Wenliang Zhang

Email: wlzhang at uic.edu

Address: UIC MSCS Department (M/C 249)

851 S. Morgan St.

Chicago, IL 60607-7045

Commutative Algebra Seminar at UIC

Algebraic Geometry Seminar at UIC

Workshop on D-modules and Hodge Theory

Papers (published or accepted):

35. On completion of graded D-modules (with N. Switala)

arXiv:1808.09035, Math. Res. Lett., accepted.

34. Stabilization of cohomology of thickenings (with B. Bhatt, M. Blickle, G. Lyubeznik, and A. Singh)

American Journal of Mathematics, 141 (2019), no. 2, 531--561.

33. Duality and de Rham cohomology for graded D-modules (with N. Switala)

Adv. Math. 340 (2018), 1141--1165.

32. Multiplicity bounds in prime characteristic (with M. Katzman)

Comm. Alg. (special issue in honor of Gennady Lyubeznik), to appear.

31. A dichotomy for the injective dimension of F-finite F-modules and holonomic D-modules (with N. Switala)

Comm. Alg. (special issue in honor of Gennady Lyubeznik), to appear.

30. F-singularities under generic linkage (with L. Ma, J. Page, R. Rebhuhn-Glanz, and W. Taylor)

Journal of Algebra, 505 (2018), 194--210.

29. F-singularities in families (with Z. Patakfalvi, and K. Schwede)

Algebr. Geom. 5 (2018), no. 3, 264--327.

28. The support of local cohomology modules (with M. Katzman)

Int. Math. Res. Not. IMRN 2018, no. 23, 7137--7155.

27. D-module and F-module length of local cohomology modules (with M. Katzman, L. Ma, and I. Smirnov)

Trans. Amer. Math. Soc. 370 (2018), no. 12, 8551–8580

26. Content of local cohomology, parameter ideals, and robust algebras (with M. Hochster)

Trans. Amer. Math. Soc. 370 (2018), no. 11, 7789--7814.

25. Global parameter test ideals (with M. Katzman, S. Murru, and J. Velez)

J. Algebra 486 (2017), 80--97.

24. On injective dimension of F-finite F-modules and holonomic D-modules

Bull. Lond. Math. Soc. 49 (2017), no. 4, 593--603.

23. Poincare duality in modular coinvariant rings (with M. Sezer)

Proc. Amer. Math. Soc., 144 (2016), no. 12, 5113–5120.

22. F-pure thresholds of homogeneous polynomials (with D. Hernandez, L. Nunez Betancourt, and E. Witt)

Michigan Math. Journal, 65 (2016), no.1, 57–87 .

21. Frobenius splitting in commutative algebra (with K. Smith)

Commutative algebra and noncommutative algebraic geometry. Vol. I, 291-345, Math. Sci. Res. Inst. Publ., 67, Cambridge Univ. Press.

20. A survey on Lyubeznik numbers (with L. Nunez Betancourt and E. Witt)

Contemp. Math. 657, 137--163.

19. An extension of a theorem of Hartshorne (with M. Katzman and G. Lyubeznik)

Proc. Amer. Math. Soc. 144 (2016), no. 3, 955--962.

18. Eulerian Graded D-modules (with L. Ma)

Math. Res. Lett. 21 (2014), no. 1, 149--167.

17. Local cohomology modules of a smooth Z-algebra have finitely many associated primes (with B. Bhatt, M. Blickle, G. Lyubeznik, and A. Singh)

Invent. Math. 197 (2014), no. 3, 509--519.

16. Rings of Frobenius operators (with M. Katzman, K. Schwede, and A. Singh)

Math. Proc. Cambridge Philos. Soc. 157 (2014), no. 1, 151–167.

15. Annihilators of Artinian modules compatible with a Frobenius map (with M. Katzman)

J. Symbolic Comput. 60 (2014), 29--46.

14. Castelnuovo-Mumford regularity and the discreteness of F-jumping coefficients in graded rings (with M. Katzman)

Trans. Amer. Math. Soc. 366 (2014), no. 7, 3519--3533.

