**Date & Time:** Wednesday, April 15, 2015, 16:00-17:00.

**Venue:** Ramanujan Hall

**Speaker:** C. S. Rajan, TIFR Mumbai

**Title:** Groups via Conjugacy Classes

**Abstract:** The study of conjugacy classes naturally arises for groups occurring in arithmetic. For example the Galois group
of a finite Galois extension over the rationals comes equipped with a collection of conjugacy classes, the Frobenius conjugacy classes. After talking about some questions in this regard, I will focus on one particular question: the distribution of the
fields which arise as splitting fields of the characteristic polynomials of these conjugacy classes with respect to some representation of the group. If time permits, I will talk about a unitary trick in the context of $l$-adic representations of Galois groups.