Sanyam Gupta (Université de Lille) : Modular forms and Galois Representations

Galois representations attached to modular forms play a central role in modern number theory and form a key bridge between analysis, algebra, and arithmetic geometry. In this talk, we will give a brief introduction to modular forms and their basic properties, emphasizing their arithmetic significance. We will then explain how modular forms give rise to Galois representations, highlighting the fundamental results of Pierre Deligne and Jean-Pierre Serre that establish this correspondence. The goal of the talk is to provide an accessible overview of this deep connection and illustrate why it has become one of the cornerstones of modern arithmetic.