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MARCH 2009 |
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Department Colloqium |
Topic: |
Quantum Unique Ergodicity and Number Theory |
Presenter: |
K. Soundararajan, Stanford |
Date: |
Wednesday, March 11, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
A fundamental problem in the area of quantum chaos is to understand the distribution of high eigenvalue eigenfunctions of the Laplacian on certain Riemannian manifolds. A particular case which is of interest to number theorists concerns hyperbolic manifolds arising as a quotient of the upper half-plane by a discrete ``arithmetic" subgroup of SL_2(R) (for example, SL_2(Z), and in this case the corresponding eigenfunctions are called Maass cusp forms). In this case, Rudnick and Sarnak have conjectured that the high energy eigenfunctions become equi-distributed. I will discuss some recent progress which has led to a resolution of this conjecture, and also on a holomorphic analog for classical modular forms. |
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Graduate Student Seminar |
Topic: |
Morse theory |
Presenter: |
Michael McBreen, Princeton University |
Date: |
Thursday, March 12, 2009, Time: 12:30 p.m., Location: Fine Hall 314 |
Abstract: |
Morse theory gives the cell structure of a manifold in terms of the critical points of a 'random' real-valued function on this manifold. Besides being clever and pleasing to the eye, it has given us Bott periodicity, counts of geodesics, periodic orbits of dynamical systems, Heegard Floer homology, the foundations of Mirror Symmetry and many many more riches. I will explain the construction in detail, then sketch the applications. |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
Random walks with memory and statistical mechanics |
Presenter: |
Thomas Spencer, Institute for Advanced Study |
Date: |
Thursday, March 12, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
Abstract: |
This talk will review some results and conjectures about history dependent random walks. For example, edge reinforced random walk (ERRW) is a random walk which prefers to visit edges it has visited in the past. Diaconis showed that ERRW can be expressed as a random walk in a random environment. This environment is highly correlated and is described in terms of statistical mechanics. Phase transitions for closely related models are believed to occur in three dimensions. One phase corresponds to diffusion and the other phase to localization. This talk is based work of Merkl and Rolles on ERRW and my recent preprint with Disertori and Zirnbauer on a hyperbolic sigma model. |
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Discrete Mathematics Seminar |
Topic: |
Inverse Littlewood-Offord theory, Smooth Analysis and the Circular Law |
Presenter: |
Van Vu, Rutgers University |
Date: |
Thursday, March 12, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
Abstract: |
A corner stone of the theory of random matrices is Wigner's semi-circle law, obtained in the 1950s, which asserts that (after a proper normalization) the limiting distribution of the spectra of a random hermitian matrix with iid (upper diagonal) entries follows the semi-circle law. The non-hermitian case is the famous Circular Law Conjecture, which asserts that (after a proper normalization) the limiting distribution of the spectra of a random matrix with iid entries is uniform in the unit circle.
Despite several important partial results (Ginibre-Mehta, Girko, Bai, Edelman, Gotze-Tykhomirov, Pan-Zhu etc) the conjecture remained open for more than 50 years. Last year, T. Tao and I confirmed the conjecture in full generality. I am going to give an overview of this proof, which relies on rather surprising connections between various fields: combinatorics, probability, number theory and theoretical computer science. In particular, ideas from ADDITIVE COMBINATORICS play crucial roles. |
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Number Theory Seminar |
Topic: |
The Rudnick-Sarnak Conjectures |
Presenter: |
Roman Holowinsky, University of Toronto |
Date: |
Thursday, March 12, 2009, Time: 4:30 p.m., Location: IAS S-101 |
Abstract: |
We'll discuss the quantum unique ergodicity conjecture of Rudnick and Sarnak and its holomorphic analogue. Highlighting the key ideas in recent joint with with K. Soundararajan, we'll demonstrate how one may use number theoretic techniques to solve this problem. |
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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. |
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Applied Mathematics Seminar |
Topic: |
Parallel-in-time algorithms and long-time integration |
Presenter: |
Claude Le Bris, University of Minnesota |
Date: |
Friday, March 13, 2009, Time: 1:00 p.m., Location: Fine Hall 224 |
Abstract: |
We investigate some issues related to the integration of Hamiltonian systems when using integrators that are parallel in time (the so-called class of parareal integrators, introduced by JL Lions, Y. Maday and G. Turinici in C. R. Acad. Sci., Paris, Sér. I, Math. 332, No.7, 661-668 (2001)). We show that, when appropriately adjusted, this original class of integrators enjoy excellent properties of conservation over long times. We present some elements of numerical analysis that explain the numerical observations. We also present a possible symmetrized version of such algorithms, with similar, agreeable properties. This is joint work with Yvon Maday (University Paris 6) and Frederic Legoll (Ecole des Ponts). |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
The Einstein-Weyl Equations, Scattering Maps, and Holomorphic Disks |
Presenter: |
Claude LeBrun, SUNY Stony Brook |
Date: |
Friday, March 13, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
Abstract: |
This talk will show that conformally compact, globally hyperbolic, Lorentzian Einstein-Weyl 3-manifolds are in natural one-to-one correspondence with orientation-reversing diffeomorphisms of the 2-sphere. The proof hinges on a holomorphic-disk analog of Hitchin's mini-twistor correspondence. |
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Number Theory Seminar |
Topic: |
p-adically completed cohomology and the p-adic Langlands program |
Presenter: |
Matthew Emerton, Northwestern University |
Date: |
Thursday, March 19, 2009, Time: 4:30 p.m., Location: IAS S-101 |
Abstract: |
Speaking at a general level, a major goal of the p-adic Langlands program (from a global, rather than local, perspective) is to find a p-adic generalization of the notion of automorphic eigenform, the hope being that every p-adic global Galois representation will correspond to such an object. (Recall that only those Galois representations that are motivic, i.e. that come from geometry, are expected to correspond to classical automorphic eigenforms).
