Galois Representations Reading Group

This is a biweekly learning seminar and reading group that meets Fridays 3:30-4:30 pm (15:30-16:30) GMT virtually via Zoom. We also occasionally meet Tuesdays at the same time. Note that you will need to register an account with Zoom if you want to join. Topics range across a lot of number theory, with Galois representations as a loose organizing theme. Talk recordings are available upon request and at the speaker’s discretion.

TopicDateSpeaker
IntroductionJune 18, 2021N/A
Local Fields and Their Galois TheoryJune 25, 2021Zachary GardnerNotes
Introduction to Galois RepresentationsJuly 2, 2021Zachary Gardner Notes
L-FunctionsJuly 9, 2021William DudarovNotes
Basics of Elliptic CurvesJuly 16, 2021Ehsan ShahoseiniNotes
Isogenies of Elliptic CurvesJuly 23, 2021Ehsan ShahoseiniNotes
Reading group schedule

References and Supplemental Resources

June 25, 2021 – Local Fields and Their Galois Theory

  • D. Benois. An Introduction to p-adic Hodge Theory. (link) [§1.1-1.3 & §2.1-2.3]

July 2, 2021 – Introduction to Galois Representations

  • S. Marks. Galois representations. (link)
  • Supplemental Resources:
    • S. Marks. A (non)introduction to modular forms. (link)
    • A. Youcis. Weil-Deligne representations and p-adic Hodge theory: motivation. (link)
    • S. Bhattarchya. The p-adic Cyclotomic Character. (link)

July 16, 2021 – Basics of Elliptic Curves

  • J. Silverman. The Arithmetic of Elliptic Curves. (link) [§III.1-III.3]

July 23, 2021 – Isogenies of Elliptic Curves

  • J. Silverman. The Arithmetic of Elliptic Curves. [§III.4-III.6]

Other Resources

  • http://people.math.harvard.edu/~smarks/mod-forms-tutorial/index.html
  • https://people.math.ethz.ch/~mmornev/padic.html
  • S. Bhattacharya. Basics of Group Cohomology. (link)