**Date & Time:** Monday, September 02, 2013, 15:30-17:00.

**Venue:** Ramanujan Hall

**Title:** Local Cohomology Modules I

**Speaker: ** Jugal Verma, IIT Bombay

**Abstract:** Local Cohomology modules were introduced by A. Grothendieck. These
modules provide a powerful tool for investigations in commutative algebra,
algebraic geometry and combinatorics. In this series of 6 lectures, we will
describe several equivalent constructions of local cohomology modules of
modules over Noetherian rings. We will prove vanishing theorems due to
Grothendieck and Hartshorne. Among applications we will prove connectedness
theorems for punctured spectrum and algebraic varieties due to Hartshorne,
Faltings and Fulton-Hansen.