

AlCoVE 2023 will be held virtually on Zoom on June 26 – 27, 2023 (Monday and Tuesday).
Past conferences: AlCoVE 2020, AlCoVE 2021, and AlCoVE 2022.
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 26 and June 27. Applications to present a poster have now closed.
List of Confirmed Speakers:
- Michela Ceria, Politecnico di Bari
- Sylvie Corteel, CNRS, Université Paris Cité
- Colin Defant, MIT
- Rafael González D’León, Loyola University Chicago
- Takeshi Ikeda, Waseda University
- Luc Lapointe, Universidad de Talca
- Chiara Meroni, ICERM
- Leonid Monin, Institute of Mathematics, EPFL
- Bruce Sagan, Michigan State University
- Johanna Steinmeyer, Hebrew University of Jerusalem/Københavns Universitet
- Mariel Supina, KTH Royal Institute of Technology
- Ben Young, University of Oregon
Schedule (subject to change, all times EDT):
The password for Zoom and Gather is the same, and will be sent to registered participants.
JUNE 26 (MONDAY):
10:00 - 10:30 AM | Welcome | Zoom link | |||
10:30 - 11:00 | Sylvie Corteel | Colored vertex models | Zoom link | ||
11:00 - 11:30 | Ice breakers | Zoom link | |||
11:30 - noon | Johanna Steinmeyer | Combinatorial Hodge theory and IDP lattice polytopes | Zoom link | ||
noon - 1:30 | Lunch and poster session A | Gather link | |||
1:30 - 2:00 | Bruce Sagan | Chromatic symmetric functions and change of basis | Zoom link | ||
2:00 - 2:30 | Critter time | Zoom link | |||
2:30 - 3:00 | Leonid Monin | Polyhedral models for K-theory | Zoom link | ||
3:00 - 4:00 | Puzzles | Zoom link | |||
4:00 - 4:30 | Colin Defant | Permutoric promotion: Gliding globs, sliding stones, and colliding coins | Zoom link | ||
4:30 - 5:00 | Coffee break | Gather link | |||
5:00 - 5:30 | Takeshi Ikeda | Equivariant homology of the affine Grassmannian of the symplectic group | Zoom link | ||
5:30 - 6:00 | Happy hour | Gather link |
JUNE 27 (TUESDAY):
10:00 - 10:30 AM | Welcome | Gather link | |||
10:30 - 11:00 | Rafael González D’León | On Whitney numbers of the first and second kind, or is it the other way around? | Zoom link | ||
11:00 - 11:30 | Critter showcase | Zoom link | |||
11:30 - noon | Michela Ceria | Alternatives for the | Zoom link | ||
noon - 1:30 PM | Lunch and poster session B | Gather link | |||
1:30 - 2:00 | Chiara Meroni | Cutting polytopes | Zoom link | ||
2:00 - 2:30 | Virtual expedition: Math in virtual reality | Zoom link | |||
2:30 - 3:00 | Mariel Supina | Invitation to equivariant Ehrhart theory | Zoom link | ||
3:00 - 4:00 | Puzzles | Zoom link | |||
4:00 - 4:30 | Luc Lapointe | Positivity conjectures for m-symmetric Macdonald polynomials | Zoom link | ||
4:30 - 5:00 | Coffee break | Gather link | |||
5:00 - 5:30 | Ben Young | A Minecraft tour of the tripartite double dimer model | Zoom link | ||
5:30 - 6:00 | Happy hour | Gather link |
Posters presentations
POSTER SESSION A, JUNE 26 (MONDAY):
Esther Banaian | Algebras from orbifolds | poster |
Aritra Bhattacharya | The Clebsch-Gordan rules for Macdonald polynomials | poster |
Trung Chau | Barile-Macchia resolutions | poster |
Patty Commins | Invariant theory for the free left-regular band and a | poster |
Bishal Deb | Continued fractions using a Laguerre digraph interpretation of the Foata–Zeilberger bijection | poster |
Danai Deligeorgaki | Inequalities for | poster |
Yifeng Huang | Spiral shifting operators and punctual Quot schemes on cusp | poster |
Aryaman Jal | Polyhedral geometry of bisectors and bisection fans | poster |
V. Sathish Kumar | Decomposition of certain Demazure characters twisted by roots of unity | poster |
Nishu Kumari | Factorization of classical characters twisted by roots of unity | poster |
Ezgi Kantarcı Oğuz | Oriented posets | poster |
Weihong Xu | Quantum K-theory of incidence varieties | poster |
POSTER SESSION B, JUNE 27 (TUESDAY):
Abstracts of talks and posters
Michela Ceria
Alternatives for the
Sylvie Corteel
Colored vertex models
I will explain how Macdonald and modified Macdonald polynomials and generalizations can be defined combinatorially using vertex models and how their symmetry is a trivial consequence of the Yang-Baxter equation. This also gives rise to nonsymmetric versions. This is joint work with David Keating (Wisconsin).
