Learning Seminar on Modular Forms, Automorphic Representations, and $L$-functions

This is the page for the Fall 2026 learning seminar on Modular Forms, Automorphic Representations, and $L$-functions at Fordham University.

Description: This will be an intense learning seminar on the arithmetic theory of automorphic forms and their \(L\)-functions from both the classical and the representation theoretic perspectives. The seminar will be in-person at the Lincoln Center campus, having two sessions with a small break in between with each session lasting for an hour and 15 minutes.

  • Session - I (S-I), Modular Forms, 2:30-3:45PM. This session will be on the theory of modular forms, especially Hecke theory and \(L\)-functions, based on such references: first 4 chapters of Miyake’s Modular Forms and the first 3 chapters of Shimura’s Arithmetic Theory of Automorphic Functions.

  • Session - II (S-II), Automorphic Representations, 4:00-5:15PM. This session will be on Automorphic Representations for GL(2) based on the references: Bump’s Automorphic Forms and Representations, and the first five chapters of Gelbart’s Automorphic forms on Adele Groups. Depending on how the seminar progresses, we may graduate to automorphic forms on GL(n) or a reductive group over a number field based on Goldfeld and Hundley’s book and Getz and Hahn’s book.

Venue: Fordham University at Lincoln Center, Room: LL902

Day/time: Monday’s at 2:30-5:15PM, starting from August 31, 2026

Schedule

The first meetings on 8/31 will also serve as an organizational meeting to seek volunteers to speak in the seminar.

Learning Seminar on Modular Forms

  • (S-I) Fall 2026, Monday’s at 2:30-3:45PM.
Date   Reading   Speaker
8/31   Invariant metric and measure on $\mathbb{H}$ (notes)   Raghuram
9/7   Labor Day    
9/14   Fuchsian groups and fundamental domains   Sevan Bharathan
9/21   $\Gamma\backslash\mathbb{H}^*$ as a Riemann surface   Sevan Bharathan
9/28   Automorphic forms   TBD
10/5   Automorphic forms and differentials   TBD
10/12   Columbus Day    
10/19   Dimensions of $G_k(\Gamma)$ and $S_k(\Gamma)$   Cris Poor
10/26   Poincaré series and Eisenstein series   Jayadev Athreya
11/2   Hecke algebras and Hecke operations   TBD
11/9   $\text{SL}_2(\mathbb{Z})$   Asimina Hamakiotes
11/16   Congruence subgroups $\Gamma_0(N)$, $\Gamma_1(N)$, $\Gamma(N)$   Asimina Hamakiotes
11/23   Modular forms and Dirichlet series   Raghuram
11/30   Hecke $L$-functions for modular forms   Raghuram
         

Learning Seminar on Automorphic Representations

  • (S-II) Fall 2026, Monday’s at 4:00-5:15PM.
Date   Reading   Speaker
8/31   Universal enveloping algebra (notes)   Raghuram
9/7   Labor Day    
9/14   Basic representation theory   Ajmain
9/21   Irreducible $(\mathfrak{g},K)$-module for $\text{GL}_2(\mathbb{R})$   Ajmain
9/28   Intertwining operations   TBD
10/5   Discrete series representations of $\text{GL}_2(\mathbb{R})$   TBD
10/12   Columbus Day    
10/19   Local Langlands correspondence of $\text{GL}_2(\mathbb{R})$   Raghuram
10/26   Representations of $\text{GL}_2(\mathbb{F}_q)$   TBD
11/2   Smooth and Admissible representations   TBD
11/9   Distribution and Sheaves   Sevan Bharathan
11/16   Whittaker Models and Jacquet functors   David Luo
11/23   Unramified principal series representations   Sevan Bharathan
11/30   Local Langlands correspondence of $\text{GL}_2(F)$ for a $p$-adic $F$   Raghuram
         

For any questions, contact ahamakiotes@fordham.edu.