Wenliang Zhang
Department of Mathematics
University of Michigan
1859 East Hall
Email: wlzhang@umich.edu
(734)6475368
Commutative Algebra, Algebraic Geometry
Grants:
1. NSF Grant DMS #1068946 (2011--2014)
2. NSF Grant DMS #1160927 for the conference Computational Workshop on Singularities and Invariants Defined by Frobenius (with Karl Schwede nd Kevin Tucker)
Papers and preprints:
17. Bertini theorems for F-singularitites, (joint with Karl Schwede), arXiv: 1112.2161, submitted.
16. Target elements and test ideals, (joint with Mel Hochster), in preparation.
15. Content with respect to parameters, (joint with Mel Hochster), in preparation.
14. Estimates for F-jumping numbers and bounds for Hartshorne-Speiser-Lyubeznik numbers, (joint with Mircea Mustata), arXiv:1110.5687, submitted.
13. Castelnuovo-Mumford regularity and the discreteness of F-jumping coefficients in graded rings, (joint with Mordechai Katzman), arXiv:1110.2093, submitted.
12. Cartier modules on toric varieties, (joint with Jen-Chieh Hsiao and Karl Schwede), arXiv:1011.0804, submitted.
11. Test ideals via a single alteration and discreteness and rationality of $F$-jumping numbers, (joint with Karl Schwede and Kevin Tucker), arXiv:1107.4059, accepted by Math. Res. Letters.
10. Two interesting examples of D-modules in characteristic p>0, (joint with Gennady Lyubeznik and Mordechai Katzman), arXiv:1010.1890, accepted by Bulletin of London Math. Soc.
9. An upper bound on the number of F-jumping coefficients of a principal ideal, (joint with Gennady Lyubeznik and Mordechai Katzman), arXiv:1010.2525, Proc. Amer. Math. Soc. 139 (2011), 4193--4197.
8. Lyubeznik numbers of projective schemes, Adv. Math. 228 (2011), 575--616.
7. A property of the Frobenius map of a polynomial ring, (joint with Gennady Lyubeznik and Yi Zhang), Contemp. Math. (Proceeding of PASI 2009), 137--144, also available at arXiv:1001.2949.
6. Discreteness and Rationality of F-jumping numbers on Singular Varieties, (joint with Manuel Blickle, Karl Schwede and Shunsuke Takagi), Math. Ann., 347 (2010), no. 4, 917--949.
5. On the localization theorem for F-pure rings, (joint with Kazuma Shimomoto), Journal of Pure and Applied Algebra, (2009), no. 6, 1133--1139.
4. On Frobenius powers and colon ideals, Comm. Alg. 37 (2009), no.7, 2391--2395.
3. On the rationality and discreteness of F-jumping coefficients, (joint with Gennady Lyubeznik and Mordechai Katzman), Journal of Algebra, 322 (2009), no. 9, 3238--3247, Special Issue in Honor of Paul Roberts.
2. On Lyubeznik numbers of projective schemes, arXiv:0709.0747. (This is the 2nd part of my thesis; the results in this paper have been improved substantially since I came to Michigan.)
1. On the highest Lyubeznik number of a local ring, Compos. Math. 143 (2007), no. 1, 82--88. (This the 1st part of my thesis.)
1. Mel Hochster and I are currently organizing the Commutative Algebra seminar. You can find more information at:
http://www.math.lsa.umich.edu/seminars_events/events.php?eventdefid=5&dt_begin=2011-07-01&dt_end=2011-12-31
2. Karl Schwede, Kevin Tucker and I are organizing a Computaional Workshop on Singularities and Invariants Defined by Frobenius (May 29th--June 1st, 2012, Ann Arbor, Michigan). For more information, see:
http://sites.google.com/site/computingfinvariantsworkshop/
Math 115 (Calculus I) Fall 2008
Math 615 (Commutative Algebra II) Winter 2009
Math115 (Calculus I) Fall 2009
Math 412 (Introduction to Modern Algebra) Winter 2010
Math 412 (Introduction to Modern Algebra) Fall 2010
Math 425 (Introduction to Probability) Winter 2011
Math 116 (Calculus II) Fall 2011