The Cartan Geometry of the Rotating Kepler Problem

Otto van Koert
Seoul National University
January 21, 2011

GEOMETRY/DYNAMICAL SYSTEMS

In this talk we shall discuss the Cartan geometry of the rotating Kepler problem. The rotating Kepler problem appears as the limit of the restricted planar three-body body when one of the masses goes to zero. As such, this problem plays the role of a simple approximation. We shall discuss the Cartan curvature and some of its relations with indices in the three-body problem. This is joint work with Kai Cieliebak and Urs Frauenfelder.

Fluctuations of the Nodal Line Length of Laplace eigenfunctions on the Arithmetic torus

Igor Wigman
KTH, Stockholm
January 20, 2011

ANALYSIS AND MATHEMATICAL PHYSICS SEMINAR

Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspace with Gaussian probability measure. This induces a notion of a random Gaussian Laplace eigenfunctions on the torus. We study the distribution of nodal length of the random Laplace eigenfunctions for high eigenvalues ("high energy limit").

Mechanizing the Odd Order Theorem: Local Analysis

Georges Gonthier
INRIA, France
January 20, 2011

Abstract: In addition to formal definitions and theorems, mathematical theories also contain clever, context-sensitive notations, usage conventions, and proof methods. To mechanize advanced mathematical results it is essential to capture these more informal elements. This can be difficult, requiring an array of techniques closer to software engineering than formal logic, but it is essential to obtaining formal proofs of graduate-level mathematics, and can give new insight as well.

Local-Global Compatibility and Monodromy

Ana Caraiani
Harvard University
January 20, 2011

Given a cuspidal automorphic representation of GL(n) which is regular algebraic and conjugate self-dual, one can associate to it a Galois representation. This Galois representation is known in most cases to be compatible with local Langlands. When n is even, the compatibility is known up to semisimplification or when the representation satisfies an additional regularity condition. I will extend the compatibility to Frobenius semisimplification by identifying the monodromy operators.

Contacting the Moon

Urs Frauenfelder
Seoul National University
January 19, 2011

GEOMETRY/DYNAMICAL SYSTEMS

The restricted 3-body problem has an intriguing dynamics. A deep observation of Jacobi is that in rotating coordinates the problem admits an integral. In joint work with P. Albers, G. Paternain and O. van Koert, we proved that the corresponding energy hypersurfaces are contact for energies below and slightly above the first critical value.

Moment-Angle Complexes, Spaces of Hard-Disks and Their Associated Stable Decompositions

Fred Cohen
University of Rochester; Member, School of Mathematics
January 10, 2011

Topological spaces given by either (1) complements of coordinate planes in Euclidean space or (2) spaces of non-overlapping hard-disks in a fixed disk have several features in common. The main results, in joint work with many people, give decompositions for the so-called "stable structure" of these spaces as well as consequences of these decompositions.

This talk will present definitions as well as basic properties.