Past Seminar Talks

The following talks were given in past semesters.

Fall 2025

• September 11: Alex Wilson, Centralizers in the Plactic Monoid
  Click here for abstract

  Let $u$ be a word over the positive integers. Motivated in part by a question of representation theory, we study the centralizer set $C(u)$, which consists of words $w$ for which $wu$ and $uw$ are Knuth-equivalent. In particular, we characterize $C(u)$ when $u$ has few letters or is a certain type of decreasing sequence, and we address related enumerative questions.

• September 18: There will be a watch party for a relevant talk from this ICERM workshop.

• September 25: Jesse Huang, A Combinatorial Gateway to Calabi-Yau Toric Geometry
  Click here for abstract

  The goal of this talk is to introduce Calabi-Yau toric geometry from a purely combinatorial perspective, through the rich structures carried by an embedded bipartite graph on a torus called a dimer model.
  
  In the pre-talk, we will demonstrate how matchings, tilings, and quivers naturally encodes deep geometric and physical content. No background in algebraic geometry will be assumed; instead, we’ll build the story from the ground up, with an emphasis on visual intuition and discrete structures.
  
  Next, I will discuss how dimer models simultaneously encode the data of a toric Calabi-Yau singularity and its mirror dual, unifying perspectives from the B-model and A-model of homological mirror symmetry through noncommutative algebras. We will proceed with some recent developments and open problems, including connections to the symplectic geometry of Landau-Ginzburg models and Van den Bergh’s noncommutative resolution conjecture for toric Gorenstein affine singularities. To conclude the talk, we will discuss an example of a higher dimensional generalization and its connection to my recent research works.
  
  This talk is also partially based on two undergraduate research projects in the present semester, where we study variations of dimer models of the same lattice polygon from different choices in the fast inverse algorithm, and implications on the two sides of mirror symmetry:
  - (DRP) Dimer Variation and Geometry of Landau-Ginzburg Models, with Kenneth Xiao and Elizabeth Cai (A-model)
  - (NSERC USRA) Dimer Variation and NCCR Mutations, with Filip Mildrag and Elana Kalashnikov (B-model)
  

• October 2: Nathan Pagliaroli, Enumerating planar stuffed maps as hypertrees of mobiles
  Click here for abstract

  A planar stuffed map is an embedding of a graph into the 2-sphere, considered up to orientation-preserving homeomorphisms, such that the complement of the graph is a collection of disjoint topologically connected components that are each homeomorphic to the 2-sphere with multiple boundaries. This is a generalization of planar maps whose complement of the graph is a collection of disjoint topologically connected components that are each homeomorphic to a disc. In this talk I will outline my work in constructing a bijection between bipartite planar stuffed maps and collections of integer-labelled trees connected by hyperedges such that they form a hypertree. This bijection directly generalizes the Bouttier-Di Franceso-Guitter bijection between bipartite planar maps and mobiles. Additionally, we show that the generating functions of these trees of mobiles satisfy both an algebraic equation, generalizing the case of ordinary planar maps, and a new functional equation. As an example, we explicitly enumerate a class of stuffed quadrangulations.

• October 9: Graham Denham, Distances in trees and inequalities for matroids
  Click here for abstract

  The distance matrix of a tree appears in a range of contexts, from phylogenetics to physical chemistry. I will describe a new result about the spectrum of this matrix, one that gives affirmative answers to two questions about matroid positivity properties. These are both strengthenings of Mason's conjectures about the log-concavity of sequence of numbers of independent sets of a matroid, proposed by Igor Pak and by Giansiracusa, Rincón, Schleis, Ulirsch, respectively.
  
  This is joint work with Federico Ardila, Sergio Cristancho, Chris Eur, June Huh, and Botong Wang.

• October 16: No seminar on account of reading week

• October 23: Krystal Guo, Counting Substructures in Hypergraphs with Spectrum
  Click here for abstract

  Jacobi’s classical result expresses the generating function for closed walks at a vertex of a graph as the ratio of two characteristic polynomials. We find a hypergraph analogue of this relationship, showing that the same rational function for a hypergraph also counts combinatorial substructures within it, called infragraphs. We use Viennot’s Heaps of Pieces framework to establish this result for the adjacency tensor of a hypergraph. As an immediate consequence, we obtain an alternative proof for the monotonicity of the principal eigenvalue of a hypergraph. This is based on joint work with Joshua Cooper and Utku Okur (arXiv: 2411.03567).

