## Reading seminar on
harmonic analysis on p-adic Lie algebras
(Math 592, Term II 2014/2015)

Math 592 is organized by Lior Silberman, Bill Casselman and myself.

### References:

We will closely follow the lecture notes by R. Kottwitz in

2004 Clay lecture notes volume .

### Time and place:

Tuesdays 3:34-5:15pm in Math 126.
However, there will be many scheduling changes, please check this page
often.
- It's moving to Fridays for the rest of the term (and not every week)
-- please watch the schedule and announcements! After March 10, the
seminar will meet on Fridays March 13, March 27, and April 27 only!

### Schedule

- January 8: Organization meeting and introduction: local Trace formula
for compact groups (J. Gordon). In
Math 126, 3:30pm.
- January 13: The tree and unipotent orbital
integrals for GL(2). (Radhika)

Useful reference for this and next talk: Notes by W.
Casselman on the tree for SL(2).

Here is a summary of this
computation
that only uses double cosets and not the tree.
- January 20: Semisimple orbital integrals in GL(2) (Laura).
- January 27: Weyl integration formula (Athena).
- February 3 and February 10: no
meeting.
- February 17: Preliminary discussion of the local Trace formula for
the Lie
algebra (Ed).
- February 24: Preliminary discussion of the Local Trace Formula for
the Lie algebra -- computing the weight function. Statement of the
local TF for GL(2) (Ed and Julia). (This was Sections 9 -- 10.2).
- March 3: a glimpse of Arthur's Trace Formula in the case of GL(2)
(Justin).
- March 10: From nice-ness of orbital integrals to nice-ness of their
Fourier transform, via local Trace formula. (Julia)
(This is based on Sections 10.3-10.4 and 25, 26).
- Friday March 13 (note the
date!) 12pm, in Math 126:
Continuation from March 10.
- Friday March 27 (note the
date!) 12pm, in Math 126:
Shalika germs: definition and main properties (Athena).
- Friday April 10 (note the
date!) 12pm, in Math 126:
Finishing the proof of nice-ness of orbital integrals (Laura?)