Abstract for the talk on 23.01.2018 (10:00 h)Seminar on Nonlinear Algebra
Madeleine Weinstein (University of California, Berkeley)
Emil Horobet (Târgu-Mureş - Sapientia Hungarian University of Transylvania)
Offset hypersurfaces and persistent homology of algebraic varieties
In this talk we present connections between the true persistent homology of algebraic varieties and their corresponding offset hypersurfaces. By Hardt's theorem, true persistent homology events occur at algebraic numbers. By studying the offset hypersurface, we characterize when true persistent homology events occur. The degree of the offset hypersurface is bounded by the Euclidean Distance Degree of the starting variety, so this way we show a bound on the degree of the algebraic numbers at which the homological events occur.