NUmber Theory Seminar 2021

TL;DR: Global Jacquet-Langlands theory, following Godement's notes; the 1-3 of modular forms

18 March 2021: Adelic groups and cuspidal functions for \(\mathrm{GL}(2)\), by Chenyan Wu
25 March 2021: Decomposition of space of cuspidal functions -- compact operators, by Chenyan Wu
1 April 2021: Decomposition of space of cuspidal functions -- tensor product decomposition, by Alex Ghitza
15 April 2021: Global Hecke algebra, by Simon Thomas
22 April 2021: Review of admissible representations and Whittaker models, by Chenyan Wu
29 April 2021: Uniqueness of global Whittaker model and multiplicity one theorem for \(\mathrm{GL}_2\), by Chenyan Wu
6 May 2021: Global L-functions I, by Alex Ghitza
20 May 2021: Global L-functions II, by Alex Ghitza
3 June 2021: The converse theorem, by Chenyan Wu
10 June 2021: Archimedean theory I, by Lance Gurney
17 June 2021: Archimedean theory II, by Lance Gurney
8 July 2021: Report on lifting puzzles and congruences, by Chenyan Wu
15 July 2021: Eisenstein congruences for \(\mathrm{GL}_2\), by Alex Ghitza
12 August 2021: Introduction to modular forms, by Alex Ghitza
19 August 2021: Modular groups, modular functions, and modular forms, by Alex Ghitza
26 August 2021: Examples of modular forms -- Eisenstein series and the discriminant function I, by Chenyan Wu
2 September 2021: Examples of modular forms -- Eisenstein series and the discriminant function II, by Chenyan Wu
9 September 2021: Hecke operators, Hecke eigenfunctions, and related L-series, by Alex Ghitza
16 September 2021: Theta series, by Simon Thomas
30 September 2021: L-series continued, by Alex Ghitza
7 October 2021: Introduction to Siegel modular forms, by Chenyan Wu
14 October 2021: Eisenstein series in the Siegel setting, by Alex Ghitza
21 October 2021: Singular forms, theta series, and Fourier-Jacobi expansions, by Chenyan Wu