Tue, 07 May 2013

15:45 - 16:45
L3

Descent for n-Bundles

Jesse Wolfson
(Northwestern)
Abstract

Given a Lie group $G$, one can construct a principal $G$-bundle on a manifold $M$ by taking a cover $U\to M$, specifying a transition cocycle on the cover, and then descending the trivialized bundle $U \times G$ along the cocycle. We demonstrate the existence of an analogous construction for local $n$-bundles for general $n$. We establish analogues for simplicial Lie groupoids of Moore's results on simplicial groups; these imply that bundles for strict Lie $n$-groupoids arise from local $n$-bundles. We conclude by constructing a simple finite dimensional model of the Lie 2-group String($n$) using cohomological data.

Tue, 22 Mar 2011

02:15 - 03:15
L3

Factorization algebras and perturbative quantum field theory

Kevin Costello
(Northwestern)
Abstract

I'll describe an approach to perturbative quantum field theory
which is philosophically similar to the deformation quantization approach
to quantum mechanics. The algebraic objects which appear in our approach --
factorization algebras -- also play an important role in some recent work
in topology (by Francis, Lurie and others).  This is joint work with Owen
Gwilliam.

Mon, 31 Oct 2005
17:00
L1

Divergence-Measure Fields, Geometric Measures,
and Conservation Laws

Gui-Qiang Chen
(Northwestern)
Abstract

In this talk we will discuss a theory of divergence-measure fields and related

geometric measures, developed recently, and its applications to some fundamental

issues in mathematical continuum physics and nonlinear conservation laws whose

solutions have very weak regularity, including hyperbolic conservation laws,

degenerate parabolic equations, degenerate elliptic equations, among others.

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