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Fall 2012 GRASP Seminar – Jean Gallier, University of Pennsylvania, “The Classification Theorem for Compact Surfaces”

September 14, 2012 @ 11:00 am - 12:00 pm

Abstract: The
classification theorem for compact surfaces is one of the great achievements of early 20th
century mathematics. The statement of this theorem is quite intuitive but it took about
sixty years until a rigorous proof was finally given by Brahana in 1921. Early
versions of the
classification theorem were given by Mobius in 1861, and by Jordan in 1866. More definite
proofs were given later by von Dyck in 1888 and Dehn and Heegaard in 1907.

This talk is
about the history of the theorem and the techniques used to prove it. We will give a
guided tour of the proof, pointing out which tools from algebraic topology are needed, and
give an abbreviated  history of the
“proof.” A byproduct of the
theorem yields  “global
parametrizations,” using fundamental domains,
a recent topic of research.


Jean Gallier is a
Professor of Computer and Information Science at the University
of Pennsylvania, with a secondary appointment in Mathematics. He
obtained his Ph.D in Computer Science at UCLA in 1978. Gallier has done
research in a number of areas of CS,
including program
correctness, incremental parsing and error recovery, logic
programming, unification, term-rewriting and equational logic,
polymorphic lambda calculi, and linear logic. For the past eighteen years,
he has focused on geometric modeling, surfaces splines, surface
reconstruction from meshes and recently on optimization problems arising
in computer vision. Generally, he is interested in applying differential and
algebraic geometry tools to problems in computer science.
He is the author of six books, the last one with Dianna Xu, “A Guide to
the Classification theorem for compact surfaces,” to appear in 2012


September 14, 2012
11:00 am - 12:00 pm
Event Category: