Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.

This course will survey a variety of recent research topics in arithmetic geometry, with an aim to expose open problems which may be reasonable entry points to a Ph.D. thesis. Topics will include: special cycles and arithmetic theta functions, the Langlands correspondence and its geometrizations, the Breuil—Mezard Conjecture, the Artin—Tate Conjecture, and more as time permits. The lectures will assume familiarity with background material such as perverse sheaves, six-functor formalisms, algebraic stacks, p-adic groups, homotopy theory, and representation theory of algebraic groups; but these can be black-boxed to some exte

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