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SUMMARY:Shira Zerbib (Iowa State University)
DTSTART:20220609T141500Z
DTEND:20220609T160000Z
DTSTAMP:20260422T065546Z
UID:CJCS/73
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/73/">KK
 M-type theorems and their applications</a>\nby Shira Zerbib (Iowa State Un
 iversity) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstr
 act\nThe KKM theorem\, due to Knaster\, Kuratowski and Mazurkiewicz in 192
 9\, is a topological lemma reminiscent of Sperner's lemma and Brouwer's fi
 xed point theorem. It has numerous applications in combinatorics\, discret
 e geometry\, economics\, game theory and other areas. Generalizations of t
 his lemma in several different directions were proved over the years (e.g.
 \, by Shapley\, Gale\, Komiya\, Soberon) and have been widely applied as w
 ell. We will discuss a recent common generalization of all these theorems.
  We will also show two very different applications of KKM-type theorems: o
 ne is a proof of a conjecture of Eckhoff from 1994 on the line piercing nu
 mbers in certain families of convex sets in the plane\, and the other is a
  theorem on fair division of multiple cakes among players with subjective 
 preferences.\n
LOCATION:https://researchseminars.org/talk/CJCS/73/
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