Many of the familiar invariants in topology are derived from basic invariants in finite dimensional linear algebra over $R$, $C$, $Z_p$, $p$ a prime number. Not all basic invariants in such linear algebras and not all finite dimensional linear algebras have been fully explored so far.

In these talks I invite the students to join the research on these lines. My illustration will be based on "determinant" of a square matrix (with entries in $R$ or $C$) and on the finite dimensional linear algebra 'a la von Neumann. Both are very promising new tools in topology and a source of new invariants. They also provide interesting mathematical problems.