# Algebra Seminar talk

2023-03-08 (Wednesday! 14:45!)

Raphaël **Carroy***Various ways to compare spaces, subsets, and functions*

Abstract:

One can consider a quasi-order like topological embeddability when one wants to compare a Polish (or analytic) space to another.
If instead one tries to rank the complexities emerging among subsets of a given space, continuous reducibility becomes relevant. Both these quasi-orders have extensions to functions between Polish (or analytic) spaces. Some natural questions about these quasi-orders are then: the existence of simple bases, characterizing the simplicity or complexity of the quasi-order in itself, and describing it when it turns out to be simple enough.

I will try to give some context on these quasi-orders and review known and more recent results and applications.

*Snacks and drinks will be served before the talk at 14:00 in the Besprechungsraum, 5th floor*