AlCoVE 2024 will be held virtually on Zoom on June 17 – 18, 2024 (Monday and Tuesday).
Past conferences: AlCoVE 2020, AlCoVE 2021, AlCoVE 2022, and AlCoVE 2023.
Organizers: Laura Colmenarejo, Maria Gillespie, Oliver Pechenik, and Liam Solus
Conference poster: Download here.
AlCoVE brings together researchers interested in algebraic combinatorics from around the world. Each talk will be 30 minutes and between talks, there will be casual social activities for spending time with your friends and making new friends.
Registration and poster session application
To access the Zoom links, you must first register for the conference:
We will be holding virtual poster sessions in Gather on June 17 and June 18. Applications to present a poster have now closed.
List of Confirmed Speakers:
- José Aliste-Prieto, Universidad Andrés Bello
- Matthias Beck, San Francisco State University
- Sarah Brauner, LaCIM
- Christian Gaetz, Cornell University
- Sam Hopkins, Howard University
- Ezgi Kantarcı Oğuz, Galatasaray University
- Eric Marberg, HKUST
- Greta Panova, University of Southern California
- Anna Pun, CUNY-Baruch College
- Dominic Searles, University of Otago
- Kris Shaw, University of Oslo
- Vasu Tewari, University of Toronto Mississauga
Schedule (subject to change, all times EDT):
TBA. The password for Zoom and Gather is the same, and will be sent to registered participants.
JUNE 17 (MONDAY):
| 10:00 - 10:30 AM | Welcome | Zoom link | |||
| 10:30 - 11:00 | Matthias Beck | q-chromatic polynomials | Zoom link | ||
| 11:00 - 11:30 | Ice breakers | Zoom link | |||
| 11:30 - noon | Ezgi Kantarcı Oğuz | Oriented posets and cluster expansions | Zoom link | ||
| noon - 1:30 | Lunch and poster session A | Gather link | |||
| 1:30 - 2:00 | Vasu Tewari | Quasisymmetric divided differences | Zoom link | ||
| 2:00 - 2:30 | Critter time | Zoom link | |||
| 2:30 - 3:00 | José Aliste-Prieto | Counting subtrees with the chromatic symmetric function | Zoom link | ||
| 3:00 - 4:00 | Puzzles | Zoom link | |||
| 4:00 - 4:30 | Anna Pun | Combinatorial identities for vacillating tableaux | Zoom link | ||
| 4:30 - 5:00 | Coffee break | Gather link | |||
| 5:00 - 5:30 | Dominic Searles | Modules of 0-Hecke algebras and quasisymmetric functions in type B | Zoom link | ||
| 5:30 - 6:00 | Happy hour | Gather link |
JUNE 18 (TUESDAY):
| 10:00 - 10:30 AM | Welcome | Gather link | |||
| 10:30 - 11:00 | Eric Marberg | An invitation to shifted key polynomials | Zoom link | ||
| 11:00 - 11:30 | AlCoVE art time | Zoom link | |||
| 11:30 - noon | Sarah Brauner | Spectrum of random-to-random shuffling in the Hecke algebra | Zoom link | ||
| noon - 1:30 PM | Lunch and poster session B | Gather link | |||
| 1:30 - 2:00 | Greta Panova | Computational complexity in algebraic combinatorics | Zoom link | ||
| 2:00 - 2:30 | Virtual expedition | Zoom link | |||
| 2:30 - 3:00 | Kris Shaw | Real phase structures on matroid fans and filtrations of tope spaces | Zoom link | ||
| 3:00 - 4:00 | Puzzles | Zoom link | |||
| 4:00 - 4:30 | Christian Gaetz | Hypercube decompositions and combinatorial invariance for Kazhdan–Lusztig polynomials | Zoom link | ||
| 4:30 - 5:00 | Coffee break | Gather link | |||
| 5:00 - 5:30 | Sam Hopkins | Upho posets | Zoom link | ||
| 5:30 - 6:00 | Happy hour | Gather link |
Posters presentations
POSTER SESSION A, JUNE 17 (MONDAY):
| Ron Adin | Higher Lie characters and root enumeration for type D |
| Divya Aggarwal | Splitting subspaces of linear operators over finite fields and their \(q = 1\) analogue |
| Herman Chau | On the cardinality of higher Bruhat orders |
| Bishal Deb | A remark on continued fractions for permutations and D-permutations with a weight \(-1\) per cycle |
| Danai Deligeorgaki | Ehrhart positivity of panhandle matroids and a bound for paving matroids |
| Nadia Lafreniere | Rowmotion on interval-closed sets |
| Kevin Liu | Signs of cosine functions |
| Teemu Lundström | f-vector inequalities for order and chain polytopes |
| Son Nguyen | Temperley–Lieb crystals |
| Sagar Sawant | Proper q-caterpillars are distinguished by their chromatic symmetric functions |
| Velmurugan S | Locally invariant vectors in representations of symmetric groups |
| Yuan Yao | Fine mixed subdivisions of dilated simplices |
POSTER SESSION B, JUNE 18 (TUESDAY):
| Amrita Acharyya | Zero divisor graphs of rings and posets |
| Ashleigh Adams | Cyclic sieving on permutations and FindStat database |
