Math 205: Topics in Algebra (Winter 2017)

Automorphic forms - the adelic point of view - with emphasis on GL(2) forms; time permitting, we will explore the differences between GL(2) and GL(n) with n>2, as well as other reductive groups.

Instructor:	Alina Bucur (alina at math dot ucsd dot edu), APM 7151
Lectures:	MWF 1-2pm, APM B412
Office hours:	M 2-3pm
	if you cannot make this time, email me for an appointment

Books:	For the adelic point of view, our main resource will be Gelbart's Automorphic forms on adele groups (freely available electronic reference through UCSD library). If you prefer your automorphic forms without adeles, Terras' books on Harmonic Analysis on Symmetric Spaces vol 1 and vol 2 (again free through UCSD library) give a wonderful exposition. Two other good reference books are Bump's Automorphic forms and representations (again free through UCSD library) and Goldfeld's Automorphic forms and L-functions for the group GL(n,R). A trove of notes on this and related subjects can be found on Garrett's vignettes page.
Prerequisites:	MATH 200 series; some familiarity with modular forms and/or adeles would be useful.
Corequisites:	MATH 204B (at least the first few weeks that will cover adeles) or knowledge thereof.
Grading:	If you need a meaningful grade (e.g., if you are an undergraduate) then let me know at the start of the course.

First lecture: Monday, January 9.
Last lecture: Friday, March 17.
UCSD holidays this term: Monday, January 16 and Monday, February 20.
Other dates with no lectures: Friday, January 12 and Monday, March 14. (We might schedule makeup lecture(s).)
No office hours Monday, January 23. Sorry for the inconvenience.
For the local theory, The local Langlands conjecture for GL(2) by Bushnell and Henniart is a great reference. The link gives you free access throught UCSD.