Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, May 26, 2020.

     .
events for the
events containing  

(Requires a password.)
More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
      April 2020              May 2020              June 2020      
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
           1  2  3  4                   1  2       1  2  3  4  5  6
  5  6  7  8  9 10 11    3  4  5  6  7  8  9    7  8  9 10 11 12 13
 12 13 14 15 16 17 18   10 11 12 13 14 15 16   14 15 16 17 18 19 20
 19 20 21 22 23 24 25   17 18 19 20 21 22 23   21 22 23 24 25 26 27
 26 27 28 29 30         24 25 26 27 28 29 30   28 29 30            
                        31                                         

Tuesday, May 26, 2020

2:00 pm in Zoom,Tuesday, May 26, 2020

Colorful phenomena in discrete geometry and combinatorics via topological methods

Shira Zerbib (Iowa State University)

Abstract: We will discuss two recent topological results and their applications to several different problems in discrete geometry and combinatorics involving colorful settings.

The first result is a polytopal-colorful generalization of the topological KKMS theorem due to Shapley. We apply this theorem to prove a colorful extension of the d-interval theorem of Tardos and Kaiser, as well as to provide a new proof to the colorful Caratheodory theorem due to Barany. Our theorem can be also applied to questions regarding fair-division of goods (e.g., multiple cakes) among a set of players. This is a joint work with Florian Frick.

The second result is a new topological lemma that is reminiscent of Spernerís lemma: instead of restricting the labels that can appear on each face of the simplex, our lemma considers labelings that enjoy a certain symmetry on the boundary of the simplex. We apply this to prove that the well-known envy-free division theorem of a cake is true even if the players are not assumed to prefer non-empty pieces, whenever the number of players is prime or equal to 4. This is joint with Frederic Meunier.

Please email Sean at SEnglish (at) illinois (dot) edu for the Zoom ID and password.