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UID:www.tcs.tifr.res.in/event/587
DTSTAMP:20230914T125930Z
SUMMARY:Topology in Combinatorics: The Borsuk-Ulam Theorem
DESCRIPTION:Speaker: Rakesh Venkat\n\nAbstract: \nAbstract: We will see an
application of topology to prove combinatorial results. The Borsuk-Ulam th
eorem states that any continuous function f from the surface of the (n+1)-
sphere to R^n should have a point x on the sphere such that f(x) = f(-x).
For instance when n=2\, it implies that if one deflates a football and pla
ces it flattened out (arbitrarily) on a table\, then there must be two *di
ametrically opposite* points that land up on top of each other on the tabl
e.\n\nPerhaps surprisingly\, this theorem can be used to prove the fact th
at the Kneser-Graph (n\,k) has chromatic number exactly n-2k+2 (conjecture
d by Kneser\, proven first by Lovasz in 1978). We will see this and a coup
le more applications of (variants of) the Borsuk-Ulam theorem in the talk.
For some of these results\, no purely combinatorial proofs are known.\n
URL:https://www.tcs.tifr.res.in/web/events/587
DTSTART;TZID=Asia/Kolkata:20150312T140000
DTEND;TZID=Asia/Kolkata:20150312T150000
LOCATION:D-405 (D-Block Seminar Room)
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