Schedule:
09:00-10:00 am, Arrival/Registration/Meet and Greet
09:59-10:00 am Welcome, Welcome speech
10:00-11:00 am, Greg Blekherman (Georgia Tech)
11:00-11:30 am, Coffee Break
11:30-12:30 pm, Sarah Brauner (Max Planck Institute & LACIM UQAM)
12:30-02:30 pm, Lunch Break
02:30-03:15 pm, Problem Session
03:15-04:00 pm, Tea time and the One Picture/One Theorem Poster Session
04:00-05:00 pm, Khrystyna Serhiyenko (U. Kentucky)
06:00-08:00 pm, Conference Dinner
All talks will take place in CH 240. All coffee breaks, poster session and Saturday dinner will take place in MW 724
url for the event: see https://sites.google.com/view/koicombinatorics/home
Greg Blekherman, Tropicalization in extremal combinatorics
Tropicalization has been frequently applied in algebraic geometry to give "combinatorial shadows" of complicated objects. But one can also tropicalize (in the sense of log-limits) manifestly non-algebraic sets, such as counts of combinatorial substructures. I will give several examples of combinatorial sets, where tropicalization remembers interesting information (for instance, log-concavity of a sequence). An interesting (but to at all well-understood) phenomenon emerges: tropicalizations of interesting combinatorial objects are rational polyhedral cones.
Sarah Brauner, Positive geometry and wonderful polytopes
A positive geometry is a certain type of space that is equipped with a canonical meromorphic form. While the construction originates in theoretical physics, many beloved objects in algebraic combinatorics and geometry turn out to be examples of positive geometries. In this talk, I will focus on one such example: polytopes. Given any convex polytope, we will study its corresponding "wonderful" polytopes, which arise from the wonderful compactification of a hyperplane arrangement in the same way that polytopes arise as the regions of a hyperplane arrangement. I will describe on-going work with Chris Eur, Lizzie Pratt, and Raluca Vlad showing that any simple wonderful polytope is a positive geometry. I aim to make this talk accessible, and no prior knowledge of positive geometries or wonderful compactifications will be assumed.
Khrystyna Serhiyenko, Leclerc's conjecture on a cluster structure for Richardson varieties
Coordinate rings of many varieties naturally occurring in representation theory are known to admit a cluster algebra structure. Leclerc constructed a conjectural cluster structure on Richardson varieties using categorification in terms of module categories of the preprojective algebras. We show that in type A, his conjectural cluster structure is in fact a cluster structure. We do this by comparing s construction with another cluster structure due to Ingermanson, which is defined quite differently using the combinatorics of wiring diagrams and the Deodhar stratification. This is joint work with Melissa Sherman-Bennett.
