Topic: Holomorphic disks and invariants for 3-manifolds and smooth 4-manifolds April 4

Presenter: Zoltan Szabo, Princeton University

Abstract: We will introduce and study topological invariants for closed 3-manifolds and smooth 4-manifolds. The 3-manifold construction uses Heegaard diagrams and a version of Lagrangian Floer homology. The 4-manifold invariant uses the previous construction, a pairing on Floer-homology and a handle decomposition of the 4-manifold. We will also present some applications in three and 4-manifold topology. This is a joint result with Peter Ozsvath.

Topic: Existence of a Family of Periodic Orbits in Hill's Problem Near the Zero April 5

Velocity Curves

Presenter: Ed Belbruno, Princeton University and IOD

Abstract: Hill's problem is considered. It was formulated by G. Hill back in 1865 and is sometimes called the lunar problem. It is highly nonintegrable, and models the motion of a zero mass point about the smaller of the two primaries in the restricted three-body problem. Little is proven about this problem, unless the zero mass is assumed to move very close to the primary. It is assumed here that the initial conditions of the zero mass lie far from the primary, and near the zero-velocity curves, which is very far from integrable. A method is presented which proves that a family of periodic orbits exists with these initial conditions provided the Jacobi energy is very near to the value of 3^(4/3). A small part of this proof is numerically assisted. Numerical work indicates that this family is part of a bifurcated branch of the so called classical Hill's family shown to exist numerically by Henon in 1969, he labeled g'. It is surprising to me that this proof would find this particular family.

Topic: A matroid-theoretic construction of BO(n) and the topology of combinatorial April 5

differential manifolds

Presenter: Daniel Biss, MIT

Abstract: MacPherson's combinatorial differential (CD) manifolds are an attempt to bridge the gap between the category of smooth manifolds and the category of simplicial complexes. That is, they are purely combinatorial objects which, one hopes, provide a good model for smooth manifolds. We will present a result which gives evidence for the case that CD manifolds succeed in capturing much of the structure of the smooth category. More precisely, the world of CD manifolds has a natural (purely combinatorial) bundle theory, and we show that the classifying space of this bundle theory is homotopy equivalent to BO(n), that is, that these combinatorial vector bundles are precisely the same as ordinary vector bundles. This result has applications to the topology of CD manifolds and to the computation of characteristic classes.

Topic: Free boundary regularity for the Poisson kernel April 5

Presenter: Tatiana Toro, University of Washington

Topic: Dirac operators and vanishing theorems on foliations April 5

Presenter: Weiping Zhang, MIT

Topic: Global well-posedness for the KdV equation April 5

Presenter: Gigliola Staffilani, Stanford University

Topic: Gluing and Wormholes for the Einstein Constraint Equations April 6

Presenter: Daniel Pollack, University of Washington

Topic: L^p and dispersive estimates for the wave equation with the inverse-square April 9

potential

Presenter: Shadi Tahvildar-Zadeh, Rutgers University

Topic: Stability and Dynamics of Self-similarity in Evolution Equations April 9

Presenter: Andrew Bernoff, Harvey Mudd College

Abstract: Similarity methods have been used to derive special solutions for a broad variety of physical problems in the past few decades. In this talk I will discuss a methodology for studying linear stability for self-similar blow-up and pinch-off. I will present three problems: a simple ODE model, the Sivashinsky equation which arises in solidification, and the pinch-off of a solid filament due to the action of surface diffusion. The goal is to show that self-similar phenomena can be studied using many of the now familiar ideas that have arisen in the study of dynamical systems. In particular, I will discuss rescaling methods, linearization and the role of symmetries in the context of self-similarity. I will demonstrate that the symmetries in the problem give rise to "anomalous" positive eigenvalues associated with the rescaling symmetries as opposed to instability, and show how this stability analysis can identify a unique stable (and observable) solution from a countable infinity of similarity solutions.

Topic: TBA April 9

Presenter: A. Bertram, University of Utah

Topic: Stories about pseudo-random graphs April 10

Presenter: Michael Krivelevich, Tel Aviv University

Topic: Relative Gromov-Witten invariants and the mirror formula April 10

Presenter: A. Gathmann, Harvard University

Topic: Revisting an Old Concept: Random Close Packing of Hard Spheres April 11

Presenter: Salvatore Torquato, Princeton University

Topic: Regularity properties of nonlinear wave equations April 11

Presenter: Igor Rodnianski, Princeton University

Abstract: I will discuss recent interactions of Fourier and geometric analysis in the well posedness theory for quasilinear wave equations, wave maps, and the Einstein equations.

