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.