Colin Defant
Permutoric promotion: Gliding globs, sliding stones, and colliding coins
We introduce toric promotion as a cyclic variant of Schützenberger's famous promotion operator. Toric promotion acts on the labelings of a graph
Rafael González D’León
On Whitney numbers of the first and second kind, or is it the other way around?
The Whitney numbers of the first and second kind are a pair of poset invariants that are relevant in various areas of mathematics. One of the most interesting appearances of these numbers is as the coefficients of the chromatic polynomial of a graph. They also appear as counting regions in the complement of a real hyperplane arrangement. In this talk, I will share a very curious phenomenon: sometimes the Whitney numbers of the first and second kind of a poset happen to be also the Whitney numbers of the second and first kind but of a different poset. We call this phenomenon Whitney duality and to find examples we rely on the techniques of edge labelings and quotient posets. I will present some key results in the theory of Whitney duality and in particular recent results regarding nonuniqueness. Joint work with Josh Hallam and Yeison Quiceno.
Takeshi Ikeda
Equivariant homology of the affine Grassmannian of the symplectic group
Schubert calculus of the affine Grassmannian
Luc Lapointe
Positivity conjectures for
We will explain how the construction of Macdonald polynomials in superspace can be naturally extended to define
Chiara Meroni
Cutting polytopes
We obtain a parametric, semialgebraic description of properties of the hyperplane sections of a polytope. Using this structure, we provide algorithms for the optimization of several combinatorial and metric properties over all hyperplane slices of a polytope. This relies on four fundamental hyperplane arrangements. This is a joint work with Marie-Charlotte Brandenburg (Max Planck Institute for Mathematics in the Sciences, Leipzig) and Jesús A. De Loera (University of California, Davis).
Leonid Monin
Polyhedral models for K-theory
Every homogeneous polynomial
In my talk, I will recall these results and present their recent generalizations. In particular, I will explain how to associate an algebra with Gorenstein duality to any function
Bruce Sagan
Chromatic symmetric functions and change of basis
For a graph
Johanna Steinmeyer
Combinatorial Hodge theory and IDP lattice polytopes
One of the fundamental questions of Ehrhart theory lies in characterizing the possible
I will give an overview of the results and techniques. No prior knowledge of combinatorial Hodge theory is assumed. Based on joint work with Adiprasito, Papadakis, and Petrotou.
Mariel Supina
Invitation to equivariant Ehrhart theory
Ehrhart theory is a topic in geometric combinatorics which involves counting the lattice points inside of lattice polytopes. Alan Stapledon (2010) introduced equivariant Ehrhart theory, which combines discrete geometry, combinatorics, and representation theory to give a generalization of Ehrhart theory that accounts for the symmetries of polytopes. In this talk, I will demonstrate an example of equivariant Ehrhart theory and discuss some open problems in the area. I will mention joint work with Federico Ardila and Andrés Vindas-Meléndez (2020) and with Sophia Elia and Donghyun Kim (2022).
Ben Young
A Minecraft tour of the tripartite double dimer model
What's up, mathematicians! Bizarrely, tripartite double dimers appear in two unrelated ways in the enumerative geometry of toric CY threefolds. In recent joint work with Ava Bamforth and Tatyana Benko, we find a simple, purely
combinatorial explanation. Both theories involve
Esther Banaian
Algebras from orbifolds
We discuss two algebras associated to triangulated unpunctured orbifolds with all orbifold points of order three - a gentle algebra and a generalized cluster algebra, in the sense of Chekhov and Shapiro. To each algebra, we associate a map which can be seen as taking arcs on the orbifold to Laurent polynomials. The first map was defined by Caldero and Chapoton; the second is the snake graph map, defined for surfaces by Musiker, Schiffler, and Williams and for orbifolds by B. and Kelley. We show that the outputs of these two maps agree. This poster is based on joint work with Yadira Valdivieso.