Topic: Recent results about Orbit Equivalence for actions of non-amenable groups April 12

Presenter: Alex Furman, University of Illinois at Chicago

Abstract: Let G be a discrete group acting ergodically by m.p.t. on a probability space (X,m) and let R_G denote the equivalence relation on X defined by the G-orbits (mod 0). How much information about the group G and its action (X,m,G) is encoded in the relation R_G ? What can be said about the Out(R_G) - the group of measurable maps of X permuting the G-orbits? These purely measure-theoretical questions in Ergodic Theory turn out to be connected to Geometry and to rigidity of lattices in semisimple Lie groups. In the talk we shall survey recent developments in this theory.

Topic: Twisted Orbifold K-theory April 12

Presenter: Alejandro Adem, Madison

Topic: TBA April 13

Presenter: Hartmut Schwetlick, MPI

Topic: TBA April 13 IAS

Presenter: Bob Vaughan, PSU

Topic: The generalized KdV equation on the half-line April 16

Presenter: Jim Colliander, University of California - Berkeley

Topic: Creating Stability from Instability April 16

Presenter: Christopher Jones, Brown University

Abstract: The current state-of-the-art technology in optical communications is based on the use of Dispersion Managed Solitons (DMS). These propagate on fibers with dispersion compensating itself periodically. Using variational methods and averaging, a full mathematical theory for DMS will be given. Surprisingly, it is shown that the strategy can be pushed to the point where the "pulse" is oscillating between unstable states and yet remains stable itself. Another case in which two unstable objects are put together to make a stable pulse is exhibited in the FitzHugh-Nagumo system, originally derived as a model of nerve impulse propagation. While these two phenomena are unrelated, mathematically and scientifically, they both suggest that two "wrongs" can make a "right."

Topic: TBA April 17

Presenter: John Conway, Princeton University

Topic: Change of Variable Formula for Complex Genera and Its Applications to April 17

Higher Dimensional Flops

Presenter: Chin-Lung Wang, Harvard University

Topic: Syzygies over the exterior algebra and Chow forms April 17

Presenter: F. Schreyer, University of Bayreuth

Topic: Amenable groups and their actions April 18

Presenter: Benjamin Weiss, Hebrew University of Jerusalem

Abstract: After explaining what amenable groups are and why they are the natural setting for ergodic theory I will survey some new developments related to entropy, uniform mixing, and limit theorems.

Topic: Gibbsian Dynamics and Ergodicity for some Stochastically Forced Dissipative April 19

Equations

Presenter: Di Liu, Princeton University

Abstract: We study the stationary measures for the stochastically perturbed one dimensional Ginzburg-Landau equation, Cahn-Hilliard equation and Kuramoto-Sivashingski equation with periodic boundary conditions. We proved the uniqueness of the stationary measures of these equations under the condition that all ``determining modes'' are forced. The main idea behind the proof is to study the Gibbsian dynamics of the low modes obtained by representing the high modes as functionals of the time-history of the low modes.

Topic: TBA April 20

Presenter: Howard Jacobowitz

Topic: On KdV and completely integrable systems April 23

Presenter: François Trèves, Rutgers University

Topic: TBA April 24

Presenter: János Pach, New York University

Topic: Concordant sequences and integer-valued entire functions April 24

Presenter: Jonathan Pila, Melbourne, Australia

Topic: Hyperbolicity,diophantine approximation and complex two ball quotients April 24

Presenter: S.K.Yueng, Purdue University

Topic: TBA April 25

Presenter: Yosi Avron, Technion, Haifa

Topic: TBA April 26

Presenter: B. Doug Park, McMaster University

Topic: TBA April 27

Presenter: Joel Hass, Institute for Advanced Study and University of California at Davis

Topic: TBA April 30

Presenter: Eric Vanden-Eijnden, CIMS, New York University

Topic: TBA May 1

Presenter: Jeff Kahn, Rutgers University

Topic: TBA May 3

Presenter: Lenny Ng, MIT

Topic: TBA May 3

Presenter: Johan de Jong, M.I.T.

Topic: TBA May 4

Presenter: Guan Bo, University of Tennessee

Topic: TBA May 4

Presenter: C. Margerin, Ecole Polytechnique

Topic: Time-dependent Taylor Vortices in Wide-Gap Spherical Couette Flow May 7

Presenter: Rainer Hollerbach, Geosciences, Princeton University