• October 30: Isabella Fosberry, Minimising the Martin invariant
  Click here for abstract

  The Martin invariant of an even degree regular graph is an integer, defined by a recurrence at a vertex. In this talk, we define this invariant and review some of its properties, and then focus on the following question: which graphs minimise the Martin invariant?

• November 6: Leigh Foster, Tilings of Benzels (and other finite regions) in the hexagon grid
  Click here for abstract

  In 1990, Conway and Lagarias introduced tilability criteria for tilability for finite regions of the hexagon and square grids. In the same year, Thurston expanded upon their work, introducing the height function criterion. We will discuss some new results in tilability: A new tilability criteria via the $\textsf{SL}_2(\mathbb{C})$ double dimer model, and enumeration of tilings of special regions called Benzels, introduced in 2020 by Propp, using a technique called compression. If time allows, we will also discuss ongoing work that expands Thurston's height function to stone-and-bone tilings of the hexagon grid.

• November 13: Pierre Popoli, Generalized Abelian Complexities for Pisot-Type Substitutive Sequences
  Click here for abstract

  Two finite words are said to be abelian equivalent if one is a permutation of the letters of the other. For an infinite word, one can investigate the associated complexity function, called abelian complexity, which is a classical object of study in combinatorics on words. In particular, many works study the abelian complexity of automatic sequences, where a longstanding conjecture states that the abelian complexity of an automatic sequence is a regular sequence. We have studied when the abelian complexity can be computed efficiently, in particular using the theorem prover Walnut. To this end, we study words that are fixed points of Pisot-type substitution and prove that these words satisfy the conjecture.
  
  If time permits, I will present k-abelian complexities, which are intermediate complexities between the abelian complexity and the factor complexity. I will also explain how our results can be extended to these complexities and how we can obtain a two-dimensional linear representation of some examples.
  
  This talk is based on joint work with J-M Couvreur, M. Delacourt, N. Ollinger, J. Shallit, and M. Stipulanti (arXiv: 2504.13584).
  

• November 20: No seminar on account of Tim Miller’s defense

• November 27: Zeus Dantas E Moura, Deterministic and Probabilistic Bijections for Macdonald Polynomials
  Click here for abstract

  Permuted-basement Macdonald polynomials \(E_α^σ(x_1, ..., x_n; q, t)\) are nonsymmetric generalizations of symmetric Macdonald polynomials indexed by a composition α and a permutation σ. They can be described combinatorially as generating functions over augmented fillings of shape α and basement σ.
  
  We construct deterministic and probabilistic bijections on fillings that prove identities relating \(E_α^σ, E_α^{σ s_i}, E_{s_i α}^σ,\) and \(E_{s_i α}^{σ s_i}\). These identities arise from two operations on the shape and basement: swapping adjacent parts of the shape, which expands \(E_α^σ\) into \(E_{s_i α}^σ\) and \(E_{s_i α}^{σ s_i}\); and swapping adjacent basement entries, which gives \(E_α^σ = E_α^{σ s_i}\) when \(α_i = α_{i+1}\).
  
  This is joint work with Olya Mandelshtam.

• December 4: Taylor Brysiewicz, The degrees of Stiefel Manifolds
  Click here for abstract

  The set of orthonormal bases for $k$-planes in $\mathbb{R}^n$ is cut out by the equations
  $X*X^T = I$
  where $X$ is a $k \times n$ matrix of variables and $I$ is $k \times k$ identity. This space, known as the Stiefel manifold $\textrm{St}(k,n)$, generalizes the orthogonal group and can be realized as the homogeneous space $O(n)/O(n-k)$. Its algebraic closure gives a complex affine variety, and thus, it has a degree.
  
  I will discuss our derivation of these degrees. Extending 2017 work on the degrees of special orthogonal groups, joint work with Fulvio Gesmundo gives a combinatorial formula in terms of non-intersecting lattice paths. This result relies on representation theory, commutative algebra, Ehrhart theory, polyhedral geometry, and enumerative combinatorics.
  
  I will conclude with some open problems inspired by these objects.

