Welcome! I am currently a Hedrick postdoc at UCLA. From 2021 to 2024, I was an NSF postdoc and instructor at MIT. I completed my PhD in August 2021 at Louisiana State University. My primary advisor was Milen T. Yakimov, and my secondary advisor was Daniel K. Nakano. Before that, I did my Master's degree at Wake Forest University under the supervision of Ellen Kirkman.

My research interests broadly are at the intersection of homological algebra, noncommutative algebra, and representation theory. One of the primary focuses of my work has been studying monoidal triangulated categories (especially those arising from the representation theory of finite-dimensional Hopf algebras) via tensor triangular geometry and cohomological support varieties. I am also interested in universal quantum groups (in the sense of Manin), Artin-Schelter regular algebras, noncommutative invariant theory, and semisimplifications of tensor categories of finite group schemes.

CV (last updated October 2024).

Publications and preprints:

1. (Joint with Peter Goetz, Ellen Kirkman, and W. Frank Moore) Some Artin-Schelter regular algebras from dual reflection groups and their geometry.
• arXiv.
2. (Joint with Merrick Cai) Formal extension of noncommutative tensor-triangular support varieties.
• arXiv.
3. (Joint with Hongdi Huang, Van C. Nguyen, Padmini Veerapen, and Xingting Wang) Quantum-symmetric equivalence is a graded Morita invariant.
• Accepted for publication in Proc. Amer. Math. Soc.
• arXiv.
4. (Joint with Hongdi Huang) Group actions on monoidal triangulated categories and Balmer spectra.
• arXiv.
5. (Joint with Daniel K. Nakano and Milen T. Yakimov) A Chinese remainder theorem and Carlson's theorem for monoidal triangulated categories.
• arXiv.
6. (Joint with George Cao) On the decomposition of tensor products of monomial modules for finite 2-groups.
• arXiv.
7. (Joint with Hongdi Huang, Van C. Nguyen, Charlotte Ure, Padmini Veerapen, and Xingting Wang) Twisting Manin's universal quantum groups and comodule algebras.
• Adv. Math. 445 (2024), Paper No. 109651.
• arXiv.
8. (Joint with Daniel K. Nakano and Milen T. Yakimov) On the spectrum and support theory of a finite tensor category.
• Math. Ann. 390 (2024), no. 1, 205–254.
• arXiv.
9. (Joint with Hongdi Huang, Van C. Nguyen, Charlotte Ure, Padmini Veerapen, and Xingting Wang) A cogroupoid associated to preregular forms.
• J. Noncommut. Geom. 18 (2024), no. 4, 1453–1483.
• arXiv.
10. (Joint with Hongdi Huang, Van C. Nguyen, Charlotte Ure, Padmini Veerapen, and Xingting Wang) Twisting of graded quantum groups and solutions to the quantum Yang-Baxter equation.
• Accepted for publication in Transform. Groups, DOI:10.1007/s00031-022-09779-9.
• arXiv.
11. Balmer spectra and Drinfeld centers.
• Algebra Number Theory 18 (2024), no. 6, 1081–1116.
• arXiv.
12. (Joint with Daniel K. Nakano and Milen T. Yakimov) Noncommutative tensor triangular geometry and the tensor product property for support maps.
• Int. Math. Res. Not. IMRN (2022), no. 22, 17766–17796.
• arXiv.
13. (Joint with Daniel K. Nakano and Milen T. Yakimov) Noncommutative tensor triangular geometry.
• Amer. J. Math. 144 (2022), no. 6, 1681-1724.
• arXiv.
14. (Joint with Milen Yakimov) Prime spectra of abelian 2-categories and categorifications of Richardson varieties.
• Representations and nilpotent orbits of Lie algebraic systems, 501–553, Progr. Math., 330, Birkhäuser/Springer, Cham, 2019.
• arXiv.

