Discrete CATS Seminar
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UNIVERSITY OF KENTUCKY **

DISCRETE CATS SEMINAR

113 PATTERSON OFFICE TOWER

FALL 2007

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"The Topological Tverberg Conjecture"

Benjamin Braun

University of Kentucky

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Monday, September 24, 2007

4:00 pm, 113 Patterson Office Tower

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Abstract:

The Topological Tverberg Conjecture is as follows: Given
integers n and d, set N=(d+1)(n-1); for every continuous map f from
the N-simplex to d-dimensional Euclidean space, there exist n disjoint
faces of the simplex whose images intersect under f. This conjecture
is one of the most challenging open problems in topological
combinatorics and is known to be valid when n is a prime power. We
will sketch a proof of this for the case when n is prime and discuss
some of the trouble one runs into when attempting the non-prime-power
cases. The proof method we will discuss involves generalized
Borsuk-Ulam theorems and numerical index theory, which we will develop
from scratch.