Seminar on the things we are thinking about
This term (at the suggestion of Bill Casselman) we'll have an informal
seminar just to discuss the things we
are currently working on, in the broad area of representation theory of
p-adic and real Lie groups and other related topics.
When and where:
Tuesdays, 3:30-5pm (the ending time approximate), in Math 126.
Tentative schedule (the titles are approximate):
- September 25.
V. Vatsal, p-adic L-functions.
- October 2. NO MEETING.
- October 9. Boaz Elazar.
SCHWARTZ FUNCTIONS ON ALGEBRAIC AND QN VARIETIES
Abstract: We introduce a new category called Quasi-Nash,
unifying
Nash manifolds and algebraic varieties. We define Schwartz functions,
tempered functions and tempered distributions in this category. We show
that
the classical properties of these spaces, that hold on Nash manifolds and
real affine algebraic varieties, hold in this category as well.
- October 16. Thomas Rud.
Algebraic tori in SAGE.
- October 23. Kimball Martin, University of Oklahoma.
The basis problem for quaternion algebras and modular forms.
- October 30: NO MEETING
- November 6: TBD. Jeremy Usatine (Yale University). Title TBA.
- November 13: NO MEETING.
- November 20: John Enns.
Title: Local-global compatibility in the mod p Langlands program
Abstract: Let
F_w be a finite extension of Q_p, thought of as the completion of a CM field F
at the place w. We want to study the relationships between mod p
representations
of the Galois group G_{F_w} and mod p representations of GLn(F_w). If r_w is
the
restriction to w of some global automorphic mod p Galois representation of F,
it
is possible to naturally associate with it a smooth admissible representation
of
GLn(F_w) using spaces of mod p automorphic forms. In this talk I will describe
what is known about these globally defined representations of GLn(F_w), and
some
open questions.
- November 27: No meeting
- December 4: V. Vatsal,
Gorenstein orders, quadratic forms, and supercuspidal representations of
GL_2.
Abstract: I'll give an overview of the basic properties of Gorenstein
orders in
quaternion algebras, and describe how they are related to ternary
quadratic
forms and supercuspidal representations. The goal is to prove a hard
theorem
of Schiemann, originally proved by a large computer search, that a
positive
definite integer valued ternary quadratic form is determined up to
isometry
by its theta function. I will sketch a strategy for proving this theorem
in
an automorphic way via a formula due to Waldspurger, and show (I hope) how
to prove a key global lemma which is an important step along the way.
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