Time：14:00-15:45, Wednesday, April 16 2025
Venue: E10-312
Speaker：Antoine Ducros, Sorbonne Université
Biography: Antoine Ducros is now a full professor at Sorbonne Université. He was former Junior member of the Institut universitaire de France. Professor Ducros obatined his Ph.D degree at the Université Paris-Sud.
Title: p-adic numbers and p-adic geometry
Abstract: To every prime number p one can associate a field of « strange » numbers called p-adic numbers. I will introduce them, give examples to show how one can manipulate them, and present various classical results showing their arithmetic interest. In a second part, I will explain why it is difficult to build a reasonable geometry theory over such fields, and how one can bypass the obstacles. I also plan to invoke during the talk (without too much details!) more recent developments in these areas, like Scholze's perfectoid fields and spaces.
