Michael K. Brown

I am an Assistant Professor at Auburn University.

CV

Office: Parker Hall 235

Email: mkb0096 at auburn dot edu

Auburn Algebra Seminar

My research is supported by NSF award DMS-2302373.

Publications/preprints:

  • The Hodge structure on the singularity category of a complex hypersurface (with Mark E. Walker).

  • Orlov's Theorem for dg-algebras (with Prashanth Sridhar).

  • Dévissage for periodic cyclic homology of complete intersections (with Mark E. Walker), to appear in Annals of K-theory.

  • Periodicity of ideals of minors in free resolutions (with Hailong Dao and Prashanth Sridhar).

  • 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).

  • 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), to appear in Algebra & Number Theory.

  • Linear strands of multigraded free resolutions (with Daniel Erman), Mathematische Annalen, published online (2024).

  • Tate resolutions on toric varieties (with Daniel Erman), Journal of the European Mathematical Society, published online (2024).

  • 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:

  • The multigraded BGG correspondence in Macaulay2 (with Maya Banks, Tara Gomes, Prashanth Sridhar, Eduardo Torres Davila, and Alexandre Zotine).

  • 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.