Nicolle González

nicolle [at] math [dot] ubc [dot] ca

Office: MATHX 1225

Address: Mathematics Department

1984 Mathematics Rd

Vancouver, BC V6T 1Z2

Canada

I am an Assistant Professor of Mathematics at The University of British Columbia. Prior to this, I was an ICERM Research Fellow at Brown University for the Fall 2025 Categorification and Computation in Algebraic Combinatorics semester program. Before this I was at UC Berkeley as Charles B. Morrey Visiting Assistant Professor working with Sylvie Corteel, at UCLA as Presidential Postdoctoral Fellow under the mentorship of Raphaël Rouquier, and at MSRI as a Berlekamp Postdoctoral Fellow for the Higher Categories and Categorification program in Spring 2020. I finished my PhD in 2019 at the University of Southern California under the supervision of Aaron Lauda and Sami Assaf.

Most of my work is in algebraic combinatorics and representation theory, with applications to link homology theory.

I am currently organizing the UBC Discrete Math Seminar alongside Josh Turner and Steph van Willigenburg.

Past Organizational Activities

Published Papers and Pre-Prints

Smooth correspondences between quiver varieties - with with E. Gorsky and J. Simental. -https://arxiv.org/abs/2601.22287
A whittled complex for the Khovanov homology of torus links - with C. Caprau, C. Lee, R. Sazdanovic - https://arxiv.org/abs/2601.09079
A Local Characterization of Unions of Demazure Crystals - with S. Assaf - https://arxiv.org/abs/2512.19814
Structure and geometry of the tableaux algebra - with S. Daugherty, B. Muniz, P. Ocal, J. Pan, J. Torres - https://arxiv.org/abs/2510.27209
Pinnacles for Complex Reflection Groups - with A. Burnham-Schmidt - https://arxiv.org/abs/2510.03580
The elliptic Hall algebra and the double Dyck path algebra - with with E. Gorsky and J. Simental. - https://arxiv.org/abs/2502.16113
Keys and Evacuation via Virtualization - with O. Azenhas, D. Huang, and J. Torres - https://arxiv.org/abs/2409.12666
Khovanov-Rozansky homology of Coxeter knots and Schröder polynomials for paths under any line - with C. Caprau, M. Hogancamp and M. Mazin - https://arxiv.org/abs/2407.18123
Calibrated representations of the double Dyck path algebra- with E. Gorsky and J. Simental. - Mathematische Annalen (2024). https://doi.org/10.1007/s00208-024-02937-2
Triangular (q,t)-Schröder Polynomials and Khovanov-Rozansky Homology- with C. Caprau, M. Hogancamp, and M. Mazin - Séminaire Lotharingien de Combinatoire (2024), #157
Mesas of Stirling permutations - with P. Harris, G. Kirby, M. Vega, and B. Tenner - Journal of Combinatorics (Vol. 16, Issue 3 (2025), pp. 387-403) https://arxiv.org/abs/2306.12158
Higher rank (q,t)-Catalan polynomials, Affine Springer Fibers, and a Finite Rational Shuffle Theorem - with J. Simental and M. Vazirani - Transactions of the AMS 377 (2024), 5087-5127 DOI: https://doi.org/10.1090/tran/9115
Extremal tensor products of Demazure crystals are direct sums of Demazure crystals- with S. Assaf and A. Dranowski - Séminaire Lotharingien de Combinatoire 89B (2023), Article #12
Semi-standard parking functions and a finite Shuffle theorem - with J. Simental and M. Vazirani , Séminaire Lotharingien de Combinatoire 89B (2023), Article #84
Pinnacle sets of signed permutations - with P. Harris, G. Kirby, M. Vega, and B. Tenner - Discrete Math, Vol 346, Issue 7, July 2023,
Extremal tensor products of Demazure crystals - with S. Assaf and A. Dranowski - Algebras and Representation Theory (2023)
On Khovanov homology and related invariants - joint with C. Caprau, C. Lee, A. Lowrance, R. Sazdanovic, M. Zhang. - Research Directions in Symplectic and Contact Geometry and Topology, AWMS vol 27. Springer
Affine Demazure crystals for specialized nonsymmetric Macdonald polynomials - joint with Sami Assaf, Algebraic Combinatorics, Volume 4 (2021) no. 5, pp. 777-793.
Demazure Crystals for specialized nonsymmetric Macdonald polynomials -joint with Sami Assaf Journal of Combinatorial Theory-Series A Vol 182 (2021)
Categorical Bernstein Operators and the Boson-Fermion correspondence , Selecta Mathematica 26, Article number: 51 (2020) -
Crystal graphs, key tabloids, and nonsymmetric Macdonald polynomials, Séminaire Lotharingien de Combinatoire, 80B (2018) Article #81, 12pp.- joint with Sami Assaf.

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