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Graduate Topics Courses

Fall 2021

Math GR8674 – Topics in Number Theory

Instructor: Eric Urban
Day/Time: TR 11:40 AM – 12:55 PM
Title: Simplicial deformation of Galois representations and application
Abstract: The goals of this course is to introduce the theory of simplicial deformation rings in the style of Galasius-Venkatesh and apply it to the study of Selmer groups.

Math GR9903 – Topics in Algebraic Geometry

Instructor: Giulia Sacca
Day/Time: TR 2:40 – 3:55 PM
Title: Moduli spaces and Hyper-Kahler Manifolds
Abstract: This course will offer an introduction to compact hyper-Kahler (HK) manifolds. These form a special class of Kahler manifolds, which have recently attracted attention in algebraic geometry. After an introduction to the general theory, basic results, and more recent developments, I will focus on the examples of HK manifolds constructed as moduli spaces: from the classical Gieseker moduli spaces, to moduli spaces of Bridgeland stable objects in the derived category of a K3 surface and, if time allows, in the Kuznetsov component of the derived category of a cubic fourfold.


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