Fall 2026

Unless otherwise noted, all talks will take place in Thornton Hall 211 at San Francisco State University.

Wednesday, September 9, 4:00 - 5:00

Madeleine Goertz

University of California, Berkeley

Title: Linear optimization degrees of varieties

Abstract: An affine variety is the set of common solutions to a system of polynomial equations. Given a generic linear objective function, we can ask for its number of critical points restricted to a fixed variety. This integer measures the algebraic complexity of linear optimization over the variety. In practice, optimization problems often involve slicing a variety with linear spaces, leading to the study of sectional linear optimization (LO) degrees. We analyze the relationship between sectional LO degrees and classical polar degrees, demonstrating that the gap between them can be surprisingly large. We derive an exact formula for the sectional LO degrees of arbitrary Segre-Veronese varieties. This yields new bounds for the algebraic complexity of computing the Wasserstein distance to independence models in statistics.