K. Lakshmanan Memorial Distinguished Lecture:
Integration and Topology
TIFR Bangalore Centre.
The study of the determination of certain integrals with fixed limits of integration has been a principal source for the topological contributions of Riemann and Poincare. This relationship between integrals and topology was formalised in de Rham's Theorem, which was stated implicitly by Poincare and made explicit by Elie Cartan. Riemann's work on abelian integrals was generalised by Hodge with profound applications to algebraic geometry.
The lecture will be concerned with this topic and with some of the concepts involved. I hope to make the lecture accessible also to the students.