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 (specifically those arising from the representation theory of finite-dimensional Hopf algebras) via tensor triangular geometry and cohomological support varieties.

Publications and CV:

  • CV (last updated October 2022).
  • (Joint with Hongdi Huang, Van C. Nguyen, Charlotte Ure, Padmini Veerapen, and Xingting Wang) Twisting Manin's universal quantum groups and comodule algebras. Preprint. arXiv.
  • (Joint with Daniel K. Nakano and Milen Yakimov) On the spectrum and support theory of a finite tensor category. Preprint. arXiv.
  • (Joint with Hongdi Huang, Van C. Nguyen, Charlotte Ure, Padmini Veerapen, and Xingting Wang) A cogroupoid associated to preregular forms. Preprint. 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 Transformation Groups. arXiv.
  • Balmer spectra and Drinfeld centers. Preprint. arXiv.
  • (Joint with Daniel K. Nakano and Milen Yakimov) Noncommutative tensor triangular geometry and the tensor product property for support maps. Accepted for publication in the International Mathematics Research Notices. arXiv.
  • (Joint with Daniel K. Nakano and Milen Yakimov) Noncommutative tensor triangular geometry. Accepted for publication in the American Journal of Mathematics. arXiv.
  • (Joint with Milen Yakimov) Prime spectra of abelian 2-categories and categorifications of Richardson varieties. In "Representations and Nilpotent Orbits of Lie Algebraic Systems, in honour of the 75th birthday of Tony Joseph", Progr. in Math. vol. 330, eds. M. Gorelik et al, pp. 501-553, Birkhäuser, 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 the study of dual reflection groups, which arise in the search for a noncommutative analogue of the classical Shephard-Todd-Chevalley Theorem.

mail: kentv@mit.edu

Activities

Awards

Teaching and Seminars

  • 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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