Hall 401
   
Discrete Mathematics Seminar
Topic: Square-paths and square-cycles in graphs with high minimum degree
Presenter: Jan Hladky, Charles University, Prague
Date:  Thursday, February 12, 2009, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: We investigate under which minimum-degree condition does a graph G contain a square-path and a square-cycle of a given length. We give precise thresholds, assuming that the order of G is large. This extends results of Fan and Kierstead [J. Combin. Theory Ser. B, 67(2), 167-182, 1996] and of Komlos, Sarkozy, and Szemeredi [Random Structures Algorithms, 9(1-2), 193-211, 1996] concerning containment of a spanning square-path and a spanning square-cycle, respectively. Joint work with P. Allen and J. Bottcher.
   
Topology Seminar
Topic: Computational geometry of moduli spaces of curves
Presenter: Peter Zogarf, Steklov Mathematical Institute
Date:  Thursday, February 12, 2009, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: A fast algorithm for computing intersection numbers of $\psi$- and $\kappa$-classes on moduli spaces of complex algebraic curves is proposed. As a consequence, the exact large genus asymptotics of these numbers (in particular, Weil-Petersson volumes) is numerically derived.
   
Differential Geometry and Geometric Analysis Seminar
Topic: Compactness Properties of the Space of Genus-$g$ Helicoids
Presenter: Jacob Bernstein, MIT
Date:  Friday, February 13, 2009, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: I will discuss a recent application of the work of Colding and Minicozzi of structure of embedded minimal surfaces in $\Real3$ to the study of compactness properties of the space of genus-$g$ helicoids. I will introduce the theory of Colding and Minicozzi and then show how it can be used to show (among other results) that the space of genus-one helicoids is compact (modulo symmetries). (Joint work with C. Breiner)
   
Analysis Seminar
Topic: Regularity of singular harmonic maps and axially symmetric stationary electrovacuum spacetimes
Presenter: Luc Nguyen, Rutgers University
Date:  Monday, February 16, 2009, Time: 4:00 p.m., Location: Fine Hall 110
Abstract: According to the Ernst-Geroch reduction, to each axially symmetric stationary vacuum/electro-vacuum spacetime, one can associate an axially symmetric harmonic map with singular boundary behavior. This idea has been exploited in the literature to construct asymptotically flat, axially symmetric stationary spacetimes with disconnected horizons, i.e. having multiple black holes. This family of spacetimes is uniquely parameterized by the “masses”, the “momenta”, the “charges” of the black holes and the “distances” between them. I’ll discuss the regularity of the corresponding reduced harmonic maps and its implication on the regularity of those spacetimes.
   
PACM Colloquium
Topic: Unusual Classical Ground States of Matter
Presenter: Salvatore Torquato, Chemistry, PMI, PACM, and PCTP
Date:  Monday, February 16, 2009, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:

A classical ground-state configuration of a system of interacting particles is one that minimizes the system potential energy. In the laboratory, such states are produced by slowly cooling a liquid to a temperature of absolute zero, and usually the ground states are crystal structures. However, our theoretical understanding of ground states is far from complete. For example, it is difficult to prove what are the ground states for realistic interactions. I discuss recent theoretical/computational methods that we have formulated to identify unusual crystal ground states as well as disordered ground state [1,2,3,4]. Although the latter possibility is counterintuitive, there is no fundamental reason why classical ground states cannot be aperiodic or disordered.

1) M. Rechtsman, F. H. Stillinger and S. Torquato, Synthetic Diamond and Wurtzite Structures Self-Assemble with Isotropic Pair Interactions , Physical Review E, vol. 75, 031403 (2007).
2) S. Torquato and F. H. Stillinger, "New Duality Relations for Classical Ground States," Physical Review Letters, vol. 100, 020602 (2008).
3) R. D. Batten, F. H. Stillinger and S. Torquato, "Classical Disordered Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous Materials," Journal of Applied Physics, vol. 104, 033504, (2008).
4) A. Scardicchio, F. H. Stillinger and S. Torquato, "Estimates of the Optimal Density of Sphere Packings in High Dimensions, Journal of Mathematical Physics, vol. 49, 043301 (2008).

   
Algebraic Geometry Seminar
Topic: Vojta's conjecture on Blowups and GCD Inequalities
Presenter: Yu Yasufuku, CUNY
Date:  Tuesday, February 17, 2009, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: Vojta's conjecture is a deep conjecture in Diophantine geometry, implying for example the Bombieri-Lang conjecture and the abc conjecture. In this talk, I will show some cases of the conjecture for blowup varieties. As a consequence, we derive some interesting inequalities of greatest common divisors. An important ingredient will be Schmidt's subspace theorem, both directly and indirectly through the results of Corvaja and Zannier.
   
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.
   
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: TBA
Presenter: Avi Wigderson, Institute for Advanced Study
Date:  Thursday, February 19, 2009, Time: 2:15 p.m., Location: Fine Hall 224
   
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.

   
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: TBA
Presenter: Irene Gamba, University of Texas at Austin
Date:  Monday, February 23, 2009, Time: 4:00 p.m., Location: Fine Hall 110
   
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: TBA
Presenter: Matei Machedon, University of Maryland
Date:  Monday, March 2, 2009, Time: 4:00 p.m., Location: Fine Hall 110
   
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
   
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
   
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
   
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.

   
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
   
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