Chennai Mathematical Institute

Lecture Series

Tools of the Mathematical Trade

Spectral Sequences and Applications

Prof. S. Ramanan, Chennai Mathematical Institute

November 2-11, 2009


Dates: 2, 4, 6, 9, and 11 November

Time: 14:15-15:30 hrs

Venue: Seminar Hall


After motivating the study of complexes, essentially from algebraic topological point of view, I will explain how complexes store homological information. Starting with a complex one can, for example, define homology and cohomolgy with coefficients. Exact sequences of complexes give rise to long exact sequences of homology.

In order to set up a machinery for comparing homologies of various satellite complexes, one comes upon the notion of a spectral sequence . I will explain this gadget, and give a few examples to show how it works. In particular, this enables one to get substantial (only partial, though) information about the homology of a filtered complex in terms of the homology of its associated grade complex.

This series of lectures is aimed at graduate students and interested researchers. Limited travel support and local hospitality is available for interested participants. Please send an email to in case you wish to participate.