Aritra Bhattacharya
The Clebsch-Gordan rules for Macdonald polynomials
We compute the product of a nonsymmetric Macdonald polynomial
Trung Chau
Barile-Macchia resolutions
There are many ways to explicitly construct free resolutions of monomial ideals over a polynomial ring, e.g., Taylor resolutions. However, it is hard to obtain MINIMAL free resolutions. Batzies and Welker in 2002 showed that homogeneous acyclic matchings induce free resolutions for monomial ideals, provided an algorithm to produce them, and called them Lyubeznik resolutions. In this joint work with Selvi Kara, we introduce an alternate algorithm to produce homogeneous acyclic matchings, and called the induced resolutions Barile-Macchia. We show that Barile-Macchia resolutions are minimal for large classes of monomial ideals.
Patty Commins
Invariant theory for the free left-regular band and a
We examine from an invariant theory viewpoint the monoid algebras for two monoids having large symmetry groups. The first monoid is the free left-regular band on
We then use results from the theory of random walks and random-to-top shuffling to decompose the entire monoid algebra into irreducibles, simultaneously as a module over the invariant ring and as a group representation. Our irreducible decompositions are described in terms of derangement symmetric functions introduced by Désarménien and Wachs.
Bishal Deb
Continued fractions using a Laguerre digraph interpretation of the Foata–Zeilberger bijection
A Laguerre digraph is a directed graph on
We then introduce Flajolet's combinatorial theory of continued fractions and state a continued fraction identity for the series
In a recent work (arxiv:2304.14487), I solved conjectured continued fractions due to Randrianarivony–Zeng (1996), Sokal–Zeng (2022), and Deb–Sokal (arxiv:2022) using this reinterpretation. We will state some of these results.
Danai Deligeorgaki
Inequalities for
The Ehrhart polynomial
Yifeng Huang
Spiral shifting operators and punctual Quot schemes on cusp
(Joint with Ruofan Jiang) We prove a rationality result on the motive (in the Grothendieck ring of varieties) of the Quot scheme of points on the cusp singularity
Aryaman Jal
Polyhedral geometry of bisectors and bisection fans
Every symmetric convex body induces a norm on the underlying space. The object of our study is the bisector of two points with respect to this norm. A topological description of bisectors is known in the 2 and 3-dimensional cases and recent work of Criado, Joswig and Santos (2022) expanded this to a fuller characterization of the geometric, combinatorial, and topological properties of the bisector. A key object introduced was the bisection fan of a polytope which they were able to explicitly describe in the case of the tropical norm. We discuss the bisector as a polyhedral complex, introduce the notion of bisection cones, and describe the bisection fan corresponding to other polyhedral norms. This is joint work with Katharina Jochemko.
V. Sathish Kumar
Decomposition of certain Demazure characters twisted by roots of unity.
We generalize a theorem of Littlewood concerning the factorization of Schur polynomials when their variables are twisted by roots of unity. There have been several generalizations of this result in recent times. We prove that certain families of flagged skew Schur polynomials admit a similar factorization when twisted by roots of unity. This family of polynomials includes, as a special case, a certain family of Demazure characters.
Nishu Kumari
Factorization of classical characters twisted by roots of unity
Fix natural numbers
Ezgi Kantarcı Oğuz
Oriented Posets
We define oriented posets with corresponding rank matrices, where linking two posets by an edge corresponds to matrix multiplication. In particular, linking chains via this method gives us fence posets, and taking traces gives us circular fence posets.
We give several applications, including resolution of a conjecture by Leclere and Morier-Genoud's on matrices for
Weihong Xu
Quantum K-theory of Incidence Varieties
We prove a conjecture of Buch and Mihalcea in the case of the incidence variety
Tucker Jerome Ervin
New Hereditary and Mutation-Invariant Property Arising from Forks
A hereditary property of quivers is a property preserved by restriction to any full subquiver. Similarly, a mutation-invariant property of quivers is a property preserved by mutation. Using forks, a class of quivers developed by Warkentin, we introduce a new hereditary and mutation-invariant property. We prove that a quiver being mutation-equivalent to a finite number of non-forks — which we define as having a finite forkless part — is this new property, using only elementary methods.
