James Hotchkiss
James Hotchkiss
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I am an NSF postdoc / Ritt Assistant Professor at Columbia University, working in algebraic geometry. In Spring 2024, I was at a postdoc at MSRI. Previously, I was a graduate student at the University of Michigan, where my advisor was Alex Perry.
My research interests include Hodge theory, derived categories, and Brauer groups.
With Yoonjoo Kim and Giulia Saccà, I co-organize the algebraic geometry seminar at Columbia.
My work is supported by NSF DMS-2401818.
Aaron Fagerstrom for SLMath
Papers
Papers
Complexes of stable birational invariants (with David Stapleton). Submitted.
The period-index problem for hyper-Kähler varieties via hyperholomorphic bundles (with Davesh Maulik, Junliang Shen, Qizheng Yin, and Ruxuan Zhang). Submitted.
The period-index conjecture for abelian threefolds and Donaldson–Thomas theory (with Alex Perry). Submitted.
On decompositions for Fano schemes of intersections of two quadrics (with Pieter Belmans, Jishnu Bose, Sarah Frei, Benjamin Gould, Alicia Lamarche, Jack Petok, Cristian Rodriguez Avila, Saket Shah). Advances, to appear.
Hodge theory of twisted derived categories and the period-index problem. Submitted.
The gonality of complete intersection curves (with C. Lau and B. Ullery). Journal of Algebra.
Upcoming:
Upcoming:
Moduli spaces, virtual invariants and shifted symplectic structures, KIAS, June 15 – 20
I'm an online mentor for the grad / postdoc bootcamp at the Algebraic Geometry Summer Research Institute, July 8 – 15.
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