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
rh3101@columbia.edu or
qy2266@columbia.edu .
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.
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 |