The UC Berkeley Combinatorics Seminar

Fall 2026 – Wednesdays 4:10pm – 5:30pm, Room 939
Introductory pre-talk for graduate students (open to all) 4:10pm – 4:35pm
Main talk 4:40pm – 5:30pm
Organizers: Christian Gaetz, Pranav Enugandla, and Yuhan Jiang,

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Date Speaker Title

August 26th No seminar

September 2nd Mia Smith (Michigan)

Electroid varieties and the Lagrangian Grassmannian
Recent work of Lam, Chepuri--George--Speyer, and Bychkov--Gorbounov--Kazakov--Talalaev gave a stratification of the totally nonnegative Lagrangian Grassmannian into electroid cells parameterized by cactus networks, paralleling Postnikov's stratification of the totally nonnegative Grassmannian by positroid cells. Electroid varieties arise as an algebro-geometric extension of electroid cells. In analogy to results of Knutson, Lam, and Speyer on positroid varieties, electroid varieties are reduced, irreducible, regular in codimension one, compatibly Frobenius split, and form a stratification. In this talk, I'll describe our recent work proving these geometric properties of electroid varieties and give a flavor of the combinatorics underlying some of the proofs. This talk is based on joint work with Dawei Shen and David Speyer.

September 9th Gabe Udell (UC Santa Cruz)

Grobner geometry of hybrid pipe dreams
Matrix Schubert varieties are subvarieties of the space of all n × n matrices which are defined by rank conditions on their submatrices. The equivariant cohomology classes of matrix Schubert varieties are given by double Schubert polynomials. They can be computed in terms of either pipe dreams (introduced by Bergeron–Billey), bumpless pipe dreams (introduced by Lam–Lee–Shimozono), or any of 2^n flavors of hybrid pipe dreams (introduced by Knutson–U) which interpolate between the two. In this talk I will discuss bijective proofs that the 2^n formulas agree and commutative algebraic proofs that hybrid pipe dreams index (with multiplicity) the irreducible components of Gröbner degenerations of matrix Schubert varieties for certain term orders. The latter topic is based on joint work with Tianyi Yu and Zach Hamacker and builds on work of Knutson–Miller in the pipe dream case and Klein–Weigandt in the bumpless pipe dream case.

September 16th Colin Defant (Harvard)

Braid Group Presentations and Triangulations of the Permutahedron
For each finite Coxeter group W and each standard Coxeter element of W, we construct a regular triangulation of the W-permutahedron. Our proof relies on the theory of total linear stability for Dynkin quivers. We also explore several notable combinatorial properties of these triangulations that relate the Bruhat order, the noncrossing partition lattice, and Cambrian congruences. Each triangulation gives an explicit mechanism for relating two different presentations of the corresponding braid group (the standard Artin presentation and Bessis's dual presentation). This is joint work with Melissa Sherman-Bennett and Nathan Williams.

September 23rd Sylvie Corteel (UC Berkeley)

Exclusion processes and (non)symmetric polynomials
Exclusion processes are interacting particle systems in which particles move subject to the constraint that each site can be occupied by at most one particle. These models have deep connections with algebraic combinatorics, representation theory, and special functions. In this talk, I will describe some of these connections, focusing in particular on the role played by symmetric and nonsymmetric polynomials. I will discuss how polynomial families such as Macdonald and Koornwinder polynomials arise naturally in the study of exclusion processes and related integrable models. In certain special cases, combinatorial formulas for these polynomials can be interpreted through particle configurations, lattice paths, and tableaux. I will also explain how nonsymmetric versions of these polynomials provide a richer framework for understanding boundary conditions and more general exclusion dynamics. The goal of the talk is to illustrate how probabilistic models can lead to interesting algebraic and combinatorial structures, and conversely, how the combinatorics of symmetric and nonsymmetric polynomials can shed light on exclusion processes.

September 30th Shilun Li (UC Berkeley)

A Deterministic Construction of a Large-Distance Code from the Wozencraft Ensemble
A basic goal in coding theory is to construct explicit error-correcting codes with good distance. We study this problem for the classical Wozencraft ensemble. We reduce the construction problem to a combinatorial question about controlling repeated differences, which naturally leads to Sidon sets. Using explicit Sidon set constructions, we obtain deterministic Wozencraft codes with minimum distance on the order of the square root of the message length.

October 7th Colleen Robichaux (UC Davis)

Complexity of Combinatorial Structure Constants
Structure constants of symmetric polynomial bases and their generalizations often compute certain non-negative algebraic invariants. Many large families of these structure constants have natural signed combinatorial interpretations, but non-cancellative combinatorial rules for these coefficients are largely unknown. In this talk, we discuss the computational complexity of these counting problems and their vanishing counterparts, using Schubert polynomials as a running example. This is joint work with Igor Pak.

