

MARCH 2009 


Department Colloqium 
Topic: 
What goes on in a plasma 
Presenter: 
Cedric Villani, ENS Lyon and IAS 
Date: 
Wednesday, March 25, 2009, Time: 4:30 p.m., Location: Fine Hall 314 


Graduate Student Seminar 
Topic: 
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: 
Local limit theorems in ergodic theory 
Presenter: 
Manfred Denker, Penn State University 
Date: 
Thursday, March 26, 2009, Time: 2:00 p.m., Location: Fine Hall 401 
Abstract: 
We use Stone's version of a local limit theorem from 1969: Let $(X,{\cal F},T,m)$ be a measure preserving dynamical system. A measurable function $f:X\to \mathbb R$ satisfies a local limit theorem, if there are constants $A_n$ and $B_n\to\infty$ such that $$ B_nm( f+f\circ T+...+f\circ T^{n1} \in x_n+I) \to g(x)I,$$ where $(x_nA_n)/B_n \to x$ and where $g$ is the density of some stable distribution. An analogous definition applies in the lattice case.
For GibbsMarkov dynamical systems (including certain Markov shifts), such results can be established when the function is in the domain of attraction of a stable distribution. It also generalizes to nonMarkov situations for certain maps of the interval, including betatransformations. Applications to conservativity of dynamical systems and to Poincaré exponents are briefly discussed. 


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. 


Joint Princeton and IAS Number Theory Seminar 
Topic: 
CM liftings of abelian varieties 
Presenter: 
ChingLi Chai, University of Pennsylvania 
Date: 
Thursday, March 26, 2009, Time: 4:30 p.m., Location: Fine 214 


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. 


Differential Geometry and Geometric Analysis Seminar 
Topic: 
On the structure of Lagrangian submanifolds 
Presenter: 
Knut Smoczyk, Gottfried Wilhelm Leibniz Universität Hannover 
Date: 
Friday, March 27, 2009, Time: 3:00 p.m., Location: Fine Hall 314 
Abstract: 
This is a report on a recent joint project with Lars Schaefer. We derive results related to the minimality of Lagrangian submanifolds. In particular, these apply to Lagrangian 3folds and to Lagrangian submanifolds in twistor spaces over quaternionic Kaehler manifolds. We then use a splitting theorem to give a better description in dimensions four and five. 


Analysis Seminar 
Topic: 
Landau damping 
Presenter: 
Cedric Villani, Ecole Normale Supérieure de Lyon and IAS 
Date: 
Monday, March 30, 2009, Time: 4:00 p.m., Location: Fine Hall 110 
Abstract: 
Sixty years ago, Landau discovered a paradoxical collisionless relaxation effect in plasmas. The Landau damping is now one of the cornerstones of classical plasma physics. From the mathematical point of view, it has remained elusive so far, since the best available results prove the existence of some damped solutions, without saying anything about their genericity. I shall report on new advances, and a whole new mathematical theory, for this problem. I will discuss the physical implications of these results. This is joint work with Clement Mouhot.
Note: This is part of a series of related talks, there is additionally a colloquium and a math physics seminar. 


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: 
Arakelov invariants on modular curves 
Presenter: 
Nicolas Templier, IAS 
Date: 
Tuesday, March 31, 2009, Time: 4:30 p.m., Location: Fine Hall 322 
Abstract: 
Arakelov theory provides a rich set of invariants. We shall discuss the question of their limiting behavior in several classical examples, with an emphasis on heights of special points and of modular curves. 


Mathematical Physics Seminar 
Topic: 
Warped Convolutions: A novel tool in the construction of quantum field theories 
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 noninteracting quantum field theories, giving rise to interesting examples of theories with nontrivial 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 wedgeshaped regions of Minkowski space to nets which still satisfy Einstein's principles of relativistic covariance and causality. The deformed nets still admit a scattering theory and give rise to a deformed scattering matrix. 


