Speaker: Alexander Youcis, University of Toronto

 

Title: Some recent progress on integral models of Shimura varieties

 

Abstract: Shimura varieties, higher-dimensional generalizations of modular curves, are certain geometric spaces which sit at the intersection of differential geometry, algebraic geometry, harmonic analysis, and number theory. The study of the extent to which these (ostensibly differential-geometric) spaces can be seen as algebraic or arithmetic objects has occupied a central place in many areas of algebraic geometry and number theory, most notably in the Langlands program. In this talk, I will give an introduction to these ideas, and report on recent progress which sheds light on these questions in some exotic, and hitherto inaccessible, cases.