Mathematics at IISER Pune has organised:
Overview: Modular forms and automorphic representations have played a central role in the research in number theory in the last half-century. Several important problems in mathematics, including Fermat’s Last Theorem, have been solved using modular forms. Two of the seven million dollar millennium problems are related to modular forms and related topics.
In this course, we plan to introduce the audience to the topic of Siegel modular forms. The idea is that, via the study of Siegel modular forms, the students will get to know the current directions of research in automorphic forms. We will cover topics ranging from the basic definitions and properties of Siegel modular forms, to the recent research on Langlands transfer and Deligne’s conjectures on special values of L-functions, and will also include several important open problems like the Bocherer’s conjecture.
This course has two modules that must be taken together. It is intended for graduate students interested in research in number theory. Familiarity with elliptic modular forms and associated representations is preferable but not essential. We will provide a hand out for the attendees to read to get them prepared for the lectures. The advanced topics of this course will also be of interest to young as well as established researchers in number theory.
About the Faculty: Dr Ameya Pitale is a faculty member at the University of Oklahoma, USA. His research interests include the theory of automorphic forms and automorphic representations for Siegel modular forms. He works on local and global aspects of automorphic representations related to Siegel modular forms, automorphic transfer, special values of L-functions, bounds for Rankin–Selberg L-functions, integral representations of L-functions and Boecherer’s conjecture.
