Kent Vashaw

About Me / Research

Me

I am an NSF Mathematical Science Research Postdoc and Instructor at MIT where my mentor is Pavel Etingof. 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.

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, and semisimplifications of tensor categories of finite group schemes.

CV (last updated December 2023).

Publications and preprints:

  • (Joint with Hongdi Huang) Group actions on monoidal triangulated categories and Balmer spectra.
  • (Joint with Daniel K. Nakano and Milen T. Yakimov) A Chinese remainder theorem and Carlson's theorem for monoidal triangulated categories.
  • (Joint with George Cao) On the decomposition of tensor products of monomial modules for finite 2-groups.
  • (Joint with Hongdi Huang, Van C. Nguyen, Charlotte Ure, Padmini Veerapen, and Xingting Wang) Twisting Manin's universal quantum groups and comodule algebras.
  • (Joint with Daniel K. Nakano and Milen T. Yakimov) On the spectrum and support theory of a finite tensor category.
    • Accepted for publication in Math. Ann.
    • arXiv.
  • (Joint with Hongdi Huang, Van C. Nguyen, Charlotte Ure, Padmini Veerapen, and Xingting Wang) A cogroupoid associated to preregular forms.
    • Accepted for publication in J. Noncommut. Geom.
    • arXiv.
  • (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.
    • arXiv.
  • Balmer spectra and Drinfeld centers.
    • Accepted for publication in Algebra Number Theory.
    • arXiv.
  • (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.
  • (Joint with Daniel K. Nakano and Milen T. Yakimov) Noncommutative tensor triangular geometry.
    • Amer. J. Math. 144 (2022), no. 6, 1681-1724.
    • arXiv.
  • (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.
I did my Master's degree at Wake Forest University under the supervision of Ellen Kirkman, and my Master's thesis was in the area of noncommutative invariant theory. In particular, it studied dual reflection groups, which arise in the search for a noncommutative analogue of the classical Shephard-Todd-Chevalley Theorem.

mail: kentv@mit.edu

Activities

Grants and Awards

Recorded Talks

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

Teaching and Seminars

  • 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.
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