Speaker: Beth Romano (King's College, London, U. K.)
Title: An introduction to the local Langlands correspondence
Time, day and date: 4:00:00 PM, Monday, January 20
Venue: Ramanujan Hall

Abstracts:
The local Langlands correspondence conjectures links between two seemingly unrelated areas of mathematics: the Galois theory of local fields and the theory of complex Lie groups. In this talk, we'll use examples to introduce some of the objects of interest from both number theory and geometry. We'll then use these examples to illuminate some of the beautiful interactions between these different areas.

Commutative Algebra seminar
Speaker: R. V. Gurjar (TIFR (retd))
Title: Automorphisms of algebraic varieties II
Time, day and date: 4:00:00 PM, Tuesday, January 21
Venue: Ramanujan Hall

Abstract: 

Commutative Algebra seminar
In the first lecture we will discuss general results about diffeomorphisms (resp. biholomorphisms) of compact differentiable (resp. compact complex) manifolds, and general algebraic varieties.
In the second talk we will indicate a proof of an important result.
Theorem. Let X be a smooth projective variety of general type. Then the automorphism group of X is finite.
This applies to compact Riemann surfaces of genus > 1. Using this I will indicate the proof of Hurwitz's theorem:
Theorem. Let C be a compact Riemann surface of genus g > 1. Then Aut(C) has order at most 84(g-1). This bound is best possible.