An Upper Bound on the Topological Complexity of Discriminantal Varieties

Explore an advanced mathematical lecture on the topological complexity of discriminantal varieties. Delve into the study of discriminantal varieties as complements of polynomial zero loci in complex space, with a focus on configuration spaces. Learn about a new upper bound for the topological complexity of these varieties, derived through a combination of Morse theory, equivariant homotopy theory, and complex geometry. Examine the application of this result to ordered and unordered configuration spaces of points in the plane, and discuss the challenges in extending this approach to higher-dimensional Euclidean spaces. Gain insights into the interplay between algebraic geometry and topology in this 54-minute presentation by Andrea Bianchi, delivered for the Applied Algebraic Topology Network.