Number Theory Seminar
Organizers:
Riad Masri —
Matt Papanikolas —
Shuhui Shi —
Matt Young
| |
Date
Time |
Location | Speaker |
Title – click for abstract |
 |
03/02
2:30pm |
BLOC 302 |
Larry Rolen
Vanderbilt University |
Recent problems in partitions and other combinatorial functions
In this talk, I will discuss recent work, joint with a
number of collaborators, on analytic and combinatorial properties of
the partition and related functions. This includes work on recent
conjectures of Stanton, which aim to give a deeper understanding into
the "rank" and "crank" functions which "explain" the famous partition
congruences of Ramanujan. I will describe progress in producing such
functions for other combinatorial functions using the theory of
modular and Jacobi forms and recent connections with Lie-theoretic
objects due to Gritsenko-Skoruppa-Zagier. I will also discuss how
analytic questions about partitions can be used to study Stanton's
conjectures, as well as recent conjectures on partition inequalities
due to Chern-Fu-Tang and Heim-Neuhauser, which are related to the
Nekrasov-Okounkov formula. |
|
03/09
2:30pm |
BLOC 302 |
Yen-Tsung Chen
Penn State University |
On almost holomorphic Drinfeld modular forms and their special values at CM points
It is known that the derivative of a modular form is no longer modular. One possible approach to this issue is modifying the differential operator by sacrificing the holomorphy. This leads to the study of nearly holomorphic modular forms and Maass-Shimura operators. The former object was introduced and investigated by Shimura in the 1970s. It also has a strong connection with the quasi-modular forms introduced by Kaneko and Zagier in 1995.
In this talk, we introduce the notion of almost holomorphic Drinfeld modular forms and construct an analogue of the Maass-Shimura operators in this context. The structure of almost holomorphic Drinfeld modular forms as well as its connection with Drinfeld quasi-modular forms have been developed. Furthermore, we establish the algebraic independence result for the special values of almost holomorphic Drinfeld modular forms at CM points. This is joint work with Oguz Gezmis. |
Menu
