Automorphic Forms

Spring 2018

The seminar will meet weekly at the Student Lounge or Thesis Room, from 2:00pm-3:00pm on Friday. The official homepage for the seminar is here.

I shall be following the notes of Jayce R Getz and his upcoming book with Heekyoung Hahn.

Algebraic Groups I

January 5th, 2018

Abstract: In this talk, I shall define and give examples of algebraic groups; focussing on the case of linear affine algebraic group. Notes

Algebraic Groups II

January 12th, 2018

Abstract: We continue with various notion related to affine algebraic groups such as algebraic group homomorphisms (so we get a category to work with), algebraic subgroup, derived subgroup, existence of center, quotient, extension of scalars and Weil restrictions of scalars. Notes

Algebraic Groups III

January 19th, 2018

Abstract: We continue our discussion with the notion of unipotent radical, semisimple, torus, reductive group. Notes

No talk on January 26th, 2018 for Prof. Dodziuk's birthday conference.

Algebraic Groups IV

February 2nd, 2018

Abstract: Let's talk about Lie algebra and classification of reductive groups via root system. Notes

Algebraic Groups V

February 23th, 2018

Abstract: Adelic points on algebraic groups and strong approximation. Notes

Analysis on Locally Compact Group

March 2nd, 2018

Abstract: A short introduction to Haar measures on locally compact group. Notes

Automorphic Representations I

April 27th, 2018

Abstract: We give a quick review of basic representation theory in the context of locally compact Hausdorff groups and state the first definition of automorphic representations. Notes

Automorphic Representations II

May 4th, 2018

Abstract: We continue with an alternative definition of automorphic representations and some representation theory of Lie group. Notes

Automorphic Representations III

May 11th, 2018

Abstract: Representation theory of td groups. Automorphic forms and modular forms. Notes

Automorphic Representations IV

May 18th, 2018

Abstract: The case of $GL_2$. Notes