Introduction to modular forms with a view towards the Langlands program

Mercredi, 12. février 2020 - 10:15 - 11:15
Orateur: 

Liu Kegang (Université Sorbonne Paris Nord)

Résumé: 

   The theory of modular forms is an extensive and important area in
modern number theory, in that they have deep relations with many other
fundamental - though of rather different kinds at first sight - parts of
arithmetic or more general mathematics, eg., elliptic curves. It is also
well known that they play a significant role in the proof of Fermat’s
Last Theorem by Wiles.
   In this talk we aim to explain such comprehensiveness of the theory of
modular forms, starting from early historical developments together with
motivations.  After presenting the basic definitions, properties and
possibly some elementary applications, we then move to sketch some
relatively recent results within the framework of the Langlands program,
such as the relationships between modular forms and Galois
representations, or as well various versions of the Modularity Theorem
(if time permits).