Alexander Perry Assistant Professor Department of Mathematics University of Michigan Email: arper@umich.edu Office: 4846 East Hall

I work in algebraic geometry, with a focus on derived categories and their relations to more classical topics, like birational geometry and Hodge theory.

Curriculum vitae

Upcoming events I am co-organizing

• Bootcamp for the Summer Research Institute in Algebraic Geometry, July 2025.
• Hyperkähler varieties and derived categories, session for the Summer Research Institute in Algebraic Geometry, July 2025.

Seminars

• Algebraic Geometry Seminar

Papers

• The period-index conjecture for abelian threefolds and Donaldson-Thomas theory (with J. Hotchkiss). Preprint.
• Stability conditions on crepant resolutions of quotients of product varieties (with S. Shah). Preprint.
• Derived categories of quartic double fivefolds (with R. Cheng and X. Zhao). Preprint.
• Moduli spaces of stable objects in Enriques categories (with L. Pertusi and X. Zhao). Preprint.
• The period-index problem and Hodge theory (with A.J. de Jong). Preprint.
• Kuznetsov's Fano threefold conjecture via K3 categories and enhanced group actions (with A. Bayer). J. Reine Angew. Math. 800 (2023), 107-153.
• Serre functors and dimensions of residual categories (with A. Kuznetsov). Preprint.
• The integral Hodge conjecture for two-dimensional Calabi-Yau categories. Compos. Math. 158 (2022), no. 2, 287-333.
• Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties (with L. Pertusi and X. Zhao). Geom. Topol. 26 (2022), no. 7, 3055-3121.
• Stability conditions in families (with A. Bayer, M. Lahoz, E. Macrì, H. Nuer, and P. Stellari). Publ. Math. Inst. Hautes Études Sci. 133 (2021), 157-325.
• Homological projective duality for quadrics (with A. Kuznetsov). J. Algebraic Geom. 30 (2021), no. 3, 457-476.
• Categorical cones and quadratic homological projective duality (with A. Kuznetsov). Ann. Sci. Éc. Norm. Supér. (4) 56 (2023), no. 1, 1-57.
• Categorical joins (with A. Kuznetsov). J. Amer. Math. Soc. 34 (2021), no. 2, 505-564.
• Noncommutative homological projective duality. Adv. Math. 350 (2019), 877-972.
• Hochschild cohomology and group actions. Math. Z. 297 (2021), no. 3-4, 1273-1292.
• Intersections of two Grassmannians in P⁹ (with L. Borisov and A. Căldăraru). J. Reine Angew. Math. 760 (2020), 133-162.
• Rationality does not specialize among terminal fourfolds. Algebra Number Theory 11 (2017), no. 9, 2193-2196.
• Derived categories of Gushel-Mukai varieties (with A. Kuznetsov). Compos. Math. 154 (2018), no. 7, 1362-1406.
• Rational points on twisted K3 surfaces and derived equivalences (with K. Ascher, K. Dasaratha, and R. Zhou). Brauer Groups and Obstruction Problems, Progr. Math. 320 (2017), 13-28.
• Derived categories of cyclic covers and their branch divisors (with A. Kuznetsov). Selecta Math. (N.S.) 23 (2017), no. 1, 389-423.
• Faithfully flat descent for projectivity of modules. Preprint. Version also available at the Stacks Project.
• Resolving toric varieties with Nash blowups (with A. Atanasov, C. Lopez, N. Proudfoot, and M. Thaddeus). Exp. Math. 20 (2011), no. 3, 288-303.
• A conjecture of Evans on sums of Kloosterman sums (with E. Dummit and A. Goldberg). Proc. Amer. Math. Soc. 138 (2010), no. 9, 3047-3056.

Other writing

• Serre functors of semiorthogonal components. Zoom Algebraic Geometry (ZAG) Seminar report (2024).
• The period-index problem. Oberwolfach report (2023).
• Intersections of two Grassmannians in P⁹. Oberwolfach report (2017).
• Derived categories of Gushel-Mukai varieties. Oberwolfach report (2016).
• Formal deformation theory (modified version of my writeup). Chapter for the Stacks Project.
• Keeping a Problem List. Notices of the AMS, Early Career Collection (2021).

Teaching

• Algebraic Topology (Winter 2023)
• Algebraic Geometry I (Fall 2021)
• Bridgeland stability (Winter 2021)