

NOVEMBER 2008 


Graduate Student Seminar 
Topic: 
An overview of the ladic and padic monodromy theorems 
Presenter: 
Stefan Patrikis, Princeton University 
Date: 
Thursday, November 20, 2008, Time: 12:30 p.m., Location: Fine Hall 314 
Abstract: 
I will introduce (focusing on the case of elliptic curves) two essential theorems of arithmetic geometry that bind the geometry of an algebraic variety over a local field (or number field) to its arithmetic, Galoistheoretic properties. The ladic monodromy theorem is in fact entirely elementary (one needn't even know what 'monodromy' means!) but will motivate the subtler padic theorem. Together these results will help us make sense of the FontaineMazur conjecture, one of the fundamental open problems in arithmetic geometry. 


Number Theory Seminar 
Topic: 
Comparison isomorphisms for $p$adic formal schemes and applications 
Presenter: 
Adrian Iovita, McGill University 
Date: 
Thursday, November 20, 2008, Time: 4:30 p.m., Location: Fine Hall 214 


Topology Seminar 
Topic: 
Bordered Heegaard Floer homology 
Presenter: 
Peter Ozsvath, Columbia University 
Date: 
Thursday, November 20, 2008, Time: 4:30 p.m., Location: Fine Hall 314 
Abstract: 
I will describe a construction of invariants for threemanifolds with (parameterized) boundary. The invariant associates a differential graded algebra to an oriented surface, and a (suitably generalized) module to a threemanifold whose boundary is that surface. This invaraint also enjoys a "pairing theorem" relating it with HFhat of closed threemanifolds. I will describe the basic properties of these invariants, and also the role of certain bimodules which appear in theory. This is joint work with Robert Lipshitz and Dylan Thurston. 


Special Seminar 
Topic: 
The Feller semigrops and nonlocal elliptic problems. 
Presenter: 
A.L.Skubachebski, University of Friendship of people, Moscow, Russia 
Date: 
Friday, November 21, 2008, Time: 1:30 p.m., Location: Fine Hall 801 


Discrete Mathematics Seminar ***Please note special day and location 
Topic: 
Quasiisometries, phase transitions, and other problems in additive number theory 
Presenter: 
Melvyn B. Nathanson, CUNY 
Date: 
Friday, November 21, 2008, Time: 2:15 p.m., Location: Fine Hall 1201 
Abstract: 
This is a survey of recent work in combinatorial and additive number theory suggested by a problem of Richard Schwartz in metric geometry and geometric group theory. The central object is a group with an infinite set of generators, and the induced metric. Some results and many open problems will be discussed. 


Differential Geometry and Geometric Analysis Seminar 
Topic: 
An Exotic Sphere with Positive Sectional Curvature 
Presenter: 
Fred Wilhelm, UCR 
Date: 
Friday, November 21, 2008, Time: 3:00 p.m., Location: Fine Hall 314 
Abstract: 
I'll discuss joint work with Peter Petersen that shows that the GromollMeyer exotic 7sphere admits a metric of positive sectional curvature. I'll discuss the history of the problem and give a coarse outline of the proof. 


Analysis Seminar 
Topic: 
Fifth order KdV equations 
Presenter: 
Soonsik Kwon, Princeton University 
Date: 
Monday,November 24, 2008, Time: 4:00 p.m., Location: Fine Hall 110 
Abstract: 
We study the fifthorder KdV equations, which arise in the KdV hierarchy. In this talk, we discuss the initial value problem in Sobolev spaces with low regularity. In the linear part the fifthorder equation has stronger dispersion effect and so better smoothing than KdV equation. But it comes with stronger nonlinear parts compared to dispersion. As a result, unlike KdV equation, the fifthorder equation in the hierarchy has too strong lowhigh frequency interaction. We exploit this to show a negative result. We will discuss both positive and negative results, local wellposedness in the standard sense (existence, uniqueness and continuous dependence of data) for rough data, but illposedness in the sense of failure of uniformly continuous dependence on data on a bounded set. If time allows, we will make a comment on analogous problem of the fifthorder modified KdV equation. 


Special Geometry Seminar 
Topic: 
Dynamics and ergodic theory of the space of all convex surfaces 
Presenter: 
Francois Labourie, Universite de ParisSud 
Date: 
Monday,November 24, 2008, Time: 4:00 p.m., Location: Fine Hall 801 
Abstract: 
We first decribe a compactification of the space of all locally convex surfaces in a hyperbolic compact 3manifold, which can also be thought of as a quotient of the space of immersions of the disk on the sphere. We then explain that this space can be thought of as a 2dimensional dynamical system whose properties generalise the chaotic property of the geodesic flow: density of closed leaves, genricity of dense leaves, stability, existence of many transverse invariant measures. 