APRIL 2009 


Department Colloqium 
Topic: 
On a conjecture of De Giorgi 
Presenter: 
Ovidiu Savin, Columbia 
Date: 
Wednesday, April 1, 2009, Time: 4:30 p.m., Location: Fine Hall 314 
Abstract: 
In 1978 De Giorgi made a conjecture about the symmetry of global solutions to a certain semilinear elliptic equation. He stated that monotone, bounded solutions of $$ \triangle u=u^3u$$ in $\mathbb{R}^n$ are one dimensional (i.e. the level sets of $u$ are hyperplanes) at least in dimension $n \le 8$. This problem is in fact closely related to the theory of minimal surfaces and it is sometimes referred to as "the $\varepsilon$ version of the Bernstein problem for mininimal graphs". In my talk I will explain this relation and I will give an idea about the proof of this conjecture for $n \le 8$. We mention that recently Del Pino, Kowalzyk and Wei provided a counterexample in dimension $n \ge 9$. 


Ergodic Theory and Statistical Mechanics Seminar 
Topic: 
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 nonentropic solutions of Burgers equation. 


Joint Princeton and IAS Number Theory Seminar 
Topic: 
A rigid irregular connection on the projective line 
Presenter: 
Edward Frenkel, Berkeley 
Date: 
Thursday, April 2, 2009, Time: 4:30 p.m., Location: Fine Hall 214 
Abstract: 
From the trace formula and the global Langlands correspondence one can infer the existence of a particular rigid ladic local system on the projective line with tame ramification at 0 and wild ramification, of the mildest possible kind, at infinity, for any simple algebraic group. These ladic local systems and their characteristic 0 counterparts have been constructed in some cases by Deligne and Katz. We will explain how to construct such a local system in the characteristic 0 case, uniformly for an arbitrary simple algebraic group, using the formalism of opers introduced by Beilinson and Drinfeld. Among other things, it provides an example of the geometric Langlands correspondence with wild ramification. This is joint work with Dick Gross. 


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 HFhat. This is work in progress with Peter Ozsvath and Dylan Thurston. 


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 


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 


Mathematical Physics Seminar 
Topic: 
TBA 
Presenter: 
Christian Hainzl, University of Alabama at Birmingham 
Date: 
Tuesday, April 7, 2009, Time: 4:30 p.m., Location: Jadwin 343 


Department Colloqium 
Topic: 
TBA 
Presenter: 
Igor Rodnianski, Princeton University 
Date: 
Wednesday, April 8, 2009, Time: 4:30 p.m., Location: Fine Hall 314 


Ergodic Theory and Statistical Mechanics Seminar 
Topic: 
TBA. 
Presenter: 
Corinna Ulcigrai, University of Bristol 
Date: 
Thursday, April 9, 2009, Time: 2:00 p.m., Location: Fine Hall 401 


Discrete Mathematics Seminar 
Topic: 
TBA 
Presenter: 
William Cook, Georgia Tech. 
Date: 
Thursday, April 9, 2009, Time: 2:15 p.m., Location: Fine Hall 224 


Topology Seminar ***Please note special time and location 
Topic: 
Existence and rigidity of pseudoAnosov flows transverse to Rcovered foliations 
Presenter: 
Sergio Fenley, Princeton University and Florida StateUniversity 
Date: 
Thursday, April 9, 2009, Time: 4:00 p.m., Location: Fine Hall 401 
Abstract: 
PseudoAnosov flows are extremely common in three manifolds and they are very useful. How many pseudoAnosov flows are there in a manifold up to topological conjugacy? We analyse this question in the context of flows transverse to a given foliation F. We prove that if F is Rcovered (leaf space in the universal cover is the real numbers) then there are at most two pseudoAnosov flows transverse to F. In addition if there are two, then the manifold is hyperbolic and the the foliation F blows down to a foliation topologically conjugate to the stable foliation of a particular type of an Anosov flow. The results use the topological theory of pseudoAnosov flows, the universal circle for foliations and the geometric theory of Rcovered foliations. We also discuss the existence of transverse pseudoAnosov flows in this setting. 


