Learning seminar: Trace Formulae

This is the website for the learning seminar about the trace formula organized by Héctor del Castillo and Andrei Seymour-Howell. In this seminar, we will cover the basics of the trace formula, aiming towards explicit trace formulae results in the co-compact case and explore ideas for extending the trace formula beyond this case.

The seminar will take place in Room 205 of the Education Convergence Building at Chonnam National University, Gwangju. The weekly schedule is Tuesday at 11:00 am. Topics that we will cover include:

• Trace formula for finite groups
• Basics on functional analysis: compact and trace-class operators
• Basic on adèles and algebraic groups
• L^2 space and cuspidal spectrum
• (Relative) simple trace formula: traces and orbital integrals
• Weyl's law
• Trace formula beyond the compact case: SL(2)

The seminar will be based on the following references:

• Generalized Functions Vol 6: Representation Theory and Automorphic Functions - I. M. Gelfand, M. I. Graev, I. I. Pyatetskii-Shapiro
• An Introduction to Automorphic Representations with a view toward Trace Formulae - J. R. Getz, H. Hahn
• An introduction to the trace formula - D. Whitehouse

Lectures