Predavatelj: Dejan Govc (Univerza v Ljubljani)

Povzetek: The concept of unimodal category [1] was first introduced by Baryshnikov and Ghrist in 2007. It is an invariant of functions $f:Xto[0,infty)$, similar in spirit to the Lyusternik-Schnirelmann category. I will give an overview of the basic definitions, known results and a monotonicity conjecture from [1]. Then I will discuss this conjecture in more detail. As is turns out, the conjecture holds for functions on $X=mathbb R$ as well as for certain well-behaved functions on $X=mathbb R^n$, but fails for more general functions.

[1] Y. Baryshnikov and R. Ghrist, Unimodal category and topological statistics. Proceedings of NOLTA, 2011.