Ramanujan Congruences and Beyond

The speaker will introduce the idea of Hensel to define the local fields. How can we lift solutions of equations from finite fields to fields of characteristic zero? I will then introduce the Ramanujan congruence and explain how these congruences are lifting modular forms from characteristic 691 to characteristic zero. In the process, I will define modular forms and give examples of modular forms. If time permit, speaker will talk about my work (joint with Majumdar and Kumar) that extends Ramanujan congruences. I will also state a conjecture of Harder that generalises Ramanujan congruences for Siegel modular forms (Gsp_4). One third of the talk should be accessible to the undergraduate students and two thirds of the talk should be accessible to the graduate students.