Spring 2025

• May 8: Max Wiesmann, Arrangements and Likelihood

• May 15: Félix Gélinas, Source characterization of the hypegraphic posets

• May 22: No seminar on account of CanaDAM

• Tuesday May 27: Note Tuesday date on account of AlCoVE

  • 1:30pm: Elise Catania, A Toric Analogue for Greene’s Rational Function of a Poset

  • 2:30pm: Jesse Kim, Shifted Parking functions

• June 5: Alex Fink, The external activity complex of a pair of matroids

• June 12: Laura Pierson, Power sum expansions for the Kromatic symmetric function

• June 19: Elana Kalashnikov, The Abelian/non-Abelian correspondence and Littlewood-Richardson rules for two-step flags

• June 26: Leo Jiang, Oriented graded Möbius algebras

• July 3: Farhad Soltani, Quasisymmetric harmonics in superspace

• July 10: Karen Yeats, Sizes of witnesses in covtree

• July 17: Library archives visit

• July 24: No seminar on account of FPSAC

• July 31: URA day

  • 1:30pm: Kai Choi, Alice in Quadraticspanningforestidentityspace

  • 2:10pm: Peiran Tao, Algebraic Diagonals and Asymptotics of Bivariate Generating Functions

  • 2:50pm: Stephanie Penner, Combinatorial Exploration: Counting Chord Diagrams

• August 7 (12:00pm in MC 6029): Harper Niergarth, Reflected and Nonsymmetric Crystal Graphs

• August 7 (1:30pm): Tia Ruza, Multivariate Limit Theorems and Algebraic Generating Functions

Winter 2025

• January 16: Leigh Foster, The squish map and the SL2 double dimer model

• January 23: Karen Yeats, Combinatorial interpretation of the coefficients of the causal set theory d’Alembertian

• January 30: Nantel Bergeron, Equivariant quasisymmetry

• February 6: Hunter Spink, New perspectives on quasisymmetry via divided differences, flag varieties, etc.

• February 14 (postponed on account of snow): Yasaman Yazdi, Statistical Fluctuations in the Causal Set-Continuum Correspondence

• February 20: Reading week

• February 27: Katie Waddle, Spherical friezes

• March 6: Andrew Sack, Operahedron Lattices

• March 13: Stephen Melczer, Positivity of P-Recursive Sequences Satisfying Linear Recurrences

• March 20: Allen Knutson, Schubert calculus by counting puzzles

• March 27: Michael Borinsky, Asymptotic count of edge-bicolored graphs

• April 3: Harper Niergarth and Kartik Singh, The quasisymmetric Macdonald polynomials are quasi-Schur positive at $t = 0$

• April 10: Natasha Ter-Saakov, Log-concavity of random Radon partitions

Fall 2024

• September 12: Jerónimo Valencia, A combinatorial proof of an identity involving Eulerian numbers

• September 19: Karen Yeats, Tubings of rooted trees and resurgence

• September 26: Jonathan Leake, Approximately Counting Flows via Generating Function Optimization

• October 3: John Smith, Coefficient Positivity and Analytic Combinatorics

• October 10: Josh Swanson, Cyclotomic generating functions

• Tuesday October 15 (during reading week): Christian Gaetz, Hypercube decompositions and combinatorial invariance for Kazhdan-Lusztig polynomials

• October 24: Nick Olson-Harris, Sufficient conditions for equality of skew Schur functions

• October 31: Joseph Fluegemann, Smooth points on positroid varieties and planar $N=4$ supersymmetric Yang-Mills theory

• November 7: Stephan Pfannerer, Descents for Border Strip Tableaux

• November 14: Colleen Robichaux, Vanishing of Schubert coefficients

• November 21: Torin Greenwood, Coloring the integers while avoiding monochromatic arithmetic progressions

• November 28: Mike Cummings, Combinatorial rules for the geometry of Hessenberg varieties

• December 5: David Wagner, Valuable partial orders

Spring 2024

• May 16: Sarah Brauner, Configuration spaces and combinatorial algebras

• May 23: Li Yu, Integrable systems on the dual space of Lie algebras arising from log-canonical cluster structures

• May 30: Jette Gutzeit, Introducing the interval poset associahedron

• June 6: Tia Ruza, Central Limit Theorems via Analytic Combinatorics in Several Variables

