Dmitry Feichtner-Kozlov

Combinatorial algebraic topology.

Abstract:

Combinatorial Algebraic Topology is a fascinating and dynamic field at the crossroads of Algebraic Topology and Discrete Mathematics. It concerns itself with computating algebraic invariants of combinatorial cell complexes. The methods of computations themselves are often
combinatorial as well.

In this talk we will outline philosophy of the subject, mention some of its main dramatis personae, such as acyclic categories and associated regular trisps, discuss systematic approach to computation methods, such as discrete Morse theory, and finally touch upon a couple of applications, such as the surfacing of Stiefel-Whitney characteristic classes in the questions of graph colorings and the study of moduli spaces of metric graphs with marked points.


References:

Kozlov, Dmitry, "Combinatorial algebraic topology", Algorithms and Computation in Mathematics, 21. Springer, Berlin, 2008. xx+389 pp. ISBN: 978-3-540-71961-8.