ICTP Mathematics Seminar - Wednesday 9 September, at 14:30

[Math Group]

M A T H E M A T I C S   S E M I N A R S   2015

Wednesday, 9 September, at 14:30 hrs.

Kathrin Bringmann (University of Cologne, Germany)

Title: Polar harmonic Maass forms


Abstract: Classical modular forms are holomorphic functions that are 
meromorphic at the cusps and satisfy nice modular symmetries. Harmonic 
Maass forms are real-analytic generalizations thereof in that instead of 
being holomorphic they are annihilated by the weight k Laplace operator. 
These functions generalize Maass waveforms, which are of weight 0 and 
decay in the cusps. Recently there has been an active interest in 
harmonic Maass forms, as their holomorphic parts (so-called mock modular 
forms) naturally occur in various areas of mathematics and physics. The 
probably most famous example of mock modular forms are given by 
Ramanujan's mock theta function which he introduced in his last letter 
to Hardy shortly before he died.

In this talk I instead consider Maass forms which are also allowed to 
have poles in the upper half plane and give various applications of such 
functions including Hardy-Ramanujan type formulas for meromorphic 
modular forms.
All this is joint work with Ben Kane.

Venue:  Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first 
floor)