Kolokviální přednáška se konala ve středu 9. listopadu 2016, v 16:00 v posluchárně M1

Wieslaw Kubiś (Institute of Mathematics, Czech Academy of Sciences, Prague)

Generic objects and infinite games

Abstract:

Let F be a fixed class of `small' mathematical structures (e.g. finite graphs, finite-dimensional normed spaces, etc.) and assume that a notion of `embedding' has been defined so that we can say that one structure is an extension of another. We say that a structure is `big' if it can be build as the union (or, more formally, colimit) of a chain of embeddings in F. Fix a big structure U. We consider the following infinite game for two players: Player I chooses a structure S_0 from F. Player II responds by its extension S_1, again in F. Player I responds by an extension S_2 of S_1. And so on. We say that Player II wins if the union of the infinite chain of S_ns is isomorphic to U, otherwise Player I wins. We say that U is generic, if Player II has a winning strategy.

In the talk I will present examples of generic objects in several areas of mathematics. Further, I will show some of their basic properties and relations to the theory of universal homogeneous models.

Záznam přednášky ZDE

Veřejné přednášky pozvaných uchazečů ve výběrovém řízení na pozice na  Ústavu matematiky a statistiky proběhnou formou série kolokviálních přednášek pro širokou matematickou veřejnost. Všichni zájemci jsou srdečně zváni.