David Garber
A
The (unsigned) Stirling numbers of the first kind
A known combinatorial interpretation for these numbers is given by considering them as the number of permutations of the set
Bala presented a generalization of the Stirling numbers of the first kind to the framework of Coxeter groups of type B. We denote these numbers by
A generalization of Stirling numbers was given by Broder, which is called the
In this work, we suggest a
Hans Höngesberg
Alternating sign matrices with reflective symmetry and plane partitions:
Vertically symmetric alternating sign matrices (VSASMs) of order
This is joint work with Ilse Fischer.
Joe Johnson
Plane Partitions of Trapezoid Shape
A plane partition (or P-partition) is a nonnegative integer labeling of a poset which weakly increases as you travel up cover relations. In 1983, Proctor showed that the rectangle poset and its associated trapezoid poset have the same number of plane partitions with maximum label
Siddheswar Kundu
Saturation for Flagged Skew Littlewood-Richardson Coefficients
We define an extension of Littlewood-Richardson (LR) coefficients, namely flagged skew Littlewood-Richardson coefficients, involving four partitions and a flag which is a weakly increasing finite sequence of non-negative integers. These coefficients subsume several generalizations of LR coefficients (such as Zelevinsky’s extension of LR coefficients). Then we will establish the saturation property of these coefficients, generalizing the saturation theorems of Knutson-Tao and Kushwaha-Raghavan-Viwanath.
Nadia Lafreniere
Homomesies on Permutations Using the FindStat Database
We performed a systematic study of permutation statistics and bijective maps on permutations in which we identified and proved 122 instances of the homomesy phenomenon. Homomesy occurs when the average value of a statistic is the same on each orbit of a given map. We identified some maps that are likely to exhibit the homomesy characteristics for several statistics and showed that many maps have no interesting homomesic statistics. On top of the many new homomesy results, our research method is especially interesting: we used SageMath to search the FindStat combinatorial statistics database to identify potential homomesies and to suggest theorems to prove. This method has the potential to be applied to several other problems.
Alex McDonough
Signed Determinantal Tilings of Euclidean Space
To answer a question about high-dimensional chip-firing, I previously introduced a family of periodic tilings which are obtained from considering a collection of submatrices based on a given matrix. However, this construction requires a specific class of matrices.
For this project, we generalize this construction to all square matrices using signed tiles. In this context, tiles are allowed to overlap, but each point must be covered by exactly one more positive tile than negative tile. This is joint work with Joseph Doolittle.
Duc-Khanh Nguyen
A generalization of the Murnaghan-Nakayama rule for
We introduce a generalization of
Samrith Ram
Subspace profiles of Linear Operators over Finite Fields
Let
Considering subspace profiles leads us to a new family of univariate polynomials indexed by integer partitions. At 1, 0, and -1 these polynomials count set partitions with specified block sizes, standard tableaux of specified shape, and standard shifted tableaux of a specified shape, respectively. These polynomials are generated by a new statistic on set partitions as well as a polynomial statistic on standard tableaux. They allow us to express the
Andrew Reimer-Berg
A Generalized RSK for Enumerating Linear Series on
We give a combinatorial proof of a recent geometric result of Farkas and Lian on linear series on curves with prescribed incidence conditions. The result states that the expected number of degree-
We also apply similar methods to give a combinatorial interpretation and proof of the fact that, in the modified setting in which
Florian Schreier-Aigner
(-1)-Enumerations of arrowed Gelfand-Tsetlin patterns
Arrowed Gelfand-Tsetlin patterns have recently been introduced to study alternating sign matrices.
In this talk, we present a
This is based on joint work with Ilse Fischer.
Wahiche
Combinatorial interpretations of the Macdonald identities for affine root systems
We explore some connections between vectors of integers and integer partitions seen as bi-infinite words. This methodology enables us to give a combinatorial interpretation of the Macdonald identities for affine root systems of the seven infinite families in terms of symplectic and special orthogonal Schur functions. From these results, we are able to derive