| Tao Gui | Strongly dominant weight polytopes are hypercubes |
| Siddheswar Kundu | Demazure crystals for flagged reverse plane partitions |
| Henry Kvinge | Developing machine learning benchmark datasets to advance AI for math |
| Jihyun Lee | A property of G-matrices in rank 3 quivers |
| Jianping Pan | Pattern-avoiding polytopes and Cambrian lattices |
| Samrith Ram | Diagonal matrices, tableaux, set partition statistics and q-Whittaker functions |
| Yuval Roichman | Transitive and Gallai colorings |
| Isaiah Siegl | Noncommutative Schur functions for the Stanley-Stembridge conjecture |
| Kartik Singh | Closure of Deodhar components |
| Foster Tom | A signed e-expansion of the chromatic quasisymmetric function |
| Rui Xiong | Pieri rules over Grassmannian and applications |
Abstracts of talks
José Aliste-Prieto
Counting subtrees with the chromatic symmetric function
Richard Stanley asked in 1995 whether a tree is determined up to isomorphism by its chromatic symmetric function. One approach to understanding this question is to ask which other invariants are encoded by the chromatic symmetric function: Here we consider two invariants: The subtree polynomial, which counts subtrees by cardinality and number of leaves, and the generalized degree sequence, which counts vertex subsets by cardinality, number of internal and external edges. In 2008, Jeremy Martin, Mathew Morin and Jennifer Wagner proved that the chromatic symmetric function determines the subtree polynomial, while Crew's Conjecture states that the chromatic symmetric function also determines the generalized degree sequence.
In this work, we first prove Crew’s conjecture, and then show that a restriction of the generalized degree sequence contains the same information as the subtree polynomial. Finally, we will show recurrences for the restriction of the generalized degree sequence that allow us to construct arbitrarily large families of trees sharing the same subtree polynomials, proving and generalizing a conjecture of Eisenstat and Gordon.
This is joint work with Jeremy L. Martin, Jennifer Wagner, and José Zamora.
Matthias Beck
q-chromatic polynomials
We introduce and study a q-version of the chromatic polynomial of a given graph G, defined as the sum of \(q^{l*c(v)}\) where \(l\) is a fixed integral linear form and the sum is over all proper n-colorings \(c\) of G. This turns out to be a polynomial in the q-integer \([n]_q\), with coefficients that are rational functions in q. We will exhibit several other structural results for q-chromatic polynomials, as well as connections to neighboring concepts, e.g., chromatic symmetric functions and the arithmetic of order polytopes. We offer a strengthened version of Stanley's conjecture that the chromatic symmetric function distinguishes trees, which leads to an analogue of P-partitions for graphs. This is joint work with Esme Bajo and Andrés Vindas-Meléndez.
Sarah Brauner
Spectrum of random-to-random shuffling in the Hecke algebra
The eigenvalues of a Markov chain determine its mixing time. In this talk, I will describe a Markov chain on the symmetric group called random-to-random shuffling whose eigenvalues have surprisingly elegant—though mysterious—formulas. In particular, these eigenvalues were shown to be non-negative integers by Dieker and Saliola in 2017, resolving an almost 20 year conjecture.
In recent work with Ilani Axelrod-Freed, Judy Chiang, Patricia Commins and Veronica Lang, we generalize random-to-random shuffling to a Markov chain on the Type A Iwahori Hecke algebra, prove its eigenvalues are polynomials in q with non-negative integer coefficients. Our methods simplify the existing proof for \(q=1\) by drawing novel connections between random-to-random shuffling and the Jucys-Murphy elements of the Hecke algebra.
Christian Gaetz
Hypercube decompositions and combinatorial invariance for Kazhdan–Lusztig polynomials
Kazhdan–Lusztig polynomials are of foundational importance in geometric representation theory. Yet the Combinatorial Invariance Conjecture suggests that they only depend on the combinatorics of Bruhat order. I'll describe joint work with Grant Barkley in which we adapt the hypercube decompositions introduced by Blundell-Buesing-Davies-Veličković-Williamson to prove this conjecture for Kazhdan–Lusztig R-polynomials in the case of elementary intervals in the symmetric group. This significantly generalizes the main previously-known case of the conjecture, that of lower intervals.
