Kimoi Kemboi

E-mail: firstname at princeton dot edu
Office: Fine Hall 1107

I am an Instructor in Mathematics at Princeton University. In Spring 2024, I was a postdoc fellow at MSRI, and in Fall 2023, I was a member at the IAS. Before that, I was a graduate student at Cornell University, advised by Daniel Halpern-Leistner.

My research is in algebraic geometry. I am interested in derived categories, geometric invariant theory, noncommutative geometry, and moduli theory.

research

Papers:

A looming of phantoms, joint with D. Krashen, T. Liu, Y. Liu, E. Mackall, S. Makarova, A. Perry, A. Robotis, S. Vankatesh.
We produce more examples of phantom categories on rational surfaces.

The Fano of lines, the Kuznetsov component, and a flop, joint with Ed Segal.
In this article, we prove Galkin's conjecture for cubic fourfolds.

Non-existence of phantoms on some non-generic blowups of the projective plane, joint with Lev Borisov, Proc. Amer. Math. Soc. 153 (2025) 963-968.
We show that phantoms do not appear in the derived category of the blowup of the projective plane at a finite number of points lying on a smooth cubic curve. We also posit a conjecture for an obstruction to the existence of phantoms on surfaces.

Full exceptional collections of vector bundles on rank-two linear GIT quotients, joint with Daniel Halpern-Leistner, Advances (to appear).
We produce a large class of linear GIT quotients by a reductive group of rank two that admit a “full strong exceptional collection” consisting of vector bundles using the methods of window categories.