- Series
- Job Candidate Talk
- Time
- Monday, January 27, 2020 - 3:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Jaclyn Lang – Université Paris 13
- Organizer
- Dan Margalit
Although studying numbers seems to have little to do with shapes, geometry has become an indispensable tool in number theory during the last 70 years. Deligne's proof of the Weil Conjectures, Wiles's proof of Fermat's Last Theorem, and Faltings's proof of the Mordell Conjecture all require machinery from Grothendieck's algebraic geometry. It is less frequent to find instances where tools from number theory have been used to deduce theorems in geometry. In this talk, we will introduce one tool from each of these subjects -- Galois representations in number theory and cohomology in geometry -- and explain how arithmetic can be used as a tool to prove some important conjectures in geometry. More precisely, we will discuss ongoing joint work with Laure Flapan in which we prove the Hodge and Tate Conjectures for self-products of 16 K3 surfaces using arithmetic techniques.