KTH/SU Mathematics Colloquium

07-04-25

Svante Linusson, KTH

Combinatorial and topological fix-point theorems

I will describe some rather classical results from combinatorial fix-point theorems (Sperner's Lemma, the game of Hex by Nash) and their relation to fix-point theorems in topology (e.g. Brouwer's). In fact one can often see them as equivalent. I will also describe in the combinatorial setting how to algorithmically find the fix-point which implies solutions to some problems in game theory or fair division.
An example: Assume $n$ students will share an $n$-room apartment. The rooms may be different and the students have different preferences. Assign a rent to each rooms such that it is a division of the total rent and such that the students will all prefer different rooms.