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Video recordings of my talks
Video recordings of my talks
The recording of my FPSAC 2025 talk on joint work with Olivier Bernardi where we define Shi-like and Catalan-like deformations for any restriction of a Weyl arrangement. Restrictions of Weyl arrangements may not be crystallographic or even reflection arrangements themselves, so the existence of nice deformations was very surprising. I also discuss a proof that the relative Coxeter numbers determine free multiplicities for such restrictions (this generalizes the ANN multiplicities) and conjecture (with an award!) further such free families.
The recording of my FPSAC 2023 talk on our homonymous work with Matthieu where we give a type-independent proof for the decomposition of the W-parking space (a combinatorial name for a certain rational Cherednik algebra module) in terms of noncrossing partitions. It was an open problem since 2004 by Athanasiadis-Reiner.
The recording of my ICMS talk: I give representation theoretic decompositions of the W-parking spaces (certain rational Cherednik algebra modules) and conjecture various compatible combinatorial models, including free non-constant multiplicities on restricted reflection arrangements (the conjecture on the multiplicities m^* is now proven, but m^** is open).
The recording of my FPSAC 2021 talk on common work with Alejandro Morales and Joel Lewis where we generalize Hurwitz numbers to reflection groups and prove (almost) product formulas for the genus-0 case. We were all very surprised by the generality of the new formulas and the way they specialize to Hurwitz's famous formula. If WX = W1 × ⋯ × Wr, then our formula gave the number FWfull(WX) as
an almost term by term analogue of the Hurwitz formula
The recording of my talk at the virtual Polytopics: Recent advances on polytopes workshop. It was on an application of the spectral study of the W-Laplacian on calculating the volume for the root zonotope of W. Our formula is expressed as a sum over the maximal-rank reflection subgroups W' of W, involving their Coxeter numbers and connection indices.
The recording of my first virtual talk, at the Minnesota Combinatorics seminar, about my favorite project from my time in France (joint with Guillaume Chapuy). In this project, we did quite a few exciting things: we extended the Matrix-Tree theorem to reflection groups W, we proved structural results for W-analogues of the Jucys-Murphy elements, we gave formulas for the volumes of root zonotopes. We also introduced the W-Laplacian operator that has become a very strong tool in Coxeter-Catalan combinatorics.
Slides from seminar and conference talks
Slides from seminar and conference talks
Lyashko-Looijenga morphisms and all that
Lyashko-Looijenga morphisms, braid monodromy factorizations, and combinatorics of Coxeter groups, Algebra and Combinatorics seminar at UTDallas, October 11, 2024.
Deformations of restricted reflection arrangements
Shi-like and Catalan-like deformations for restricted reflection arrangements, Northeastern Topology Seminar, October 29, 2024.
Hyperplane arrangements in combinatorics, representation theory, and geometry, Mathematics & Statistics Colloquium at UMass Lowell, October 16, 2024 (and full version here).
Deformations of restricted reflection arrangements, SIAM TX-LA Sectional Meeting at Waco, October 12, 2024.
Shi-like and Catalan-like deformations of Braid and reflection arrangements, CombinaTexas conference at Texas A&M, March 23, 2024.
Shi-like and Catalan-like deformations of Braid and reflection arrangements, CAAC conference at LACIM (UQAM), January 27th, 2024.
Shi-like and Catalan-like deformations of Braid and reflection arrangements, Combinatorics Forum at UCLA, November 17th, 2023.
Cyclic Sieving on the faces of the cluster complex
Parking functions on the cluster complex and Cyclic Sieving phenomena, CART seminar at KIAS (virtual), May 4, 2024.
Cyclic Sieving Phenomena on W-associahedra and generalized cluster complexes, Spring Eastern AMS sectional meeting at Howard U, April 7, 2024.
Cyclic Sieving Phenomena on W-associahedra and generalized cluster complexes, Algebra and Combinatorics seminar at UTDallas, March 25, 2024.
Decompositions of parking spaces and all that
Decompositions of parking spaces, reflection laplacians, and diagonal co-invariants, "Guises of reflection arrangements" conference at ICMS Edinburgh, March 16, 2023.
Hurwitz numbers via transportation polytopes, ECCO (Encuentro Colombiano de COmbinatoria) at U. de Los Andes, June 18, 2022.
Counting chains via the W-Laplacian
Recursions and Proofs in Coxeter-Catalan combinatorics, CAGE seminar at Drexel and UPenn, December 16, 2021.
Recursions and Proofs in Coxeter-Catalan combinatorics, Algebra, Combinatorics, and Number theory seminar at DePaul University, October 8, 2021.
Jucys-Murphy elements, Laplacians, and Matrix-Tree theorems for reflection groups
Volumes of root zonotopes via the W-Laplacian, Polytopics conference at MPI, April 7th, 2021.
Coxeter factorizations and the Matrix Tree theorem with generalized Jucys-Murphy weights, Combinatorics Seminar at the U. of Minnesota, April 24, 2020.
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