College of Science and Mathematics
Department of Mathematics
Mathematics Seminar Series - Fall 2002
Monday,
September 20, 2002
2:30 pm Science 2-065
2:30 pm Science 2-065
Ethan Bolker
University of Massachusetts BostonHow Is a Graph Like a Manifold?
Abstract:
Some recent developments in the theory of group actions on complex
manifolds have revealed unexpected connections between the geometry
of these manifolds and the combinatorics of graphs immersed in n-space.
In this talk I will discuss some of those connections, concentrating on
the questions in combinatorics that come from the topology.
In particular, I will explore conditions under which it makes sense
to talk about the "Betti numbers"
of an immersed graph. We can then
use those Betti numbers to approach a proof of the McMullen
conjectures for simple polytopes and to count the number of
parallel redrawings of a framework.
The presentations cover a large variety of topics and are intended for a general math audience. The seminar is organized by Prof. Alfred Noël and we usually meet Monday afternoons, from 2:30 pm to 4:00 pm.
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