• June 13: Karen Yeats, Chord diagrams, triangulations, and $\phi \rho$ amplitudes

• June 20: No seminar

• June 27: Paul Balduf, Combinatorial proof of a Non-Renormalization Theorem

• July 4: No seminar

• July 11: No seminar

• July 18: Laura Pierson, Two variations of the chromatic symmetric function Note: No preseminar this week

• July 25: no seminar on account of FPSAC

• August 1: URA day

  • 1pm: Connor Baetz, The ASEP and alternate multi-line queues

  • 1:30pm: coffee

  • 1:50pm: Arnav Kumar, Dimension of posets and random graph orders

  • 2:30pm: Ron Cherny, A Combinatorial Case of The Gerstenhaber Problem

• August 8: William Chan, Control over the Kerov-Kirillov-Reshetikhin bijection with respect to the nesting structure on rigged configurations

• August 15: Jang Soo Kim, Lecture hall graphs and the Askey scheme

Winter 2024

• January 25: Santiago Estupinan, A new shifted Littlewood-Richardson rule

• February 1: Arad Nasiri, Combinatorial Action in Causal Set Quantum Gravity

• February 8: Tim Miller, Vertex models for the product of a Schur and Demazure polynomial

• February 15: Karen Yeats, More Martin and $c_2$ details

• February 22: Reading week

• February 29: Leo Jiang, Real matroid Schubert varieties, zonotopes, and virtual Weyl group

• March 7: social time

• March 14: Nancy Wallace, Quasi-partition algebras representations, planar Quasi-partition algebras and Characters of the Motzkin-Riordan algebra

• March 21: Nathan Pagliaroli, Colored unstable map enumeration from random noncommutative geometries

• March 28: Harper Niergarth, On the faces of the Kunz cone and the numerical semigroups within them

• April 4: Olya Mandelshtam, A new formula for the symmetric Macdonald polynomials via the ASEP and TAZRP

• April 11: Alex Kroitor, Lattice Paths Through ACSV

• April 18: Jeremy Chizewer, Analytic Methods and Combinatorial Plants

Fall 2023

• September 14: Tianyi Yu, Analogue of Fomin-Stanley algebra on bumpless pipedreams

• September 21: Jeremy Chizewer, The Sunflower Problem: Restricted Intersections

• September 28: Kartik Singh, Closure of Deodhar components

• October 5: Karen Yeats, Diagrammatic boundary calculus for Wilson loop diagrams

• October 12: Reading week, no seminar

• October 19: Vasu Tewari, Forest polynomials and harmonics for the ideal of quasisymmetric polynomials

• October 26: David Wagner, Higher-order correlation inequalities for random spanning trees

• November 2: Jerónimo Valencia, Snake decompositions of lattice path matroids

• November 9: Spencer Daugherty, Extended Schur functions and bases related by involutions

• November 16: Alejandro Morales, Linear relations and Lorentzian property of chromatic symmetric functions

• November 23: Jason Bell, Filtered deformations of commutative algebras. Note, no pre-seminar this week

• November 30: Kelvin Chan, Polarization operators in superspace

Winter 2023

• January 12: Andy Wilson (Kennesaw State University), Coinvariants and superspace

• January 19: François Bergeron (LACIM), From the nabla operator to the super nabla operator

• January 26: Emily Barnard (De Paul University), Cluster combinatorics and poset topology

• February 2: Nick Olson-Harris (Waterloo), Binary tubings and Dyson-Schwinger equations

• February 9: Elana Kalashnikov (Waterloo), Quantum hooks and the Plücker coordinate mirror

• February 16: Stephen Gillen (Waterloo), Geometry of gradient flows for analytic combinatorics

• February 23: Reading week (no seminar)

• March 2: Social hour

• March 9: Joel Lewis (George Washington University), Bargain hunting in a Coxeter group

• March 16: Kartik Singh (Waterloo), Taking limits in Go-diagrams

• March 23: Lucas Gagnon (York University), Quasisymmetric varieties, excedances, and bases for the Temperley–Lieb algebra

• March 30: Freddy Cachazo (Perimeter), Arrangements of Pseudolines, Tropical Grassmannians, and Generalized Scattering Amplitudes