Nicolle González

nicolle [at] math [dot] ucla [dot] edu

Office: MS 6304

Address: UCLA Mathematics Department

Box 951555

Los Angeles, CA 90095-1555

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

I am currently a postdoc at UCLA under the mentorship of Raphaël Rouquier.

In Fall 2022, I will be moving to UC Berkeley as Charles B. Morrey Visiting Assistant Professor.

Prior to this, I was the 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 diagrammatic categorification and algebraic combinatorics, intersecting higher representation theory and low dimensional topology. Some of my current research directions include understanding categorical structures of vertex operators as well as the categorical and skein theoretic structures that arise in connection to Macdonald polynomials, Khovanov-Rozansky homology, and the double Dyck path algebra.

Publications and Pre-Prints

1. Crystal graphs, key tabloids, and nonsymmetric Macdonald polynomials, Séminaire Lotharingien de Combinatoire, 80B (2018) Article #81, 12pp.- joint with Sami Assaf.
2. Categorical Bernstein 0perators and the Boson-Fermion correspondence , Selecta Mathematica 26, Article number: 51 (2020) -
3. Demazure Crystals for specialized nonsymmetric Macdonald polynomials -joint with Sami Assaf Journal of Combinatorial Theory-Series A Vol 182 (2021) -
4. Affine Demazure crystals for specialized nonsymmetric Macdonald polynomials - joint with Sami Assaf, with an appendix by S. Kumar Algebraic Combinatorics (to appear)
5. On Khovanov homology and related invariants - joint with C. Caprau, C. Lee, A. Lowrance, R. Sazdanovic, M. Zhang.
6. Soergel bimodules, skein theory, and the Carlsson-Mellit algebra - joint with M. Hogancamp (in preparation)

Current Organizational Activities

I am organizing an online research community on link homology at the American Institute of Math with Eugene Gorsky, Matt Hogancamp, Oscar Kivinen, and Alexei Oblomkov. Information is here.

I am currently organizing a learning seminar on categorification with Ben Elias, Mikhail Khovanov and Melissa Zhang. More information on how to participate and previous recordings of the talks can be found HERE.

I am co-organizing a conference on Algebra and QFT with Raphaël Rouquier and Noah White for Summer 2022 (?).

Some Past Events:

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)

  • Combinatorics Seminar, University of Southern California, September 1, 2021 (postponed due to Covid-19).

  • Special Session on Quantum Symmetries, VI Congreso Latinoamericano de Matemáticos, Montevideo, Uruguay, September 16, 2021.

  • Special Session of Virtual Lightning Talks , AWM We Speak! , September 24, 2021.

  • Combinatorics Seminar, University of Minnesota, October 15, 2021.

  • Combinatorics Seminar, UCLA, October 21, 2021.

  • Special Session on Tensor Categories and Applications, AMS Fall Western Sectional Meeting, October 24, 2021.

  • Foam Evaluation, ICERM, Nov 5 - 7, 2021

  • University Quantum Symmetries Lectures, online, November 11, 2021.

  • Chern-Simons and Other Topological Field Theories, MSRI, Nov 16-18, 2021.

  • Blackwell-Tapia, IPAM, Nov 19-20, 2021.

  • Special Session on Latinx in Combinatorics, JMM, Seattle, Jan 5-8, 2022.

  • Recent developments in link homology theories, SwissMAP Research Station, Les Diablerets, Switzerland, Jan 30 - Feb 4, 2022

  • Braids in Representation Theory and Algebraic Combinatorics , ICERM, Feb 14 – 18, 2022.

  • Open Problems in Algebraic Combinatorics, University of Minnesota, May 16-20, 2022

  • Higher Categories and Categorification - Summer 2022 Reunion, Cuernavaca, Mexico, May 30 - June 24, 2022.

  • Special Session on Representation Theory and Applications, Pacific Rim Mathematical Association Congress , Vancouver, Canada Dec. 5-10, 2021. (Postponed to 2022)