O-minimal structures from a geometric point of view

Venue: The event will take place online trough the ZOOM platform. To get the access codes please contact the secretary office (phd.maths [at] unitn.it)

Time: 3.00 p.m.

• Antonio Carbone - PhD in Mathematics, University of Trento

Abstract:
The purpose of the seminar is to give a brief introduction to o-minimal structures from a geometric point of view. After recalling the definition of semialgebraic sets and some of their properties, we will try to introduce new families of subsets of Euclidean spaces that share the good properties of the semialgebraic sets. Some examples will convince us that in order to define tame structures we will need some extra properties; this will lead us to the notion of o-minimality. At the end of the seminar we will introduce two useful geometric invariants in the context of o-minimal structures: the definable dimension and the definable Euler characteristic. We tried to keep the seminar as much self contained as possible so, probably, only some basic notions of point-set topology are needed to understand (at least most of) it.

Contact person: Stefano Baratella

The seminar corresponds to the final exam of Model theory, a planned course within  Carbone's first year PHD study programme