Joint Princeton University and Institute for Advanced Study Analysis Seminar 
Topic: 
$h$Principle and fluid dynamics 
Presenter: 
Camillo De Lellis, Universitaet Zuerich 
Date: 
Monday, April 13, 2009, Time: 4:00 p.m., Location: Fine Hall 110 
Abstract: 
In the early nineties Scheffer produced a complicated example of a nontrivial weak solution to the incompressible Euler equations, having compact support in space and time. Subsequent papers by Shnirelman produced other examples of quite irregular solutions by different, yet complicated, methods.
In a recent joint work with L\'aszl\'o Sz\'ekelyhidi we have used a suitable ``$h$principle'' to produce solutions with the same behavior in a relatively simple way. Our approach answers to further questions left open by the works of Scheffer and Shnirelman and might be relevant in understanding a longstanding conjecture of Onsager. The same kind of analysis has relevant applications also to the theory of hyperbolic systems of conservation laws and shares some surprising similarities with aspects of the theory of fully developed turbulence.
***Please note that there will be an additional talk by the speaker at IAS 


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. 


Department Colloqium 
Topic: 
TBA 
Presenter: 
Giovanni Forni, University of Maryland 
Date: 
Wednesday, April 15, 2009, Time: 4:30 p.m., Location: Fine Hall 314 


Ergodic Theory and Statistical Mechanics Seminar 
Topic: 
TBA. 
Presenter: 
Giovanni Forni, University of Maryland 
Date: 
Thursday, April 16, 2009, Time: 2:00 p.m., Location: Fine Hall 401 


Discrete Mathematics Seminar 
Topic: 
Geometric selection theorems 
Presenter: 
Boris Bukh, Princeton University and UCLA 
Date: 
Thursday, April 16, 2009, Time: 2:15 p.m., Location: Fine Hall 224 
Abstract: 
In combinatorial geometry one frequently wants to select a point or a set of points that meets many simplices of a given family. The two examples are choosing a point in many simplices spanned by points of some P in R^d, and choosing a small set of points which meets the convex hull of every large subset of P (the weak 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. 


Topology Seminar 
Topic: 
TBA 
Presenter: 
Zoltan Szabo, Princeton University 
Date: 
Thursday, April 16, 2009, Time: 4:30 p.m., Location: Fine Hall 314 


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 


Ergodic Theory and Statistical Mechanics Seminar***Pleaset note special date 
Topic: 
An explicit approach to the control of Lyapunov exponents 
Presenter: 
Ilya Goldsheid, Queen Mary, University of London 
Date: 
Tuesday, April 21, 2009, Time: 2:00 p.m., Location: Fine Hall 401 
Abstract: 
I shall discuss a new approach to the proof the exponential growth of products of random matrices. The classical Furstenberg's analysis relies on properties of infinitedimensional unitary representations. The method I am going to discuss uses finitedimensional representations and allows one to have a more explicit control over Lyapunov exponents. 


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. 


Department Colloqium 
Topic: 
TBA 
Presenter: 
J. M. Bismut 
Date: 
Wednesday, April 22, 2009, Time: 4:30 p.m., Location: Fine Hall 314 


Ergodic Theory and Statistical Mechanics Seminar 
Topic: 
TBA 
Presenter: 
Michael Hochman, Princeton University 
Date: 
Thursday, April 23, 2009, Time: 2:00 p.m., Location: Fine Hall 401 


Discrete Mathematics Seminar 
Topic: 
TBA 
Presenter: 
Maria Chudnovsky, Columbia University 
Date: 
Thursday, April 23, 2009, Time: 2:15 p.m., Location: Fine Hall 224 


Topology Seminar 
Topic: 
TBA 
Presenter: 
Kekiko Kawamuro, IAS 
Date: 
Thursday, April 23, 2009, Time: 4:30 p.m., Location: Fine Hall 314 


Analysis Seminar 
Topic: 
Stefan Problem with Surface Tension 
Presenter: 
Yan Guo, Brown University 
Date: 
Monday, April 27, 2009, Time: 4:00 p.m., Location: Fine Hall 110 


PACM Colloquium 
Topic: 
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 


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 