Group Actions and Automorphic Seminar 
Topic: 
Limits of translates of curves on homogeneous spaces and Dirichlet's theorem on Diophantine approximation 
Presenter: 
Nimish Shah, Yale University 
Date: 
Monday,November 24, 2008, Time: 4:00 p.m., Location: Fine Hall 601 
Abstract: 
By proving an equidistribution theorem for certain sequences of expanding translates of smooth measures on curves on homogeneous spaces of SL(n,R), we show that the Dirichlet's theorem on simultaneous diophantine approximation cannot be improved for related quantities in the sense of Davenport and Schmidt. 


PACM Colloquium 
Topic: 
Emissions Market Models 
Presenter: 
René Carmona, PACM & ORFE, Princeton University 
Date: 
Monday, November 24, 2008, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract: 
The main goal of the talk is to introduce a new capandtrade scheme design for the control and the reduction of atmospheric pollution. The tools developed for the purpose of the study are intended to help policy makers and regulators understand the pros and cons of the emissions markets at a quantitative level.
We propose a model for an economy where risk neutral firms produce goods to satisfy an inelastic demand and are endowed with permits by the regulator in order to offset their pollution at compliance time and avoid having to pay a penalty. Firms that can easily reduce emissions do so, while those for which it is harder buy permits from those firms anticipating that they will not need them, creating a financial market for pollution credits.
Our model captures most of the features of the European Union Emissions Trading Scheme. We show existence of an equilibrium and uniqueness of emissions credit prices. We also characterize the equilibrium prices of goods and the optimal production and trading strategies of the firms. We choose the electricity market in Texas to illustrate numerically the qualitative properties observed during the implementation of the first phase of the European Union capandtrade CO2 emissions scheme, comparing the results of capandtrade schemes to the Business As Usual benchmark. In particular, we confirm the presence of windfall profits criticized by the opponents of these markets. We also demonstrate the shortcomings of tax and subsidy alternatives. Finally we introduce a relative allocation scheme which, despite its ease of implementation, leads to smaller windfall profits than the standard scheme. 


Algebraic Geometry Seminar 
Topic: 
Finiteness theorems for algebraic groups over function fields 
Presenter: 
Brian Conrad, Stanford University 
Date: 
Tuesday, November 25, 2008, Time: 4:30 p.m., Location: Fine Hall 322 
Abstract: 
If X is a smooth variety over a global field k, G is an algebraic group over k equipped with an action on X, and x is a point in X(k) then it is natural to ask how the property of x' in X(k) being in the G(k)orbit of x compares with being in the G(k_v)orbit of x for all places v of k. In general there is a nontrivial "localtoglobal" obstruction space, but one can ask if it is finite. Even when G is semisimple, this finiteness problem leads to the consideration of the isotropy group G_x that is generally not connected or reductive (or even smooth when char(k) > 0). In the number field case the finiteness of these obstruction spaces was proved by Borel and Serre long ago, but their method used characteristic 0 in an essential way. Recently in joint work with Gabber and G. Prasad we have developed a theory of "pseudoreductive groups" which is a very useful tool to prove results for general affine algebraic groups in the function field case that were previously known only in the reductive case. In particular, this work makes it possible to prove the analogue of the BorelSerre finiteness result over function fields (away from char. 2 for now). The first part of the talk will explain a bit about the theory of pseudoreductive groups, and the rest of the talk will show how it is used to establish the finiteness of the localtoglobal obstruction spaces in the function field case (in char. > 2). If time permits we will also discuss an application to the problem of whether the kisomorphism class of a projective kvariety is determined (up to "finite ambiguity") by its k_visomorphism class for all places v of k (a problem solved by Mazur over number fields, once again making essential use of characteristic 0). 


DECEMBER 2008 


Analysis Seminar 
Topic: 
TBA 
Presenter: 
Alessio Figalli, Université de Nice SophiaAntipolis and Ecole Polytechnique 
Date: 
Monday, December 1, 2008, Time: 4:00 p.m., Location: Fine Hall 110 


PACM Colloquium 
Topic: 
TBA 
Presenter: 
Ingrid Daubechies, PACM,, Princeton University 
Date: 
Monday, December 1, 2008, Time: 4:00 p.m., Location: Fine Hall 214 


Group Actions and Automorphic Seminar 
Topic: 
On counting Apollonian circles of bounded curvature 
Presenter: 
Hee Oh, Brown University 
Date: 
Tuesday, December 2, 2008, Time: 4:30 p.m., Location: Fine Hall 801 
Abstract: 
I will talk about an asymptotic formula for the number of circles of curvature at most T in a given bounded Apollonian circle packing. 