13. Cartier modules on toric varieties (with J.-C. Hsiao, and K. Schwede)

Trans. Amer. Math. Soc. 366 (2014), no. 4, 177--1795.

12. Bertini theorems for F-singularities (with K. Schwede)

Proc. London Math. Soc., (3) 107 (2013), no. 4, 851--874.

11. Estimates for F-jumping numbers and bounds for Hartshorne-Speiser-Lyubeznik numbers (with M. Mustata)

Nagoya Math. J. 210 (2013), 133--160.

10. Test ideals via a single alteration and discreteness and rationality of F-jumping numbers (with K. Schwede and K. Tucker)

Math. Res. Letters, 19 (2012), no. 1, 191--197.

9. Two interesting examples of D-modules in characteristic p > 0 (with M. Katzman and G. Lyubeznik)

Bulletin of London Math. Soc., (2012) 44(6): 1116--1122

8. A property of the Frobenius map on a polynomial ring (with G. Lyubeznik and Y. Zhang)

Contemp. Math. 555 (Proceedings of PASI 2009), 137--144.

7. An upper bound on the number of F-jumping coefficients of a principal ideal (with M. Katzman and G. Lyubeznik)

Proc. Amer. Math. Soc. 139 (2011), 4193--4197.

6. Lyubeznik numbers of projective schemes

Adv. Math. 228 (2011), 575--616.

5. Discreteness and rationality of F-jumping numbers on singular varieties (with M. Blickle, K. Schwede, and S. Takagi)

Math. Ann. 347 (2010), no. 4, 917--949.

4. On Frobenius powers and colon ideals,

Comm. Alg. 37 (2009), no.7, 2391--2395.

3. On the localization theorem for F-pure rings (with K. Shimomoto)

Journal of Pure and Applied Algebra, (2009), no. 6, 1133--1139.

2. On the discreteness and rationality of F-jumping coefficients (with M. Katzman and G. Lyubeznik)

Journal of Algebra, 322 (2009), no. 9, 3238--3247.

1. On the highest Lyubeznik number of a local ring

Compositio Mathematica, 143 (2007), no. 1, 82--88.

Preprints (submitted or in preparation):

1. A note on growth of regularity with respect to Frobenius

arXiv:1512:00049, submitted.

2. Vanishing of local cohomology modules in mixed characteristic

in preparation.

3. A prime-characteristic analogue of a theorem of Hartshorne-Polini (with N. Switala)

in preparation.

Teaching:

Fall 2019: Math 571 (Introduction to Perfectoid Spaces)

Fall 2018: Math 516 (Graduate Algebra I)

Fall 2018: Math 310 (Applied Linear Algebra) 2 sections and course coordinator

Spring 2018: Math 571 (Topics in Algebraic Geometry)

Fall 2017: Math 310 (Applied Linear Algebra)

Spring 2017: Math 180 (Calculus I)

Spring 2017: Math 517 (Graduate Algebra II)

Spring 2016: Math 310 (Linear Algebra)

Fall 2015: Math 330 (Abstract Algebra)

REU: Chris Skalit, Kevin Tucker and myself are organizing an REU program in Commutative Algebra in Summer 2016. More information can be found here.

Lecture notes:

1. Local cohomology workshop at UIC, 02/27--03/01, 2015. (Notes)

2. Introduction to modular curves and modular forms, Fall 2014. (Notes)

Past Events Organized:

- D-Modules in Commutative Algebra, (08/10--08/14, 2015), CIMAT, Guanajuato, Mexico.
- Mathematical Research Community in Commutative algebra, (06/07--06/13, 2015), Snowbird, UT.
- Local cohomology workshop, (02/27--03/01, 2015), Chicago, IL.
- Focus period on Local cohomology and Regularity, (04/01--04/26, 2013), Special Year in Commutative Algebra at MSRI.
- Computational workshop on Frobenius singularities and invariants, (05/29--06/01, 2012), Ann Arbor, MI.