In certain contexts (namely, when one has Shimura varieties at hand), one can begin with a geometric definition of automorphic forms, and generalize it to obtain a geometric definition of p-adic automorphic forms. However, in the non-Shimura variety context, such an approach is not available. Furthermore, this approach is somewhat remote from the representation-theoretic point of view on automorphic forms, which plays such an important role in the classical Langlands program.
In this talk I will explain a different, and very general, approach to the problem of p-adic interpolation, via the theory of p-adically completed cohomology. This approach has close ties to the p-adic and mod p representation theory of p-adic groups, and to non-commutative Iwasawa theory.
After introducing the basic objects (namely, the p-adically completed cohomology spaces attached to a given reductive group), I will explain several key conjectures that we expect to hold, including the conjectural relationship to Galois deformation spaces. Although these conjectures seem out of reach at present in general, some progress has been made towards them in particular cases. I will describe some of this progress, and along the way will introduce some of the tools that we have developed for studying p-adically completed cohomology, the most important of these being the Poincare duality spectral sequence.
This is joint work with Frank Calegari. |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Robert Strain, Princeton University |
Date: |
Monday, March 23, 2009, Time: 4:00 p.m., Location: Fine Hall 110 |
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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. |
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Analysis Seminar *** Rescheduled from March 2, 2009 - Please note special time |
Topic: |
On the evolution of solutions to a many-body Schrödinger equation |
Presenter: |
Matei Machedon, University of Maryland |
Date: |
Monday, March 23, 2009, Time: 5:00 p.m., Location: Fine Hall 110 |
Abstract: |
In part I, I will describe background material and a new proof for the uniqueness of solutions to the Gross-Pitaevskii hierarchy. This is joint work with S. Klainerman and is a simplification, based on space-time estimates, of an older proof of Erdös, Schlein and Yau.
In Part II (joint work with M. Grillakis and D. Margetis) I will discuss a new, highly non-linear but explicit NLS in two space variables, whose solutions, if they exist, provide a second order correction to the usual tensor product approximation, which works in the Fock space norm. This is inspired by recent work of Rodnianski and Schlein, as well as older work of Wu. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Junecue Suh, MIT |
Date: |
Tuesday, March 24, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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Mathematical Physics Seminar |
Topic: |
TBA |
Presenter: |
Cedric Villani, ENS Lyon and IAS |
Date: |
Tuesday, March 24, 2009, Time: 4:30 p.m., Location: Jadwin 343 |
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Department Colloqium |
Topic: |
TBA |
Presenter: |
Cedric Villani, ENS Lyon and IAS |
Date: |
Wednesday, March 25, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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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. |
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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 |
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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. |
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Topology Seminar |
Topic: |
Recurrence of random paths and counting closed geodesics in strata |
Presenter: |
Maryam Mirzakhani, Princeton University |
Date: |
Thursday, March 26, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
We discuss the problem of counting closed geodesics in a stratum of the moduli space of Abelian(quadratic) differentials. This is joint work with Alex Eskin and Kasra Rafi. |
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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 |
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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. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Nicolas Templier, IAS |
Date: |
Tuesday, March 31, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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Mathematical Physics Seminar |
Topic: |
UC Berkeley |
Presenter: |
Detlev Buchholz , Univ of Goettingen |
Date: |
Tuesday, March 31, 2009, Time: 4:30 p.m., Location: Jadwin 343 |
Abstract: |
Recently, Grosse and Lechner introduced a deformation procedure for non-interacting quantum field theories, giving rise to interesting examples of theories with non-trivial scattering matrix in any number of spacetime dimensions. In this talk we outline an extension of this procedure to the general framework of quantum field theory by introducing the concept of "warped" convolutions of operator functions. These convolutions have some intriguing properties which permit the deformation of arbitrary nets of algebras based on wedge-shaped regions of Minkowski space to nets which still satisfy Einstein's principles of relativistic covariance and causality. The deformed nets still admit a scattering theory and give rise to a deformed scattering matrix. |
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APRIL 2009 |
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Department Colloqium |
Topic: |
On a conjecture of De Giorgi |
Presenter: |
Ovidiu Savin, Columbia |
Date: |
Wednesday, April 1, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
In 1978 De Giorgi made a conjecture about the symmetry of global solutions to a certain semilinear elliptic equation. He stated that monotone, bounded solutions of $$ \triangle u=u^3-u$$ in $\mathbb{R}^n$ are one dimensional (i.e. the level sets of $u$ are hyperplanes) at least in dimension $n \le 8$. This problem is in fact closely related to the theory of minimal surfaces and it is sometimes referred to as "the $\varepsilon$ version of the Bernstein problem for mininimal graphs". In my talk I will explain this relation and I will give an idea about the proof of this conjecture for $n \le 8$. We mention that recently Del Pino, Kowalzyk and Wei provided a counterexample in dimension $n \ge 9$. |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
