Talks
Here is an (incomplete) list of study groups which I have been helped organise or given talks at:
2021/22 Term 1:
November:
The Bloch-Kato Conjecture (Warwick Maths Postgrad Seminar)
Modular forms on the Bruhat-Tits tree (Warwick Number Theory Group)
2020/21 Term 3:
June: Complex Multiplication for Shimura Varieties (Warwick Number Theory Group)
Notes
2020/21 Term 2:
February: Bloch-Kato Selmer Groups (London Number Theory Study Group)
Notes
March: Brill-Noether Theory (Reading group on Mukai's classification of Fano 3-folds)
Notes
2020/21 Term 2: Modular Forms & Modular Curves
Following Diamond/Shurman (D/S) and Milne's notes
Schedule:
Date | Title | Speaker | References | Notes |
22/1 | Introduction (Modular forms) | Elvira | Serre (A Course in Arithmetic ch 7) | Week 1 - Introduction to Modular Forms |
29/1 | Modular curves over C | Ben |
Milne ch2, Diamond/Shurman ch 2-3 |
Week 2 - Modular Forms and Geometry |
5/2 | Elliptic curves over C and lattices | Diana | Milne ch 3-4 | Week 3 - Elliptic Functions |
12/2 | Hecke operators | Xenia | Milne ch 5, D/S ch 5.1-5.5 | Week 4 - Hecke Operators |
19/2 | Eigenforms and L-functions | Barna | Milne ch 5, D/S ch 5.6-5.11 | |
26/2 | Rational models of modular curves | Steven | Milne ch 8, D/S ch 7 | Week 6 - Canonical Model of X_0(N) |
5/3 | Modular curves as moduli spaces | Phillipe | Milne ch 8, D/S ch 1.5 + more | Week 7 - Moduli Spaces |
12/3 | Reduction mod p | Horatio | D/S ch 8.1-8.4 | Week 8 - Reduction mod p |
19/3 | Eichler-Shimura relation | Muhammad | D/S ch 8.5-8.8, Milne ch 10 | Week 9 - Eichler-Shimura Relations |
26/3 | Bonus talk: Modularity | Chris W |
2020/21 Term 1:
August: Hilbert Modular Forms (Informal Göttingen Number Theory seminar)
Notes -
November: Local Class Field Theory - Cohomology (Warwick Number Theory Group)
Notes