Number Theory Seminar @ University of Melbourne
Alex Ghitza and I are running a working seminar on things number-theoretic.
Time: 13:00--14:00 Tue. (Melbourne local time) for 2024S2.
The theme for 2024S2 is an arithmetic introduction to Shimura varieties. We will mostly follow "Jared Weinstein. Reciprocity laws and Galois representations: recent breakthroughs. Bull. Amer. Math. Soc. (N.S.), 53(1):1β39, 2016."
Time: 13:00--14:00 Mon. (Melbourne local time) for 2024S1.
Venue: Peter Hall 162 (The πNEWπ seminar room)
Please go to the Number Theory Research Group website where you can find a link to join our mailing list. You will receive the Zoom link and announcements of talks.
8 Oct. 2024
Shimura varieties
Chengjing Zhang
Last talk of 2024S2. We will resume regularly in 2025S1. We may have sporadic talks during the break.
1 Oct. 2024
Arithmetic manifolds
Bowan Hafey
24 Sept. 2024
Semester break. No talk.
17 Sept. 2024
Automorphic forms and automorphic representations
Qizheng Han
10 Sept. 2024
Modular curves
3 Sept. 2024
Groups over local fields: Step one towards Ξ\G/K
I want to try to make a basic path to these coset spaces, using the kinds of tools we use
in first year Linear algebra and 2nd year GTLA. The key idea is to consider infinite n-periodic matrices
in place of the n x n matrices that are used in first and second year. The hope is that, once one sets up infinite n-periodic
matrices cleanly, then all that remains is to redo what is done in first and second year in this setting.
27 Aug. 2024
Modular curves
Miles Koumouris
20 Aug. 2024
Modular forms
Kwan Sheng Ong
13 Aug. 2024
Class field theory
Riley Moriss
6 Aug. 2024
Classical reciprocity laws
Alexander Stratov
30 July. 2024
Introduction to the "Reciprocity laws" survey by Jared Weinstein
23 July 2024
Modular Forms and Galois Representations
I will begin by recalling the basic facts about Tate modules of elliptic curves. Building on this discussion, I will recall the basic facts about Galois representations attached to modular forms, and sketch the proofs of some of them.
This is the preliminary talk to the talk, From Modular Curves to Categorification, in the representation theory seminar on 25 July, also given by Matt.
More details are on the
representation theory seminar webpage.
Last talk of 2024S1. We will resume in 2024S2.
There may be special talks during the Winter break, in which case, we will send out announcements.
27 May 2024
Quasimodular forms with examples
Miles Koumouris
20 May 2024
Serre p-adic modular forms with examples
Miles Koumouris
13 May 2024
Parabolic Induction and Eisenstein Series II with examples
Chengjing Zhang
6 May 2024
Parabolic Induction and Eisenstein Series with examples
Chengjing Zhang
This talk focuses on parabolic induction and Eisenstein series. We will discuss how induction, a powerful tool in the representation theory of finite groups, appears as parabolic induction in the theory of automorphic representations. Although parabolically induced representations are not automorphic themselves, they can be associated with automorphic representations through Eisenstein series.
29 Apr. 2024
Automorphic forms on GLn with examples
Qizheng Han
22 Apr. 2024
Automorphic forms with examples
Riley Moriss
15 Apr. 2024
Eisenstein series (GL2 and Siegel cases) with examples
Bowan Hafey
8 Apr. 2024
Parabolic subgroups with examples
Bowan Hafey
1 Apr. 2024
Easter Break. No Talk. April Fool's Day. It is true, no talk.
25 Mar. 2024
Reductive groups with examples
Riley Moriss
18 Mar. 2024
Elliptic curves and Tate modules with examples
Kwan Sheng Ong
11 Mar. 2024
Group schemes with examples
Riley Moriss
4 Mar. 2024
A grand overview of the universe of Number Theory