mail: kentvashaw@math.ucla.edu

• 2025 Joint Math Meetings, Special Session on Homological Interactions Between Commutative and Noncommutative Algebra, January 8-11, 2025 (invited talk) (expected).
• 2025 Joint Math Meetings, Special Session on New Developments in Noncommutative Algebra, January 8-11, 2025 (invited talk) (expected).
• BIRS Workshop on Poisson Geometry and Artin-Schelter Regular Algebras, October 13-18, 2024 (expected).
• AIM Workshop on Finite tensor categories: their cohomology and geometry, September 16-20, 2024.
• 2024 Fall Central Sectional Meeting of the AMS, Special Session on Homological and Combinatorial Methods in Noncommutative Algebra, September 14-15, 2024 (invited talk).
• Texas A&M University Geometry Seminar, September 9, 2024.
• 2024 Summer Research in Mathematics Program at SLMath on Quantum symmetries: noncommutative geometry and invariant theory (focused collaborative research workshop with Hongdi Huang, Van Nguyen, Padmini Veerapen, and Xingting Wang), July 1-12, 2024.
• AIM SQuaRE on Quantum symmetries: Noncommutative geometry and solutions to the QYBE (focused collaborative research workshop with Hongdi Huang, Van Nguyen, Charlotte Ure, Padmini Veerapen, and Xingting Wang), June 24-28, 2024.
• New Directions in Group Theory and Triangulated Categories Seminar, June 6, 2024 (invited talk).
• Representation Theory and Related Geometry: Progress and Prospects, on the occasion of Daniel K. Nakano's 60th birthday, May 27-31, 2024 (invited talk).
• 2024 Spring Western Sectional Meeting of the AMS, Special Session on Commutative and Noncommutative Algebra, Together at Last, May 4-5, 2024 (invited talk).
• SLMath Workshop: Advances in Lie Theory, Representation Theory, and Combinatorics: Inspired by the work of Georgia M. Benkart, May 1-3, 2024.
• University of Iowa Algebra Seminar, April 17, 2024 (invited talk).
• University of Michigan Representation Stability Seminar, April 10, 2024 (invited talk).
• 2024 Spring Eastern Sectional Meeting of the AMS, Special Session on Recent Developments in Noncommutative Algebra and Tensor Categories, April 6-7, 2024 (organizing, jointly with Van Nguyen, Xingting Wang, and Robert Won).
• University of Georgia Algebra Seminar, March 25, 2024 (invited talk).
• Quantum Groups Seminar, February 12, 2024 (invited talk).
• Introductory Workshop on Noncommutative Algebraic Geometry at SLMath, February 5-9, 2024.
• IPAM Workshop on Symmetric Tensor Categories and Representation Theory, January 8-12, 2024.
• 2024 Joint Math Meetings, Special Session on Homological Techniques in Noncommutative Algebra, January 3-6, 2024 (invited talk).
• Mentoring in the Mathematical Sciences Workshop at Rice University, November 4-5, 2023.
• 2023 Fall Southeastern Sectional Meeting of the AMS, Special Session on New Directions in Noncommutative Algebras and Representation Theory, October 13-15, 2023 (invited talk).
• 2023 Fall Southeastern Sectional Meeting of the AMS, Special Session on Representation Theory of Finite and Algebraic Groups, October 13-15, 2023 (invited talk).
• Oberwolfach workshop on Tensor-Triangular Geometry and Interactions, September 17-22, 2023.
• 2023 Fall Eastern Sectional Meeting of the AMS, Special Session on Geometry, Physics and Representation Theory, September 9-10, 2023 (invited talk).
• 2023 CMS Summer Meeting, Session on Noncommutative Algebra and Noncommutative Geometry, June 2-5, 2023 (invited talk).
• Instantons and foams, May 17-19, 2023.
• 2023 Spring Western Sectional Meeting of the AMS, Special Session on Artin-Schelter Regular Algebras and Related Topics, May 6-7, 2023 (invited talk).
• 2023 Spring Western Sectional Meeting of the AMS, Special Session on Methods in Non-semisimple Representation Categories, May 6-7, 2023 (invited talk).
• Maurice Auslander Distinguished Lectures and International Conference, May 1, 2023.
• 2023 Spring Central Sectional Meeting of the AMS, Special Session on Interactions Between Noncommutative Ring Theory and Algebraic Geometry, April 15, 2023 (invited talk).
• AIM SQuaRE on Quantum symmetries: Noncommutative geometry and solutions to the QYBE (focused collaborative research workshop with Hongdi Huang, Van Nguyen, Charlotte Ure, Padmini Veerapen, and Xingting Wang), April 3-7, 2023.
• Rice AGNT Seminar, March 1, 2023.
• Trimester Program on Spectral Methods in Algebra, Geometry, and Topology at the Hausdorff Center in Bonn , November 27 - December 16, 2022.
• Maurice Auslander Distinguished Lectures and International Conference, October 26, 2022 (invited talk).
• BIRS Workshop on Noncommutative Geometry and Noncommutative Invariant Theory, September 25-30, 2022.
• Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry, June 20-24, 2022.
• Fourth Canada-Mexico-USA Conference in Representation Theory, Noncommutative Algebra, and Categorification, June 9-12, 2022 (invited talk).
• International Workshop at the Atlantic Algebra Centre on Groups, Rings, Lie and Hopf Algebras IV, May 30-June 2, 2022 (invited talk).
• AIM SQuaRE on Quantum symmetries: Noncommutative geometry and solutions to the QYBE (focused collaborative research workshop with Hongdi Huang, Van Nguyen, Charlotte Ure, Padmini Veerapen, and Xingting Wang), March 28-April 1, 2022.
• Seattle Noncommutative Algebra Day (invited talk), March 26, 2022.
• 2021 Fall Southeastern Sectional Meeting of the AMS, Special Session on Cohomology, Representation Theory, and Lie Theory, November 20, 2021 (invited talk).
• MIT Infinite Dimensional Algebra Seminar (invited talk), November 19, 2021.
• University of Georgia Algebra Seminar, October 25, 2021 (invited talk).
• FD Seminar, July 8, 2021 (invited talk).
• Northeastern University Representation Theory and Related Topics Seminar , May 14, 2021 (invited talk).
• The UCSB Quantum Algebra and Topology Seminar , May 12, 2021 (invited talk).
• Oberseminar in Representation Theory in Bonn, April 30, 2021 (invited talk).
• 2021 Spring Central Sectional Meeting of the AMS, Special Session on Interactions between Representation Theory, Poisson Geometry, and Noncommutative Algebra , April 17, 2021 (invited talk).
• 2021 Spring Eastern Sectional Meeting of the AMS, Special Session on Hopf Algebras, Tensor Categories, and Related Homological Methods , March 20, 2021 (invited talk).
• 2021 Joint Math Meetings, Special Session on Interactions between Noncommutative Algebra and Noncommutative Algebraic Geometry , January 9, 2021 (invited talk).
• 2020 Fall Western Sectional Meeting of the AMS, Special Session on Geometry and Representation Theory of Quantum Algebras and Related Topics , October 25, 2020 (invited talk).
• Louisiana State University Algebra Seminar, February 11, 2020.
• MSRI Quantum Symmetries Introductory Workshop , January 27-January 31, 2020.
• Seminario Itinerante CCMUNAM-CIMAT-IMUNAM de Teoría de Representaciones , December 8-9, 2019 (invited talk).
• 2019 Fall Western Sectional Meeting of the AMS, Special Session on Canonical Bases, Cluster Structures and Non-commutative Birational Geometry , November 9-10, 2019 (invited talk).
• 2019 Fall Western Sectional Meeting of the AMS, Special Session on Geometric Methods in Representation Theory , November 9-10, 2019 (invited talk).
• Quantum Flag Manifolds in Prague , September 16-20, 2019 (invited talk).
• 2019 Fall Central Sectional Meeting of the AMS, Special Session on Hall Algebras, Cluster Algebras and Representation Theory , September 14-15, 2019 (invited talk).
• 2019 Fall Central Sectional Meeting of the AMS, Special Session on Connections Between Noncommutative Algebra and Algebraic Geometry , September 14-15, 2019 (invited talk).
• International Conference on Representation Theory VIII , July 7-13, 2019 (invited talk).
• OSU Quantum Symmetries Summer Research Program , June 3-14, 2019.
• 11th Southeastern Lie Theory Workshop , May 13-15, 2019 (contributed talk).
• 2019 Spring Eastern Sectional Meeting of the AMS, Special Session on Representation Theory of Quantum Algebras and Related Topics , April 13-14, 2019 (invited talk).
• University of California Santa Barbara, Algebra Seminar, April 1, 2019.
• 2019 Spring Southeastern Sectional Meeting of the AMS, Special Session on Representations of Lie Algebras, Algebraic Groups, and Quantum Groups , March 15-16, 2019 (invited talk).
• University of Georgia, Algebra Seminar, October 22, 2018.
• MSRI Derived Categories summer school, June 25-July 6, 2018.
• Representation Theory, Mathematical Physics and Integrable Systems, June 4-June 8, 2018 (poster presentation).
• 2018 Spring Western Sectional Meeting of the AMS, Special Session on Noncommutative Algebraic Geometry and Related Topics, April 14-15, 2018 (invited talk).
• Recent developements in noncommutative algebra and related areas, March 17-19, 2018 (short presentation).
• 2017 Fall Central Sectional Meeting of the AMS, Special Session on Noncommutative and Homological Algebra, September 9-10, 2017 (invited talk).
• Algebra Extravaganza! in honor of Ellen Kirkman and Martin Lorenz, July 24-28, 2017 (poster presentation).
• Fourth Conference on Geometric Methods in Representation Theory, November 19-21, 2016 (invited talk).
• 8th Southeastern Lie Theory Workshop, October 9-11, 2015.

