Oliver Thom (Pós-Doutorando no IMPA)

Friday, November 8th,2019. Room 4-111 , at 4:00 p.m.

**Title: About simultaneous resolution of singularities**

**Abstract **What does an application F : (C2; 0) -> (C2; 0) look like? More

precisely, can we do blow-ups at the source and at the target to obtain simple

forms on which we can understand the application F better? This question

looks simple, it is not so different from the classical resolution of singularities in

appearance, but is in fact much more subtle than this. For example, the most

optimistic version of this question: "after blow-ups on both sides, can we obtain

a ramified covering around the exceptionnal divisors ?", has a negative answer,

even locally.

During this talk, I would like to explore this question, explain the classical

results and the obstructions to obtain simple forms; more generally, try to give

precise answers to this vague question