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Kneser and Tverberg: On the power of topological methods in combinatorics


Speaker: Günter Ziegler, Technische Universität Berlin
Location: 2112 MSB
Start time: Tue, Oct 10 2006, 4:10PM

We discuss two classical applications of topological methods in combinatorics and discrete geometry:

  • The Kneser conjecture was proved by Lovász using the Borsuk-Ulam theorem, and for 25 years no combinatorial proof was known. Now we have combinatorial proofs, and substantial extensions, but it seems that the "point set topology" intuition is gradually being replaced by "truly-algebraic topology" tools.
  • The "topological Tverberg theorem" was established by topological methods in the prime power case, but obstruction theory shows that the topological methods fail outside this case. Does that mean that there are counter-examples, or do we need refined topological-geometric tools?

Note the change of room from 1147 to 2112.