KOALA 2023: Workshop of the Kentucky-Ohio ALgebra Alliance

May 9-10, 2023

Mathematics Department
The Ohio State University
Columbus, OH, USA

Design courtesy of Kiumars Kaveh

Poster of the workshop.

This event is funded by the Mathematics Research Institute and National Science Foundation under CAREER grants DMS 1748837 and DMS 1945212.

Registration: For planning purposes, all participants (including invited speakers), are asked to register online. Registration will be open through Friday May 5, 2023. Please fill out the following registration form.

About KOALA Speakers Schedule Titles and abstracts


The Mathematics Departments at both The Ohio State University (Columbus, OH) and the University of Kentucky (Lexington, KY) have a critical mass of faculty, postdocs and graduate students in Combinatorial Algebraic Geometry. Faculty at both institutions often have research collaborations and meet each other at conferences. Younger members of both groups do not have as many opportunities to interact.

KOALA workshops (regular 2-day meetings held once a year, and alternating between both institutions) provide a venue to further expand collaborations between these two groups. Their main goals are:


The KOALA 2023 Workshop will feature talks by two distinguished plenary speakers and three junior speakers from participating Midwest institutions:

Hannah Larson
(Harvard University)
                          Botong Wang
(University of Wisconsin-Madison)

Max Kutler
(The Ohio State University)
                Alexander Sutherland
(The Ohio State University)
                Boris Tsvelikhovskiy
(University of Pittsburgh)

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We expect participants to arrive on Tuesday May 9 at noon and leave on Wednesday May 10 in mid-afternoon. Lectures will start at 1pm on Day 1 and end around 3pm on Day 2.

The program is designed to encourage new research initiatives by allowing enough free time for discussion. In addition to the two plenary lectures (and accompanying pre-talks), we will have three additional lectures by postdocs and a lightning session of introductory talks.

All Talks (including the lightning round) will take place in room CH 240. Coffee breaks and the dinner on Day 1 will be held in MW 724.

Day Time Location Speaker/Event Title
1 1-1:55 CH 240 Alex Sutherland RDk≤ d-Versality and Resolvent Degree for the Sporadic Groups
1 2-3 MW 724 Coffee break
1 3:00-3:30 CH 240Hannah Larson Pre-talk: Introduction to Mg,n
1 3:30-4:30 CH 240 Hannah Larson Intersection theory of Mg,n
1 4:30-5 MW 724 Break
1 5-6 CH 240 Lightning Session
1 6-8 MW 724 Dinner
2 8:30-9:30 MW 724 Breakfast
2 9:30-10:25 CH 240 Boris Tsvelikhovskiy The universe inside Hall algebras of coherent sheaves on toric resolutions
2 10:30-11 MW 724 Coffee break
2 11-11:30 CH 240 Botong Wang Pre-talk: What is a perverse sheaf?
2 11:30-12:30 CH 240 Botong Wang Topological generic vanishing theorems and positivities
2 12:30-2 (free) Lunch
2 2-2:55 CH 240 Max Kutler Matroidal mixed Eulerian numbers

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Titles and abstracts

Hannah Larson:
Botong Wang:
Max Kutler:
  • Matroidal mixed Eulerian numbers

    Abstract: Berget-Spink-Tseng introduced hypersimplex classes γ1,..., γn in the Chow ring of a matroid M. Products of these classes give intersection numbers which we call the matroidal mixed Eulerian numbers. These include, as special cases, several well-known matroid invariants such as the beta invariant and the coefficients of the reduced characteristic polynomial. We show that matroidal mixed Eulerian numbers satisfy several properties analogous to those satisfied by the ordinary mixed Eulerian numbers, and they also satisfy a recursive deletion-contraction formula. We also provide a combinatorial interpretation of matroidal mixed Eulerian numbers as certain weighted counts of flags of flats. This is joint work with Eric Katz.

Alex Sutherland:
  • RDk≤ d-Versality and Resolvent Degree for the Sporadic Groups

    Abstract: Resolvent degree is a measure of complexity for objects in algebra and geometry which is deeply connected to classical interest in solving general polynomials. In this talk, we will begin by introducing resolvent degree through classical examples and discussing what is known about the resolvent degree of finite simple groups. We will then connect resolvent degree to (generalizations of) versality and use this framework to establish upper bounds on the resolvent degree of the sporadic groups.

Boris Tsvelikhovskiy:
  • The universe inside Hall algebras of coherent sheaves on toric resolutions.

    Abstract: The talk will start with an introduction to Hall algebras, different versions and appearances thereof. Then we will turn our attention to McKay correspondence in dimensions two and three. This is a correspondence between nontrivial irreducible representations of a finite subgroup G ⊂ GLn(C) and irreducible subvarieties in the central fiber of resolution of the categorical quotient X=Cn//G. In examples relevant to our discussion X will have an isolated singularity at the origin and the resolution Y will be the corresponding G-Hilbert scheme. A more modern version of McKay correspondence is the derived equivalence ψ: Db(CohG(C)(Cn)) → Db(Coh(Y)). Sometimes Hall algebras 'arising' on the right hand side admit embeddings of subalgebras in universal enveloping algebras U(g). We will see examples of such instances for Lie algebras g with simply laced Dynkin diagrams of finite or affine type. A new family of examples will be presented. The main goal of the talk will be to provide an accessible introduction to the aforementioned topics.

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Koala 23 is sponsored by The Ohio State University (through the Mathematics Research Institute) and the National Science Foundation: