https://rochester.zoom.us/j/6775967436

In my talk, I will introduce a new combinatorial invariant of a simplicial complex arising in toric topology as secondary cohomology of its moment-angle complex w.r.t. a new differential on its Koszul algebra. Our invariant also acquires a geometric description, for which no toric topology is needed, by means of the Hochster theorem on a Tor-algebra of a Stanley-Reisner ring.

This construction was motivated by our proof of the stability theorem for a certain generalization of the concept of a barcode for persistent homology we proposed in the framework of toric topology. I will introduce all the necessary notions and constructions from topological data analysis and then focus on the computational aspects of the theory of our invariant as well as its general properties that simplify calculations.

This talk is based on the ongoing joint research projects with A. Bahri, T. Panov, J. Song, and D. Stanley