
19 juin 2018 à 10h30, Salle 2
Étienne Lozes,
Procrastination in twoplayer games and continuous strategies
I will present the framework of regular infinite games with lookahead introduced Holtmann, Kaiser et Thomas [1].
A regular infinite game is a two player game where the objective of the second player is that the pair of infinite sequences of moves of the two players belong to some regular relation fixed in advance.
The variant game studied by Holtman, Kaiser, and Thomas is the one where the second player is allowed to « skip his turn » from time to time (but not cofinitely often).
It turns out that winning strategies in this setting correspond to continuous functions from the space of sequences of first players’ moves to the space of sequences of second player’s moves,
and that, in the specific setting studied by Holtman, Kaiser, and Thomas, these strategies are actually even Lipschitz fonctions. I will then come back to the buffered simulations and relate them to this framework. A notable difference is that the degree of lookahead needed for a buffered simulation cannot be bounded in advance, and that winning strategies in buffered simulations are continuous but not necessarily Lipschitz.
[1] Holtmann et al., "Degrees of Lookahead in Regular Infinite Games"

24 juillet 2018 à 10h30
Mirna Dzamonja,
Foundations of Mathematics: what is new and what is old
We consider the interplay between the settheoretic and the homotopytheoretic foundations of mathematics
and show results in mathematical logic which imply that modern mathematical foundations need to be pluralists.