Akos Matszangosz, part 1: "Schubert calculus over the reals: lower bounds"
Channel: Schubert Seminar
Date: 2023-04-24

Abstract: How many lines intersect four generic lines in projective 3-space? Over the complex field, the answer is a single number, 2. In contrast, over the reals, the answer depends on the configuration of the lines, and it can be either 0 or 2. This is a typical situation: the answer to a real enumerative geometry problem is a list of possible numbers, which is bounded above by the number of complex solutions. In certain real problems, one can associate signs to the solutions, and the sum of these signs is independent of the generic configuration. Such signed counts give rise to nontrivial lower bounds to the number of solutions.
In this talk, I will discuss such lower bounds to enumerative problems in real Schubert calculus. 

This talk is based on joint work with László Fehér, Thomas Hudson and Matthias Wendt.