Nicolle González

nicolles [at] berkeley [dot] edu



Office:  Evans 857

Address:   Mathematics Department    

                       970 Evans Hall, UC Berkeley

     Berkeley , CA 94720-3840


I am organizing various seminars and conferences at the moment, please see the details below. 


I am currently at UC Berkeley as Charles B. Morrey Visiting Assistant Professor working with Sylvie Corteel. 

Prior to this I was a Presidential Postdoctoral Fellow at UCLA under the mentorship of Raphaël  Rouquier and a Berlekamp Postdoctoral Fellow at MSRI 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 representation theory and algebraic combinatorics, with applications to diagrammatic categorification and low dimensional topology.  Some of my current research directions include understanding the categorical, combinatorial, and skein theoretic structures that arise in connection to Macdonald polynomials,  Khovanov-Rozansky homology, and the double Dyck path algebra. I am also interested in Demazure crystals and connections to nonsymmetric Macdonald polynomials.

Published Papers and Pre-Prints 

  1. Calibrated representations of the double Dyck path algebra-  with E. Gorsky and J. Simental. https://arxiv.org/pdf/2311.17653.pdf
  2. Triangular (q,t)-Schröder Polynomials and Khovanov-Rozansky Homology- with C. Caprau, M. Hogancamp, and M. Mazin (submitted) 
  3. Mesas of Stirling permutations - with P. Harris, G. Kirby, M. Vega, and B. Tenner - https://arxiv.org/abs/2306.12158
  4. 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 (to appear) - https://arxiv.org/abs/2303.15694
  5. 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
  6. Semi-standard parking functions and a finite Shuffle theorem - with J.  Simental and M. Vazirani , Séminaire Lotharingien de Combinatoire  89B (2023), Article #84
  7. Pinnacle sets of signed permutations - with P. Harris, G. Kirby, M. Vega, and B. Tenner - Discrete Math, Vol 346, Issue 7, July 2023,  
  8. Extremal tensor products of Demazure crystals - with S. Assaf and A. Dranowski - Algebras and Representation Theory (2023)
  9. 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 
  10. Affine Demazure crystals for specialized nonsymmetric Macdonald polynomials - joint with Sami Assaf, Algebraic Combinatorics, Volume 4 (2021) no. 5, pp. 777-793.
  11. Demazure Crystals for specialized nonsymmetric Macdonald polynomials -joint with Sami Assaf Journal of Combinatorial Theory-Series A Vol 182 (2021)   
  12. Categorical Bernstein 0perators and the Boson-Fermion correspondence ,  Selecta Mathematica 26, Article number: 51 (2020) -
  13.  Crystal graphs, key tabloids, and nonsymmetric Macdonald polynomials, Séminaire Lotharingien de Combinatoire, 80B (2018) Article #81, 12pp.- joint with Sami Assaf. 

Current Organizational Activities

I organize the UC Berkeley Combinatorics Research Seminar with John Leftner and Mitsuki Hanada. Updated schedule of talks is available here. 

In Fall 2025 will be organizing a semester on Categorification and Computation in Algebraic Combinatorics at ICERM alongside Chris Bowman, Nicolas Liebedinsky, Lauren Williams, Greta Panova, Rosa Orellana, Kyu-Hwan Lee, Jamie Vicary, Anna Schilling, and Adam Wagner. Information on how to participate is here.

Some Past Events:

In Fall 2023 I organized the combinatorics reading seminar at UC Berkeley on Quantum Groups and Crystal Graphs. Website is here. 

I organized an in person workshop on Algebra, geometry, and combinatorics of link homology at the American Institute of Math with Eugene Gorsky, Matt Hogancamp, Oscar Kivinen, and Alexei Oblomkov in Summer 2023.  Information is HERE.  Previously, we organized a related online research community. Recordings of that can be found here. 

Im Spring 2023 co-organized the combinatorics reading seminar at UC Berkeley alongside Chris Ryba on the Okounkov-Vershik approach to the representation theory of the symmetric group.  For the reading schedule, notes, and information click HERE. 

I organized a conference on Field theories and vertex algebras with Raphaël Rouquier on October  2-5th 2022. Website is HERE.

I organized a learning seminar on categorification with Ben Elias, Mikhail Khovanov and Melissa Zhang.  Previous recordings of the talks can be found HERE. 

I am co-organized a special session at the 2021 Mathematical Congress of the Americas focused on "Categorification, Higher Representation Theory, and Homological Link Invariants" with Matt Hogancamp and Karina Batistelli on July 19-24, 2021.

I co-organized the UC Riverside Diversity and Excellence Workshop focused on Women in Combinatorics and Representation Theory alongside Vyjayanthi Chari and Zajj Daugherty on May 15-16, 2021. For more information visit the website HERE. 

In Fall 2020 I co-organized the combinatorics reading seminar at UC Berkeley alongside Foster Tom and Sylvie Corteel on q,t-Catalan numbers, diagonal harmonics, and the combinatorics behind the Shuffle conjecture.  For the reading schedule, notes, videos, and information click HERE. 

Upcoming Schedule

(for upcoming talks click here)