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DTSTAMP:20170927T215520Z
DTSTART;TZID=America/Los_Angeles:20171012T161000
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SUMMARY:Mathematics Department Colloquium: The first hundred years of Helly’s theorem
UID:112128-ucb-events-calendar@berkeley.edu
ORGANIZER;CN="UC Berkeley Calendar Network":
LOCATION:60 Evans Hall
DESCRIPTION:Jesus De Loera\, University of California\, Davis\n\nThe classical theorem of Edouard Helly (1913) is a masterpiece of geometry. In the simplest original form it states that if a finite family $\\Gamma$ of convex sets in $R^n$ has the property that every $n+1$ of the sets have a non-empty intersection\, then all the convex sets must intersect. This theorem has since found applications in many areas of mathematics\, most particularly convex analysis\, discrete geometry\, optimization\, computational geometry\, number theory\, algebraic geometry\, etc. My lecture will begin explaining the basics and proceed with a selection of lovely applications of Helly's theorem and some of its many generalizations and variations. The last part of the talk I will present our new work about discrete versions of Helly’s theorem. This part of the story originated in the 1970’s with work of Doignon\, Bell\, and Scarf (arising in Economics theory). I present joint work with Aliev and Louveaux and with La Haye\, Oliveros\, Roldan-Pensado. I promise I will provide several open questions and students (including undergrads) are guaranteed to understand a big portion of this talk.
URL:http://events.berkeley.edu/index.php/calendar/sn/pubaff.html?event_ID=112128&view=preview
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