Michael K. Brown

Associate Professor at Auburn University

CV

Office: Govil Hall 2132

Email: mkb0096 at auburn dot edu

Auburn Algebra Seminar

Research interests: commutative algebra and algebraic geometry.

Notes for the Oberwolfach Arbeitsgemeinschaft "New Homological Methods in Toric Geometry" (co-organized with David Eisenbud and Daniel Erman) can be found here.

Current research funding:

  • NSF DMS-2412042: Collaborative Research: FRGMS: Multigraded Commutative Algebra, Toric Varieties, and Homological Mirror Symmetry

    • Preprints:

  • Derived complete intersections and polynomial growth of Betti numbers over dg-algebras (with Justin Lyle).

  • Computing weighted sheaf cohomology using noncommutative differential modules (with Daniel Erman).

  • Existence of balanced dualizing dg-modules (with Andrew J. Soto Levins and Prashanth Sridhar).

  • King's Conjecture and the Cox category (with M. R. Ballard, C. Berkesch, L. Cranton Heller, D. Erman, D. Favero, S. Ganatra, A. Hanlon, and J. Huang).

    • Published and accepted papers:

  • Computing global Ext for complexes (with Souvik Dey, Guanyu Li, and Mahrud Sayrafi), Journal of Pure and Applied Algebra 230(11) (2026), 108365.

  • Serre duality for dg-algebras (with Prashanth Sridhar), Bulletin of the London Mathematical Society 58(1) (2026), e70174.

  • Ranks of matrix factorizations and sheaf cohomology (with Mark E. Walker), Proceedings of the AMS 153(8) (2025), 3291-3301.

  • The Hodge structure on the singularity category of a complex hypersurface (with Mark E. Walker), Annals of K-theory 10(2) (2025), 237-277.

  • Orlov's Theorem for dg-algebras (with Prashanth Sridhar), Advances in Mathematics 460 (2025), 110035.

  • Dévissage for periodic cyclic homology of complete intersections (with Mark E. Walker), Annals of K-theory 9(2) (2024), 341-367.

  • Periodicity of ideals of minors in free resolutions (with Hailong Dao and Prashanth Sridhar), Journal of Algebra 677 (2025), 180-214.

  • A short proof of the Hanlon-Hicks-Lazarev Theorem (with Daniel Erman), Forum of Mathematics, Sigma (2024), Vol. 12:e56 1-6.

  • Positivity and nonstandard graded Betti numbers (with Daniel Erman), Bulletin of the London Mathematical Society 56(1) (2024), 111-123.

  • Linear syzygies of curves in weighted projective space (with Daniel Erman), Compositio Mathematica, 161 (2025), 916-944.

  • Idempotent completions of equivariant matrix factorization categories (with Mark E. Walker), Journal of Algebra 634 (2023), 554-562.

  • A short resolution of the diagonal for smooth projective toric varieties of Picard rank 2 (with Mahrud Sayrafi), Algebra & Number Theory 18-10 (2024), 1923-1943.

  • Linear strands of multigraded free resolutions (with Daniel Erman), Mathematische Annalen 390 (2024), 2707-2725.

  • Tate resolutions on toric varieties (with Daniel Erman), Journal of the European Mathematical Society, 28 (2026), no. 1, 269-304.

  • Minimal free resolutions of differential modules (with Daniel Erman), Transactions of the AMS 375(10) (2022), 7509-7528.

  • A proof of a conjecture of Shklyarov (with Mark E. Walker), Journal of Noncommutative Geometry 16(4) (2022), 1479-1523.

  • Standard Conjecture D for matrix factorizations (with Mark E. Walker), Advances in Mathematics 366 (2020), 107092.

  • On the topological K-theory of twisted equivariant perfect complexes (with Tasos Moulinos), Homology, Homotopy and Applications 25(1) (2023), 173-187.

  • A Chern-Weil formula for the Chern character of a perfect curved module (with Mark E. Walker), Journal of Noncommutative Geometry 14(2) (2020), 709-772.

  • Topological K-theory of equivariant singularity categories (with Tobias Dyckerhoff), Homology, Homotopy and Applications 22(2) (2020), 1-29.

  • Adams operations on matrix factorizations (with Claudia Miller, Peder Thompson, and Mark E. Walker), Algebra & Number Theory 11-9 (2017), 2165-2192.

  • On a conjecture of Dao-Kurano, Journal of Algebra 490 (2017), 462-473.

  • Cyclic Adams operations (with Claudia Miller, Peder Thompson, and Mark E. Walker), Journal of Pure and Applied Algebra 221 (2017), no. 7, 1589-1613.

  • Knörrer periodicity and Bott periodicity, Documenta Mathematica 21 (2016), 1459-1501.

    • Software:

  • Orlov's functors in Macaulay2 (with Souvik Dey, Geoffrey Fatin, Guanyu Li, Mahrud Sayrafi, and Tim Tribone).

  • The multigraded BGG correspondence in Macaulay2 (with Maya Banks, Tara Gomes, Prashanth Sridhar, Eduardo Torres Davila, and Sasha Zotine), Journal of Software for Algebra and Geometry 15-1 (2025), 57--68.

  • Computing Schur complexes (with Hang Huang, Robert P. Laudone, Michael Perlman, Claudiu Raicu, Steven V Sam, and João P. Santos), Journal of Software for Algebra and Geometry 9-2 (2019), 111--119.