K O I   C O M B I N A T O R I C S   L E C T U R E S

In Japan koi symbolize strength, courage, patience and success through perseverance. 

The KOI Combinatorics Lectures is a joint venture between combinatorialists from the Kentucky, Ohio and Indiana area.

The goal of this series of meetings is to foster and build intergenerational friendship and collaboration between researchers broadly defined (graduate students, postdocs, faculty) in the KOI area.

Organizing Committee:
Saúl A. Blanco (IU), Mihai Ciucu (IU), Richard Ehrenborg (UK), Eric Katz (OSU), Margaret Readdy (UK)

The organizers would like to acknowledge The Ohio State University for their generous support.

Talk titles and Abstracts:

Miklós Bóna, Negative results in enumerative combinatorics
When we cannot solve an enumeration problem, we may wonder whether we are just not using the right methods, or the problem is actually difficult. If it is actually difficult, how do we measure its level of difficulty? In this talk, we will survey recent methods to prove that the generating function of a combinatorially defined sequence is not rational or not algebraic in situation when we know very little about that generating function. Recently, these methods have been successfully applied in the area of pattern avoiding permutations, but they are applicable in other settings as well. While we will use techniques from analytic combinatorics, the talk will be self-contained and accessible for a general mathematics audience.

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.

Funding
There is partial funding available by the Combinatorics Foundation for attendees. To be considered for funding, please send a short CV and, if you are a graduate student or recent PhD, a letter of recommendation (e-mail is okay) from your PhD advisor to koi.combinatorics@gmail.com.

Pre-registered Participants (so far):

Ben Baker (Auburn U)

Kyle Binder (The Ohio State U)

Sarah Brauner (Max Planck Institute & LACIM UQAM)

Saúl A. Blanco (Indiana U)

Greg Blekherman (Georgia Tech)

Miklós Bóna (U Florida)

Caroline Boone (U Louisville)

Darragh Buckley (Indiana U)

Dustin Cartwright (U Tennessee)

Alvaro Cornejo (U Kentucky)

Cesar Cuenca (The Ohio State U)

Mihai Ciucu (Indiana U)

Maria Angelica Cueto (The Ohio State U)

Hugh Dennin (The Ohio State U)

Richard Ehrenborg (U Kentucky)

Parisa Fatheddin (Ohio State)

Zihao Fang (The Ohio State U)

Deniz Genlik (The Ohio State U)

Andrey Gogolev (The Ohio State U)

Nick Henderson (The Ohio State U)

Gábor Hetyei (UNC Charlotte)

John Huddleston (Indiana)

Jake Huryn (The Ohio State U)

Chloe Ireland (The Ohio State U)

Eric Katz (The Ohio State U)

Gary Kennedy (The Ohio State U)

Daecheol Kim (U Illinois Urbana-Champaign)

Max Kutler (The Ohio State U)

Yi-Lin Lee (Indiana)

Yongjin Lee (U Illinois Urbana-Champaign)

Rus May (Morehead State U)

Fernando Jose Mazariegos Camas (Ohio U)

Avery McNeill (The Ohio State U)

Cesar Meza (Washington U St Louis)

Mario Midence (U Kentucky)

Jaewon Min (U Illinois)

William Newman (The Ohio State U)

Evan Nixon (HS student)

Margaret Readdy (U Kentucky)

Williem Rizer (U Kentucky)

Khrystyna Serhiyenko (U Kentucky)

Jagdeep Singh (SUNY Binghamton)

Luke Wiljanen (The Ohio State U)

Kaelyn Willingham (U Minnesota)

Jue Zhang (Ohio U) 

The Fall 2023 KOI Combinatorics Lectures is partially supported by:
The Ohio State University
The Combinatorics Foundation and
Margaret Readdy's NSF grant DMS-2247382.

Area map of OSU Dept of Mathematics:

Last updated:  November 30, 2023.

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