Student Learning Seminar on Galois Deformations
The purpose of this seminar is to give an introduction to the theory of Galois deformations and discuss its most important applications in number theory. The seminar is intended for graduate students interested in the topic. The organizers will impart the lectures by default, but we encourage participants to prepare and give some of the talks. If you are an undergraduate student or external graduate student and would like to come, please email or .

When: Wednesday, 2:45pm - 3:45pm
Where: TBD
Organizers: Rafah Hajjar Muñoz, Vivian Yu

Remark: Until we have a definite room for the seminar, we will be meeting at the graduate lounge.

Date Speaker Title and Notes
September 13 Rafah Hajjar Introduction. Review of Galois Representations
Abstract: Ee will introduce the concept of Galois deformations and discuss briefly their relevance and literature. We will also give a brief review of Galois representations, stating their basic properties and discussing how they naturally arise in several areas of Number Theory.
September 20 Rafah Hajjar Galois Representations (cont.) and the representation theory of profinite groups
Abstract: We will discuss some facts about the representation theory of profinite groups that will be useful in our study of Galois deformations. Also, following the discussion of last week, we will finish our review of the literature on the theory of Galois representations. In particular, today we will talk about the representations of local Galois groups, giving brief accounts of Weil-Deligne representations, the monodromy theorem, and p-adic Hodge theory.
September 27 Kevin Chang
Introduction to Galois deformations
Abstract: I will introduce basic notions in deformation theory, such as universal deformation rings and the Zariski tangent space, and state some important properties of Galois deformations to be covered in more depth in future talks.
October 4 Vivian Yu Functors and representability. Schelssinger's criterion.
October 11 Matthew Hasse-Liu Zariski Tangent Space. Obstructed and unobstructed problems.
October 18 Sangmin Ko Local deformation conditions. Determinant, ordinary and flat conditions.
October 25 Rafah Hajjar Global deformation conditions. Galois cohomology. Duality theorems
November 1 Baiqing Zhu Explicit construction of universal deformation rings
November 8 Rafah Hajjar Modularity Lifting theorems. Taylor Wiles method
November 15 TBD The patching argument
November 22 TBD Base change. Ihara avoidance. Kisin's modification.
November 29 Rafah Hajjar Calegari Geraghty method
December 6 Rafah Hajjar Derived Galois deformations