Plenary Speakers
Frobenius Methods in Combinatorics
The Frobenius map has been used to study algebraic and singularity properties of rings and algebraic varieties. In this talk, we will discuss recent results that show how this map can help to obtain and inspire results in combinatorial commutative algebra, many of them independently of the characteristic.
Algebraic, Tropical, and Combinatorial Geometries
Tropical geometry provides a two way bridge between combinatorics and algebraic geometry. The aim of this talk is to highlight how tropical geometry provides a rich connection between these two worlds in the particular case of matroids and linear spaces. For example, many matroid invariants have been shown to arise from the topology, intersection theory, and even characteristic classes of (tropical) algebraic varieties. In recent years, these interpretations have led to many breakthroughs in the field of matroid theory. Along the way I will emphasis how many of these connections and applications can be extended to more general algebraic varieties and also discrete structures. This hints at possible new applications of these methods beyond the realm of matroids.