• AMS-Simons Travel Grant, awarded Summer 2024.
• Summer Research in Mathematics Program at SLMath on Quantum symmetries: noncommutative geometry and invariant theory, joint with Hongdi Huang, Van Nguyen, Padmini Veerapen, and Xingting Wang, awarded Fall 2023.
• Lusztig PRIMES mentorship for 2023, MIT PRIMES-USA, awarded Fall 2022.
• American Instiute of Mathematics SQuaRE on Quantum symmetries: Noncommutative geometry and solutions to the QYBE, joint with Hongdi Huang, Van Nguyen, Charlotte Ure, Padmini Veerapen, and Xingting Wang, awarded Spring 2022.
• College of Science Distinguished Dissertation Award, Louisiana State University, Spring 2022.
• NSF Mathematical Sciences Postdoctoral Research Fellowship, beginning Fall 2021.
• Arthur K. Barton Superior Graduate Student Scholarship in Mathematics, Louisiana State University, Fall 2020.
• Pasquale Porcelli Graduate Student Research Excellence Award, Louisiana State University Mathematics Department, Fall 2020.
• Pasquale Porcelli Award for Graduate Academic Excellence, Louisiana State University Mathematics Department, Spring 2017.
• Board of Regents Fellowship, Louisiana State University, Fall 2016-Spring 2020.

Some videos of talks I have given can be found here:

• A Chinese remainder theorem and Carlson's theorem for monoidal triangulated categories, IPAM Workshop on Symmetric Tensor Categories and Representation Theory, Los Angeles, CA, January 9, 2024.
• Noncommutative algebra via tensor categories, Oberwolfach Workshop on Tensor-Triangular Geometry and Applications, Oberwolfach, DE, September 20, 2023.
• On the spectrum and support theory of a finite tensor category, Trimester Program on Spectral Methods in Algebra, Geometry, and Topology, The Hausdorff Center for Mathematics, Bonn, DE, December 8, 2022.
• A cogroupoid associated to preregular forms, Workshop on Noncommutative Geometry and Noncommutative Invariant Theory at the Banff International Research Station, Banff, CA, September 27, 2022.
• Can a Zhang twist be a cocycle twist?, University of Georgia Algebra Seminar, online, October 25, 2021.

• Instructor of Record, Math 32A Calculus of Several Variables, UCLA, Fall 2024.
• Instructor of Record, Math 18.700 Linear Algebra, MIT, Fall 2023.
• Teaching Assistant, Math 18.02 Multivariable Calculus, MIT, Fall 2023.
• Co-instructor (joint with Thomas Rud and Theo McKenzie), Bridge to College Math, MCI-Framingham Correctional Facility. Responsible for writing lesson plans, lectures, worksheets, and giving lectures on material meant to prepare incarcerated people to pursue college degrees post-release. This course was jointly organized by the Petey Greene Program, the MIT Math Deparment, and the MIT Educational Justice Institute. More information here.
• Teaching Assistant, Math 18.06 Linear Algebra, MIT, Spring 2023.
• Instructor of Record, Math 18.704 Seminar in Algebra, MIT, Fall 2022. Course website.
• Instructor, Math 18.708 Topics in Algebra, mini-course on support varieties and tensor triangular geometry, MIT, Spring 2022. Course website.
• Co-organizer (joint with Pavel Etingof), Seminar on strict polynomial functors and the work of Friedlander-Suslin, Summer and Fall 2021. Seminar website.
• Instructor of Record, Louisiana State University, Summer 2021: Calculus III (online).
• Instructor of Record, Louisiana State University, Fall 2018: Calculus I.
• Teaching Assistant, Wake Forest University, Fall 2014-Spring 2016: Calculus I, Calculus II, Linear Algebra I, Discrete Mathematics.