Ezgi Kantarcı Oğuz
Oriented posets and cluster expansions
Oriented posets are posets with specialized end points, which we can connect to build larger posets. They come with corresponding matrices, where multiplication corresponds to linking posets. We look at the case of labeled fence posets and show that they can be used to calculate cluster expansions effectively. We look at more potential applications and open questions.
Sam Hopkins
Upho posets
A partially ordered set is called upper homogeneous, or "upho," if every principal order filter is isomorphic to the whole poset. This class of fractal-like posets was recently introduced by Stanley. Our first observation is that the rank generating function of a (finite type \(\mathbb{N}\)-graded) upho poset is the reciprocal of its characteristic generating function. This means that each upho lattice has associated to it a finite graded lattice, called its core, that determines its rank generating function. With an eye towards classifying upho lattices, we investigate which finite graded lattices arise as cores, providing both positive and negative results. Our overall goal for this talk is to advertise upho posets, and especially upho lattices, which we believe are a natural and rich class of posets deserving of further attention.
Eric Marberg
An invitation to shifted key polynomials
Schubert polynomials and key polynomials are two integral bases for all polynomials (in a countable set of commuting variables) with connections to the geometry of the type A flag variety. A surprising combinatorial fact, due to Lascoux and Schützenberger, is that Schubert polynomials are positive linear combinations of keys. This talk will present "shifted" versions of Schubert and key polynomials that conjecturally exhibit a similar positivity property. These polynomials are closely related to the orbits of the orthogonal and symplectic groups acting on the type A flag variety. This is joint work with Travis Scrimshaw.
Greta Panova
Computational complexity in algebraic combinatorics
Many open problems in Algebraic Combinatorics ask about "combinatorial interpretations" of some strucutre constants which are nonnegative integers because of their representation theoretic or algebro-geometric origins. We will explain how to formalize this notion through the theory of computational complexity and show, as a proof of concept, that the square of a symmetric group character can not have a combinatorial interpretation (under standard complexity theoretic assumptions). Based on work with Christian Ikenmeyer and Igor Pak.
Anna Pun
Combinatorial identities for vacillating tableaux
Vacillating tableaux, which are sequences of integer partitions that satisfy specific conditions, arise in the representation theory of the partition algebra and the combinatorial theory of crossings and nestings of matchings and set partitions. By exploring a correspondence between vacillating tableaux and pairs comprising a set partition and a partial Young tableau, we derive combinatorial identities that involve the number of vacillating tableaux, the number of standard Young tableaux and Schur functions.
In this talk, we will define vacillating tableaux and explore their correspondence with pairs of set partitions and partial Young tableaux. This correspondence will be used to derive combinatorial identities involving the number of vacillating tableaux, standard Young tableaux, and Schur functions. We will also discuss integer sequences that count associated combinatorial structures. This is a joint work with Zhanar Berikkyzy, Pamela E. Harris, Catherine Yan and Chenchen Zhao.
Dominic Searles
Modules of 0-Hecke algebras and quasisymmetric functions in type B
We give a uniform combinatorial method for constructing modules of 0-Hecke algebras in all Coxeter types, and apply this to give representation-theoretic meaning to noteworthy families of type B quasisymmetric functions. We construct a type B analogue of Schur Q-functions using domino tableaux, and discuss how these functions correspond to restrictions of certain modules of a type B variant of 0-Hecke–Clifford algebras. This is joint work with Colin Defant.
Kris Shaw
Real phase structures on matroid fans and filtrations of tope spaces
Oriented matroids are matroids with extra sign data, and they arise in the study of real hyperplane arrangements and oriented graphs. I will describe how a matroid orientation can be cryptomorphically encoded as a real phase structure on a matroid fan. This is joint work with Arthur Reaudineau and Johannes Rau. I will also discuss that three seemingly different filtrations on the tope space of an oriented matroid are equivalent. One of the filtrations arises from Heaviside functions, another from Kalinin’s spectral sequence, and the final one via Quillen’s filtration of the augmented algebra. A main ingredient in comparison are real phase structures on matroid fans. This is joint work with Chi Ho Yuen.
Vasu Tewari
Quasisymmetric divided differences
I'll introduce a quasisymmetric analogue of divided differences that is adapted to the quotient of the polynomial ring by the ideal of positive degree quasisymmetric polynomials. The role of the triple (Schubert polynomials, nil-Coxeter algebra, reduced words) from the classical coinvariant algebra story shall now be essayed by (Forest polynomials, Thompson monoid, linear extensions of forests). As one application, I will revisit expansions of Schubert polynomials in various bases and interpret the coefficients that arise as generalized Littlewood-Richardson coefficients for certain toric Richardson varieties. Joint work with Philippe Nadeau (Lyon) and Hunter Spink (Toronto).