Summer School 2025

When:

May 12 and May 15, Gibson Hall.

Topics:

Dr. Kalina Mincheva and Dr. Daniel Bernstein will lead the two courses for this summer school. Further, a problem session would be led by Dr. Nati Friedenberg

Course I: Introductory course on Tropical Geometry

Course Description:

• Introduction to tropical geometry

Define some basic concepts - varieties, valuations, (valuated) term orders, Groebner basis, polyhedral complexes.

Define the tropical variety, give equivalent definitions, properties and examples.

• Some applications of tropical varieties/methods 

This lecture will be anecdotal, the goal is to see where tropical varieties pop up: toric degenerations, blind auctions in economics, handwriting recognition, CM-varieties (and rigidity), etc.

• The algebra of tropical varieties. 

So far we have been interested in the geometry of tropical varieties. Here we will talk about tropical ideals and congruences.

Course II: Coordinate projections of combinatorially defined affine varieties

Course Description: 

Many varieties that appear in applications come naturally embedded in a vector space whose coordinates are indexed by some combinatorial object, e.g. the edge set of a graph. Understanding the dimension and degree of coordinate projections of such varieties leads to interesting questions at the intersection of algebra, combinatorics, and geometry. This course will center around these questions, including their applied motivation from rigidity theory and matrix completion. Connections to tropical geometry and matroid theory will be discussed. 

Time Schedule

lunches will be served in the common room of the math deparment.

Organizers:

Aikaterini(Katerina) Gkogkou

Ketan Vinod Kalgi

Guido Mazzuca 

Kalani Thalagoda