Statistical Mechanics Seminar 
Topic: 
Local and Global Structure of Stationary States of Macroscopic Systems 
Presenter: 
Joel Lebowitz, Rutgers University 
Date: 
Wednesday, December 3, 2008, Time: 2:00 p.m., Location: Jadwin 343 
Abstract: 
The microscopic structure of a macroscopic system in a steady state is described locally, i.e. at a suitably scaled macroscopic point $x$, by a time invariant measure of the corresponding infinite system with translation invariant dynamics. This measure may be extremal, with good decay of correlations, or a superposition of extremal measures, with weights depending on $x$ (and possibly even on the way one scales).
I will illustrate the above by some exact results for 1D lattice systems with two types of particles (plus holes) evolving according to variants of the simple asymmetric exclusion process, in open or closed systems. Somewhat surprisingly, the spatially asymmetric local dynamics satisfy (in some cases) detailed balance with respect to a global Gibbs measure with long range pair interactions. 


Department Colloquium 
Topic: 
TBA 
Presenter: 
Bruce Kleiner, Yale University 
Date: 
Wednesday, December 3, 2008, Time: 4:30 p.m., Location: Fine Hall 314 


Discrete Mathematics Seminar 
Topic: 
TBA 
Presenter: 
Robin Thomas, Georgia Tech 
Date: 
Thursday, December 4, 2008, Time: 2:15 p.m., Location: Fine Hall 224 


Number Theory Seminar 
Topic: 
Mock modular forms 
Presenter: 
Sandors Zwegers, University College Dublin 
Date: 
Thursday, December 4, 2008, Time: 4:30 p.m., Location: IAS SH101 
Abstract: 
The main motivation for the theory of mock modular forms comes from the desire to provide a framework in which we can understand the mysterious and intriguing mock theta functions, as well as related functions, like Appell functions and theta functions associated to indefinite quadratic forms.
In this talk, we will describe the nature of the modularity of the original mock theta functions, formulate a general definition of mock modular forms, and describe further examples. We will also consider a generalization to higher depth mock modular forms 


Topology Seminar 
Topic: 
TBA 
Presenter: 
Elisenda Grigsby, Columbia University 
Date: 
Thursday, December 4, 2008, Time: 4:30 p.m., Location: Fine Hall 314 


PACM Colloquium 
Topic: 
Computational Astrophysics and the Dynamics of Accretion Disks 
Presenter: 
James M. Stone, PACM & Astrophysical Sciences 
Date: 
Monday, December 8, 2008, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract: 
he ever increasing performance of computer hardware and improvements to the accuracy of numerical algorithms are revolutionizing scientific research in many disciplines, but perhaps none more so than astrophysics. I will begin by describing why computation is crucial for the solution of a variety of problems at the forefront of research in astronomy and astrophysics, with particular emphasis on understanding accretion flows onto black holes. I will outline the challenge of developing, testing, and implementing numerical algorithms for the investigation of these problems. Finally, I will present results that demonstrate how computation can help us understand the basic physics of magnetized accretion disks. 


Geometry, Representation Theory, and Moduli Seminar 
Topic: 
TBA 
Presenter: 
Kai Behrend, University of British Columbia 
Date: 
Monday, December 8, 2008, Time: 4:00 p.m., Location: Fine Hall 314 


Algebraic Geometry Seminar 
Topic: 
TBA 
Presenter: 
David Smyth, Harvard University 
Date: 
Tuesday, December 9, 2008, Time: 4:30 p.m., Location: Fine Hall 322 


Department Colloquium 
Topic: 
TBA 
Presenter: 
Kai Behrend, University of British Columbia 
Date: 
Wednesday, December 10, 2008, Time: 4:30 p.m., Location: Fine Hall 314 


Discrete Mathematics Seminar 
Topic: 
TBA 
Presenter: 
Paul Wollan, University of Hamburg 
Date: 
Thursday, December 11, 2008, Time: 2:15 p.m., Location: Fine Hall 224 


Number Theory Seminar 
Topic: 
Langlands functoriality and the inverse problem in Galois theory 
Presenter: 
Gordon Savin, University of Utah 
Date: 
Thursday, December 11, 2008, Time: 4:30 p.m., Location: IAS SH101 
Abstract: 
In a couple of recent works with C. Khare and M. Larsen we contruct finte groups of Lie type B_n, C_n and G_2 as Galois groups over rational numbers. The method combines some established, special cases of the functoriality principle with ladic representations attached to selfdual automrophic representations of GL(n). 



