Linquan Ma

ma326@purdue.edu
Office: Math 740
Office Phone: 765 49-41956

I am an Assistant Professor at Purdue University. Before coming to Purdue I was a Research Assistant Professor at University of Utah. I obtained my Ph.D in May 2014 at the University of Michigan under the direction of Melvin Hochster. My research interests are in commutative algebra and algebraic geometry.


Curriculum Vitae

My CV is here.

Papers and Preprints

  1. Lim Cohen-Macaulay sequences of modules (with Bhargav Bhatt and Melvin Hochster), in preparation.
  2. Regularity, singularities and h-vector of graded algebras (with Hailong Dao and Matteo Varbaro), submitted.
  3. Recent applications of p-adic methods to commutative algebra (with Karl Schwede), Notices Amer. Math. Soc., to appear.
  4. A Kunz-type characterization of regular rings via alterations (with Karl Schwede), submitted.
  5. F-signature under birational morphisms (with Thomas Polstra, Karl Schwede and Kevin Tucker), Forum Math. Sigma, to appear.
  6. Lech's inequality, the Stuckrad-Vogel conjecture, and uniform behavior of Koszul homology (with Patricia Klein, Pham Hung Quy, Ilya Smirnov and Yongwei Yao), Adv. Math., 347 (2019), 442-472. (Oberwolfach report)
  7. Singularities in mixed characteristic via perfectoid big Cohen-Macaulay algebras (with Karl Schwede), submitted.
  8. Cohomologically full rings (with Hailong Dao and Alessandro De Stefani), submitted.
  9. Regular rings and perfect(oid) algebras (with Bhargav Bhatt and Srikanth Iyengar), Comm. Algebra (special issue dedicated to Gennady Lyubeznik), to appear.
  10. Maximal Cohen-Macaulay modules over certain Segre products, Comm. Algebra (special issue dedicated to Gennady Lyubeznik), to appear.
  11. Extended plus closure in complete local rings (with Raymond Heitmann), J. Algebra (special issue dedicated to Craig Huneke), to appear.
  12. Perfectoid multiplier/test ideals in regular rings and bounds on symbolic powers (with Karl Schwede), Invent. Math. 214 (2018), no. 2, 913-955.
  13. Big Cohen-Macaulay algebras and the vanishing conjecture for maps of Tor in mixed characteristic (with Raymond Heitmann), Algebra Number Theory 12 (2018), no. 7, 1659-1674.
  14. D-module and F-module length of local cohomology modules (with Mordechai Katzman, Ilya Smirnov and Wenliang Zhang), Trans. Amer. Math. Soc. 370 (2018), no. 12, 8551-8580.
  15. F-singularities under generic linkage (with Janet Page, Rebecca R.G., William Taylor and Wenliang Zhang), J. Algebra 505 (2018), 194-210.
  16. Frobenius actions on local cohomology modules and deformation (with Pham Hung Quy), Nagoya Math. J. 232 (2018), 55-75.
  17. The dualizing complex of F-injective and Du Bois singularities (with Bhargav Bhatt and Karl Schwede), Math. Z. 288 (2018), no. 3-4, 1143-1155.
  18. The vanishing conjecture for maps of Tor and derived splinters, J. Eur. Math. Soc. 20 (2018), no. 2, 315-338.
  19. Lech's conjecture in dimension three, Adv. Math. 322 (2017), 940-970. (Oberwolfach report)
  20. Local cohomology of Du Bois singularities and applications to families (with Karl Schwede and Kazuma Shimomoto), Compos. Math. 153 (2017), no. 10, 2147-2170.
  21. F-injectivity and Buchsbaum singularities, Math. Ann. 362 (2015), no. 1-2, 25-42.
  22. Eulerian graded D-modules (with Wenliang Zhang), Math. Res. Lett. 21 (2014), no. 1, 149-167.
  23. A sufficient condition for F-purity, J. Pure Appl. Algebra 218 (2014), 1179-1183.
  24. The category of F-modules has finite global dimension, J. Algebra 402 (2014), 1-20.
  25. Finiteness properties of local cohomology for F-pure local rings, Int. Math. Res. Not. (2014), no. 20, 5489-5509.
  26. The Frobenius endomorphism and multiplicities, Thesis, University of Michigan (2014).

Teaching

At Purdue University: At University of Utah: At University of Michigan:

Miscellaneous

I have been doing some very fun Crosstalks with my friends. Check our performances if you are interested!