Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

Dr. Rohith Varma
Indian Institute of Technology Palakkad

6

(1.5

hours)

Presheaves, sheaves, sheafificaiton, ringed spaces, schemes, morphisms of schemes, sheaves of modules, constructions of sheaves.

Prof. Manoj Kummini
Chennai Mathematical Institute

4

(1.5

hours)

Homological tools (Mapping cones, Spectral sequences)

Dr. Sanjay Amrutiya
Indian Institute of Technology Gandhinagar

4

(1.5

hours)

Separated and proper morphisms, divisors, differentials, invertible sheaves, Leray spectral sequence.

Dr.Vivek Mukundan
Indian Institute of Technology Delhi

4

(1.5

hours)

Injective resolutions and Matlis duality

Prof. Jugal K Verma
Indian Institute of Technology Gandhinagar

5

(1.5

hours)

Gorenstein rings and canonical modules

Prof.Krishna Hanumanthu
Chennai Mathematical Institute

4

(1.5

hours)

Derived functors, sheaf cohomology, Grothendieck vanishing, cohomology of affine schemes, Serre’s affineness criterion, Cech cohomology, cohomology of projective spaces.

Prof. Tony J. Puthenpurakal
Indian Institute of Technology Bombay

5

(1.5

hours)

Local cohomology, local duality and some applications

Prof. A J Parameswaran
Kerala School of Mathematics

4

(1.5

hours)

Serre’s vanishing, ext groups and sheaves, higher direct image sheaves, formal function theory, semi continuity, vanishing theorems (Kodaira-Akizuki -Nakano,Grauert-Riemenschneider), Formal duality.