Still at UGA, at the very enjoyable but weirdly named conference TAAAG. The conference featured a very interesting talk by Padmavathi Srinivasan, as well as mini-courses by Michel Raibaut, Ben Williams, and Arnav Tripathy (whose website I can't find).
Arnav's great talk on the integral Hodge and Tate conjecture, with lots of gestures
There were also many short talks, by many of the other participants.
Padma gave a great talk about her work comparing
- The discriminant of a hyperelliptic curve, with
- The conductor of the curve.
As I understand it, the conductor only depends on the family of curves (it is more or less the difference in Euler characteristic between the general fiber and the special fiber of a minimal regular model), whereas the discriminant only depends on the covering of the base given by the family of Weierstrass points. In the case of a minimal regular model, these numbers are just the Euler characteristics of the vanishing cycles sheaf on the family of curves (resp. the family of Weierstrass points). It would be nice to enhance her inequality to a map of sheaves...