From: Gary L Mullen 
Subject: MARKER LECTURES
Date: Tue, 4 Mar 2003 15:42:09 -0500 (EST)

Dear Colleagues,

I'm delighted to be able to announce that Shmuel Weinberger
(University of Chicago) will give the 2002-2003 Marker Lecture Series
in the Mathematics Department March 31 - April 3, 2003. Some details
are provided below.

Thanks!

Cheers,

Gary

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MARKER LECTURES IN MATHEMSTICS

March 31 -April 3, 2003

Professor Shmuel WEINBERGER

University of Chicago

GEOMETRY AND COMPLEXITY; TOPOLOGY AND CALCULUS

This series will discuss some nontraditional techniques in geometry
and geometric topology that are related either to logic and computer
science, or to "nonlinear extensions of the sheaf concept".

LECTURE 1:
Monday, March 31 8pm
Wartik 111

COMPLEXITY AND GEOMETRIC OPTIMIZATION

Many quantitative problems in the sciences and economics involve the
interactions of large numbers of particles or agents.  Finding
explicit solutions to the problems can be very difficult, so we
usually are satisfied with less: proving existence, analyzing
uniqueness, understanding the properties of solutions.

One of the most powerful ideas that we have at our disposal is
"geometricization".  This has roots going back to Descartes and
Newton, and pervades modern physics, and to a lesser extent, other
fields.  I will try to give some examples of how one is naturally lead
by the consideration of very simple problems into geometric
considerations of high dimensional, and occasionally, infinite
dimensional spaces, and how the geometric considerations really help
in solving the problems.

The crudest geometric techniques gain power when coupled with tools
from calculus, but, even these taken together have natural limits to
their effect.  My goal is to explain this, and also show how tools
from logic and theoretical computer science can sometimes go further.

LECTURE  2:
Tuesday April 1, 4:30 pm
Osmond 109

THE CASE OF EMBEDDINGS

We will consider a special case: configurations of certain membranes
in spaces subject to external air pressure as well as an internal
force that keeps the membrane from passing through itself. The
existence of many equilibria is known in almost all cases, and the
argument is ultimately an application of Godel's incompleteness
theorem of the style pioneered by Nabutovsky.

LECTURE 3:
Wednesday April 2, 4:30pm
Osmond 109

THE LOCAL-GLOBAL PRINCIPLE FOR SINGULAR SPACES

We will discuss how symmetries are related to singularities, and some
ideas on how to modify the traditional tools of geometric topology to
deal with spaces that have singularities.

LECTURE 4
Thursday Aprli 3, 4:30pm
Osmond 109

THE CALCULUS OF SYMMETRY

Inspired by ideas of Goodwillie, we will discuss ways in which the
familiar idea of sheaf cohomology can sometimes be modified and how
such extensions play a role in a variety of problems, geometric and
algebraic, including I hope, symmetry.