**Date & Time:** Wednesday, December 31, 2014, 16:00-17:00.

**Venue:** Ramanujan Hall

**Speaker:** Mahan Mj, RKM Vivekananda University

**Title:** 3-manifolds and (quasi) projective varieties

**Abstract:** Quasiprojective varieties are of the form X \ D where X is
a projective variety and D a normal crossing divisor. Affine varieties and the moduli space of curves are examples. A closed smooth manifold M admits a good complexification
(in the sense of Totaro) if it can be realized as the set of real points of an affine variety X such that the inclusion of M into X is a homotopy equivalence. The relationship between the complex geometry of 3 dimensional varieties and the topology of closed 3 manifolds (3 dimensional version of Hilbert's 16th problem) is not well understood.

We shall classify 3-manifold groups that can appear as fundamental groups of quasiprojective and projective varieties answering questions by Dimca-Papadima-Suciu and Friedl-Suciu. We shall use this to classify 3-manifolds admitting a good complexification answering a question of Totaro. This is joint work with Indranil Biswas.