My teaching focuses on algebraic and geometric topology.
“The undeniable power of algebraic topology would alone command a leading place in mathematics; but it has great beauty too, in organizing intuitively different structures which defied earlier purely analytic or geometric approaches. It has also a leading place in physics, for its success in organizing the most fundamental physical theories.”
— C.T.J. Dodson and Phillip E. Parker,
the authors of the book “A User’s Guide to Algebraic Topology”.
A broad consensus exists that a basic knowledge of algebraic topology is indispensable in modern mathematical student’s education. The education should include also some aspects of geometric topology understood in the restrictive sense where the focus is on the study of manifolds, central objects of interest in geometry, topology, and global analysis. Knots, links, and braids are especially intriguing objects in geometric topology, and some theoretical backgroud regarding these objects is advisable as well.
Following these guidelines, I choose topics for student’s courses and seminars.