October 14th Olya Mandelshtam (Waterloo)

Type C multiline queues and the open-boundary TASEP
The multispecies TASEP on a circle is a particle model whose partition function is connected to Macdonald polynomials at t=0. Multiline queues were introduced by Ferrari and Martin (2007) to compute the stationary distribution of the TASEP on a circle. Their construction admits a natural interpretation in terms of tensor products of Kirillov–Reshetikhin crystals of affine type A, and a map from these tensor products to TASEP states is given by crystal-theoretic operations. We show that there is a natural Markov chain on the crystal that projects to the TASEP via this map.
The multispecies open boundary TASEP can be viewed as a type C analogue, with its partition function connected to Koornwinder polynomials at t=0. However, computing its stationary distribution beyond rank 1 has remained a longstanding open problem. Using Kirillov–Reshetikhin crystals of affine type C, we construct type C multiline queues and a corresponding Ferrari–Martin pairing algorithm, and show the crystal likewise admits a Markov chain that projects to the TASEP. Our construction is a combinatorial interpretation of the virtualization map for Kashiwara–Nakashima columns. We thus obtain a crystal-theoretic formula for the stationary distribution of the multispecies open boundary TASEP at the specialization alpha=beta=1. This is joint work with Jeronimo Valencia Porras.

October 21st Joel Kamnitzer (McGill)

Arboreal webs, their web varieties, and canonical bases
A web is a planar graph which defines an invariant vector in a tensor product of fundamental representations of sl_n. An arboreal web is one whose underlying graph is a tree. These webs are the simplest to understand for the following reasons. First, their corresponding web varieties are smooth, and second the invariant vectors that they define lie in the canonical basis. I will explain the proofs of both of these facts. This is joint work with Pierre Baumann, Oliver Pechenik, and Stephan Pfannerer.

October 28th JungTao (Ronnie) Cheng (Stanford)

From tangent bundles of matroids to a stone game
The Hodge theory of matroids illustrates how geometric ideas can lead to combinatorial results. In this talk, I will introduce a tangent class for a matroid and explain how it provides a matroidal Riemann–Roch formula. I will then discuss a numerical Kawamata–Viehweg vanishing theorem for rank-three matroids and explain how it reduces to an inequality for a stone game. Time permitting, I will give a combinatorial proof and the geometric insights behind the argument.

November 4th Iva Halacheva (Northeastern) TBA

November 11th No seminar (Veterans Day)

November 18th Amanda Schwartz (UC Davis) TBA

November 25th No seminar (Thanksgiving)

December 2nd Ethan Partida (Brown) TBA

December 9th Alexei Oblomkov (UMass Amherst) TBA

Older seminar webpages: Fall 2025 Spring 2025 Fall 2024 Spring 2024 Fall 2023 Spring 2023 Fall 2022 Spring 2022 Fall 2021 Spring 2021 Fall 2020 2018–2020

