Fall 2026

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.

Title: The Eigenvalue Method in coding theory

Abstract: One of the main goals in spectral graph theory is to deduce the principal properties and structure of a graph from its graph spectrum. In this talk we will show how spectral graph theory provides powerful methods for obtaining results concerning substructures of graphs, and also how these results can be useful in other mathematical fields such as coding theory. In particular, we will derive sharp eigenvalue bounds for the k-independence number of a graph (or equivalently, the independence number of the k-th graph power), which is known to be very hard to compute. We will see how to use polynomials and mixed integer linear programming in order to optimize and compute such spectral bounds. Finally, we will illustrate some recent applications of the obtained eigenvalue bounds to coding theory. The obtained results are encouraging and strongly suggest that spectral graph theory can uncover structural properties of ambient spaces that are relevant to coding theory, but that are often not captured by classical coding theory techniques. There is no question that eigenvalues play a central role in our fundamental understanding of graphs. The goal of this talk is to show that we can also use them for deepening our understanding of codes.

Title: Quantum representations and sightings of QFT 

Abstract: In this talk I will try to "approach" quantum field theory (QFT) from the perspective of quantum algebra. I'll begin with a casual discussion of classical, versus quantum phenomena in mathematics. Classical mathematics is, from the algebraic perspective, typified in the representation theory of finite groups and Lie groups. One can consider, for example, beautiful analyses of representations of SL_n(C) or Gl_n(C). Starting from this point, we'll travel into the world of QFT, approaching the subject through the lease of so-called quantum group representations.

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