Algecom-XXVIII

Algebra, Geometry and Combinatorics Day (AlGeCom) is a one day, informal meeting of mathematicians from the Midwest and beyond, with interests in algebra, geometry and combinatorics (widely interpreted). 

Algecom usually happens twice a year.

AlGeCom Committee:

 Alexander Yong  David Speyer Uli Walther Saugata Basu  Evgeny Mukhin Peter Tingley  Chris Drupieski Laura Escobar Kyle Petersen Vic Reiner Anna Weigandt  Dave Anderson

AlGeCom XXVIII Date:   Saturday November 14, 2026

Location: At U Illinois Urbana-Champaign. 

Local Organizers (questions related to Algecom XXVIII): Alexander Yong and Abigail Price. 

See here  for more information on the conference.

General information about traveling to UIUC can be found here.

All talks will be held in Lincoln Hall, Room 1002. The pizza dinner will be held in Harker Hall. 

The speakers will be

• Shiyue Li

• Colin Defant

• Pavlo Pylyavskyy

The program at a glance:

8:00–8:50 — Registration, bagels, coffee

8:50–9:00 — Welcome / logistics

9:00–10:00 — Pasha Pylyavskyy

10:00–10:20 — Break

10:20–11:10 — Lightning Talks I

11:10–11:20 — Break

11:20–12:20 — Shiyue Li

12:20–1:50 — Lunch

1:50–2:40 — Lightning Talks II

2:40–3:00 — Break

3:00–4:00 — Colin Defant

4:00–4:20 — Break

4:20–5:10 — Lightning Talks III

6:00 — Pizza dinner

The abstracts and titles of the talks:

Pasha Pylyavskyy (University of Minnesota) — “Homomesy of Tropical T-systems: Finite Type”

In 2007, Fomin and Zelevinsky introduced the bipartite belt, a sequence of bipartite cluster mutations whose exchange relations form a discrete dynamical system. For each Dynkin diagram, this system is periodic, as a special case of Zamolodchikov periodicity. In the associated tropical dynamics, every mutation along the belt can be naturally colored red or blue, according to which term attains the maximum in the tropical exchange relation. This gives a red-blue statistic on tropical orbits. We prove that this statistic is homomesic, i.e. that the average numbers of red and blue mutations are independent of the orbit. Moreover, the number of red mutations is given by the number of roots in the associated root system. This is joint work with Ariana Chin.

Shiyue Li (University of Michigan) — “A tale of two polynomials: positivity in wonderful varieties and matroids”

I will share a story of two polynomials, the Poincaré polynomial of Chow rings of toric varieties of matroids, and the h-polynomials of nested set complexes of matroids. The story is set in a rich network of positivity properties coming from geometry and combinatorics of matroids, with connections to moduli spaces of rational stable curves. The main theorems are matroidal analogues of Gal’s conjecture, as well as strong flawlessness and real-rootedness of some of these polynomials. Joint work with Basile Coron and Luis Ferroni.

Colin Defant (Harvard University) — "Stack-Sorting”

Stack-sorting is a niche topic that should be less so. It exhibits rich enumerative structure and relates to algebraic topics like free probability theory and Lorentzian polynomials. Let me tell you about it.

ALGECOM is partially funded by a grant from the National Science Foundation, which provides limited support for students and postdocs to offset the cost of attendance.  Everyone should apply by filling out the registration form below and indicating their interest in financial support (and we appreciate early applications).

Registration is free, but please use the registration link  here.

Funding decisions will be made by Oct 14.  New registrants can still request funding, and we will try to accommodate requests but cannot guarantee it.

Important Note: (in case we can offer reimbursement)

The NSF conference grant requires the use of a US carrier. In addition, if you intend to purchase an itinerary that is a non-direct return flight to the conference, i.e., a multi-city flight or use of a stopover (this does not include regular connections), you must provide a comparable direct return flight in order to be reimbursed.

PLEASE READ this statement here for detailed instructions on what must be done to get reimbursed.

This ALGECOM will have five-minute lightning talks by early-career participants. Please indicate your interest in giving a lightning talk on the registration form.

Recommended Parking:

Information on visitor parking may be found here . A list of some free parking options can be found here. The parking lot closest to Lincoln Hall is Lot 9, which is located on the corner of Chalmers and Sixth Street (here). 

Lodging:

Participants who wish to stay at the Illini Union Hotel may call (217) 333-1241 to reserve a room at the ALGECOM rate of $134 per night, plus applicable taxes. Participants should make and pay for their own reservations; those receiving travel support may seek reimbursement afterward.