Large deviations of the current and phase transitions |
Presenter: |
Thierry Bodineau, IAS |
Date: |
Thursday, April 2, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
Abstract: |
Using the framework of the hydrodynamic limits, we will discuss the large deviations of a particle current through a diffusive system. The deviations can lead to dynamical phase transitions. In the case of asymmetric dynamics we will explain how the large deviation functional of the current provides a physical interpretation to the non-entropic solutions of Burgers equation. |
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Topology Seminar |
Topic: |
Bordered Floer homology: bimodules and computations |
Presenter: |
Robert Lipshitz, Columbia University |
Date: |
Thursday, April 2, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
We will review the structure of bordered Floer homology, including how it depends on the parametrization of the boundary. We will then discuss how to compute it, and consequently another algorithm for computing HF-hat. This is work in progress with Peter Ozsvath and Dylan Thurston. |
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Discrete Mathematics Seminar ***Please note special day |
Topic: |
TBA |
Presenter: |
Jeff Kahn, Rutgers University |
Date: |
Friday, April 3, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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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 |
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PACM Colloquium |
Topic: |
TBA |
Presenter: |
Shannon Hughes, PACM, Princeton University |
Date: |
Monday, April 6, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Jarod Alper, Columbia University |
Date: |
Tuesday, April 7, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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Department Colloqium |
Topic: |
TBA |
Presenter: |
Igor Rodnianski, Princeton University |
Date: |
Wednesday, April 8, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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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 |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
William Cook, Georgia Tech. |
Date: |
Thursday, April 9, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Camillo De Lellis, Universitaet Zuerich |
Date: |
Monday, April 13, 2009, Time: 4:00 p.m., Location: Fine Hall 110 |
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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. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Brian Osserman, UC Davis |
Date: |
Tuesday, April 14, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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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. |
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Department Colloqium |
Topic: |
TBA |
Presenter: |
Giovanni Forni, University of Maryland |
Date: |
Wednesday, April 15, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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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 |
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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. |
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Topology Seminar |
Topic: |
TBA |
Presenter: |
Zoltan Szabo, Princeton University |
Date: |
Thursday, April 16, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Diogo Arsenio, Courant Institute |
Date: |
Monday, April 20, 2009, Time: 4:00 p.m., Location: Fine Hall 110 |
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PACM Colloquium |
Topic: |
TBA |
Presenter: |
Jennifer Chayes, Microsoft Corporation |
Date: |
Monday, April 20, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
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Algebraic Geometry Seminar |
Topic: |
Automorphisms mapping a point into a subvariety |
Presenter: |
Bjorn Poonen, MIT |
Date: |
Tuesday, April 21, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
Abstract: |
Given a variety X, a point x in X, and a subvariety Z of X, is there an automorphism of X mapping x into Z? We prove that this problem is undecidable. |
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Department Colloqium |
Topic: |
TBA |
Presenter: |
J. M. Bismut |
Date: |
Wednesday, April 22, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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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 |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Maria Chudnovsky, Columbia University |
Date: |
Thursday, April 23, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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Topology Seminar |
Topic: |
TBA |
Presenter: |
Kekiko Kawamuro, IAS |
Date: |
Thursday, April 23, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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Analysis Seminar |
Topic: |
Stefan Problem with Surface Tension |
Presenter: |
Yan Guo, Brown University |
Date: |
Monday, April 27, 2009, Time: 4:00 p.m., Location: Fine Hall 110 |
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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. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Chad Schoen, Duke University |
Date: |
Tuesday, April 28, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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Mathematical Physics Seminar |
Topic: |
TBA |
Presenter: |
Mihai Stoiciu, Williams College |
Date: |
Tuesday, April 28, 2009, Time: 4:30 p.m., Location: Jadwin 343 |
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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. |
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MAY 2009 |
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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 |
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