(Mathur talk) The relationship between analytic and algebraic geometry (GAGA) is a rich area of study. For example, Grothendieck's existence theorem states that if X is proper over a complete local Noetherian ring A, then a coherent sheaf on the formal scheme X^, a priori only definable using formal power series, is actually algebraic. Such GAGA-type results are now standard tools for studying varieties and their families. One sample consequence: a compatible system of line bundles L_n on the thickenings X_n of the special fiber of X/A uniquely algebraizes to a line bundle L on X. In this talk, we answer a question Grothendieck posed in the 1960s about Brauer classes: can a Brauer class be determined from a compatible system of classes on the X_n? This is joint work with Andrew Kresch.

(Haines talk) TBA

(Ure talk) TBA

(Singh talk) TBA

(Frei talk) TBA