Description
Algebraic geometry seminar.
Speaker: Arjun Paul.
Affiliation: IIT Bombay.
Date and Time: Friday 06 March, 11:00 am - 12:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Mehta-Ramanathan's restriction theorems and their applications.
Abstract: Fundamental groups of algebraic varieties and their
representations are very interesting objects, and have given rise to a lot
of mathematics. The famous Narasimhan-Seshadri Theorem states that on a
compact Riemann surface there is a bijective correspondence between stable
holomorphic vector bundles with vanishing Chern classes and unitary
representations of the topological fundamental group. This result was
generalized to smooth projective surfaces by Donaldson. The Stable
Restriction Theorem of Mehta-Ramanathan then enables us to generalize this
correspondence, between stable holomorphic vector bundles with vanishing
Chern classes and unitary representations of the fundamental group, to
arbitrary smooth projective varieties. This consequence is the main
application we have in mind. We will also give an overview of the proof of
the Stable and Semi-stable Restriction theorems.