Date	Speaker	Title
August 26th	No seminar
September 2nd	Mia Smith (Michigan)	Electroid varieties and the Lagrangian Grassmannian Recent work of Lam, Chepuri--George--Speyer, and Bychkov--Gorbounov--Kazakov--Talalaev gave a stratification of the totally nonnegative Lagrangian Grassmannian into electroid cells parameterized by cactus networks, paralleling Postnikov's stratification of the totally nonnegative Grassmannian by positroid cells. Electroid varieties arise as an algebro-geometric extension of electroid cells. In analogy to results of Knutson, Lam, and Speyer on positroid varieties, electroid varieties are reduced, irreducible, regular in codimension one, compatibly Frobenius split, and form a stratification. In this talk, I'll describe our recent work proving these geometric properties of electroid varieties and give a flavor of the combinatorics underlying some of the proofs. This talk is based on joint work with Dawei Shen and David Speyer.
September 9th	Gabe Udell (UC Santa Cruz)	Grobner geometry of hybrid pipe dreams Matrix Schubert varieties are subvarieties of the space of all n × n matrices which are defined by rank conditions on their submatrices. The equivariant cohomology classes of matrix Schubert varieties are given by double Schubert polynomials. They can be computed in terms of either pipe dreams (introduced by Bergeron–Billey), bumpless pipe dreams (introduced by Lam–Lee–Shimozono), or any of 2^n flavors of hybrid pipe dreams (introduced by Knutson–U) which interpolate between the two. In this talk I will discuss bijective proofs that the 2^n formulas agree and commutative algebraic proofs that hybrid pipe dreams index (with multiplicity) the irreducible components of Gröbner degenerations of matrix Schubert varieties for certain term orders. The latter topic is based on joint work with Tianyi Yu and Zach Hamacker and builds on work of Knutson–Miller in the pipe dream case and Klein–Weigandt in the bumpless pipe dream case.
September 16th	Colin Defant (Harvard)	Braid Group Presentations and Triangulations of the Permutahedron For each finite Coxeter group W and each standard Coxeter element of W, we construct a regular triangulation of the W-permutahedron. Our proof relies on the theory of total linear stability for Dynkin quivers. We also explore several notable combinatorial properties of these triangulations that relate the Bruhat order, the noncrossing partition lattice, and Cambrian congruences. Each triangulation gives an explicit mechanism for relating two different presentations of the corresponding braid group (the standard Artin presentation and Bessis's dual presentation). This is joint work with Melissa Sherman-Bennett and Nathan Williams.
September 23rd	Sylvie Corteel (UC Berkeley)	Exclusion processes and (non)symmetric polynomials Exclusion processes are interacting particle systems in which particles move subject to the constraint that each site can be occupied by at most one particle. These models have deep connections with algebraic combinatorics, representation theory, and special functions. In this talk, I will describe some of these connections, focusing in particular on the role played by symmetric and nonsymmetric polynomials. I will discuss how polynomial families such as Macdonald and Koornwinder polynomials arise naturally in the study of exclusion processes and related integrable models. In certain special cases, combinatorial formulas for these polynomials can be interpreted through particle configurations, lattice paths, and tableaux. I will also explain how nonsymmetric versions of these polynomials provide a richer framework for understanding boundary conditions and more general exclusion dynamics. The goal of the talk is to illustrate how probabilistic models can lead to interesting algebraic and combinatorial structures, and conversely, how the combinatorics of symmetric and nonsymmetric polynomials can shed light on exclusion processes.
September 30th	Shilun Li (UC Berkeley)	A Deterministic Construction of a Large-Distance Code from the Wozencraft Ensemble A basic goal in coding theory is to construct explicit error-correcting codes with good distance. We study this problem for the classical Wozencraft ensemble. We reduce the construction problem to a combinatorial question about controlling repeated differences, which naturally leads to Sidon sets. Using explicit Sidon set constructions, we obtain deterministic Wozencraft codes with minimum distance on the order of the square root of the message length.
October 7th	Colleen Robichaux (UC Davis)	Complexity of Combinatorial Structure Constants Structure constants of symmetric polynomial bases and their generalizations often compute certain non-negative algebraic invariants. Many large families of these structure constants have natural signed combinatorial interpretations, but non-cancellative combinatorial rules for these coefficients are largely unknown. In this talk, we discuss the computational complexity of these counting problems and their vanishing counterparts, using Schubert polynomials as a running example. This is joint work with Igor Pak.
October 14th	Olya Mandelshtam (Waterloo)	Type C multiline queues and the open-boundary TASEP The multispecies TASEP on a circle is a particle model whose partition function is connected to Macdonald polynomials at t=0. Multiline queues were introduced by Ferrari and Martin (2007) to compute the stationary distribution of the TASEP on a circle. Their construction admits a natural interpretation in terms of tensor products of Kirillov–Reshetikhin crystals of affine type A, and a map from these tensor products to TASEP states is given by crystal-theoretic operations. We show that there is a natural Markov chain on the crystal that projects to the TASEP via this map. The multispecies open boundary TASEP can be viewed as a type C analogue, with its partition function connected to Koornwinder polynomials at t=0. However, computing its stationary distribution beyond rank 1 has remained a longstanding open problem. Using Kirillov–Reshetikhin crystals of affine type C, we construct type C multiline queues and a corresponding Ferrari–Martin pairing algorithm, and show the crystal likewise admits a Markov chain that projects to the TASEP. Our construction is a combinatorial interpretation of the virtualization map for Kashiwara–Nakashima columns. We thus obtain a crystal-theoretic formula for the stationary distribution of the multispecies open boundary TASEP at the specialization alpha=beta=1. This is joint work with Jeronimo Valencia Porras.
October 21st	Joel Kamnitzer (McGill)	Arboreal webs, their web varieties, and canonical bases A web is a planar graph which defines an invariant vector in a tensor product of fundamental representations of sl_n. An arboreal web is one whose underlying graph is a tree. These webs are the simplest to understand for the following reasons. First, their corresponding web varieties are smooth, and second the invariant vectors that they define lie in the canonical basis. I will explain the proofs of both of these facts. This is joint work with Pierre Baumann, Oliver Pechenik, and Stephan Pfannerer.
October 28th	JungTao (Ronnie) Cheng (Stanford)	From tangent bundles of matroids to a stone game The Hodge theory of matroids illustrates how geometric ideas can lead to combinatorial results. In this talk, I will introduce a tangent class for a matroid and explain how it provides a matroidal Riemann–Roch formula. I will then discuss a numerical Kawamata–Viehweg vanishing theorem for rank-three matroids and explain how it reduces to an inequality for a stone game. Time permitting, I will give a combinatorial proof and the geometric insights behind the argument.
November 4th	Iva Halacheva (Northeastern)	TBA
November 11th	No seminar (Veterans Day)
November 18th	Amanda Schwartz (UC Davis)	TBA
November 25th	No seminar (Thanksgiving)
December 2nd	Ethan Partida (Brown)	TBA
December 9th	Alexei Oblomkov (UMass Amherst)	TBA