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) TBA

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) TBA

October 14th Olya Mandelshtam (Waterloo) TBA

October 21st Joel Kamnitzer (McGill) TBA

October 28th JungTao (Ronnie) Cheng (Stanford) TBA

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 TBA 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)	TBA
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)	TBA
October 14th	Olya Mandelshtam (Waterloo)	TBA
October 21st	Joel Kamnitzer (McGill)	TBA
October 28th	JungTao (Ronnie) Cheng (Stanford)	TBA
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	TBA	TBA