 19921998: University of Michigan.

Calculus, Business calculus.
 19981999: University of Illinois at UrbanaChampaign.

Calculus, Linear algebra.
 19992002: University of Utah.

Business algebra, Business calculus, Abstract algebra, Local cohomology, Intersection multiplicities.
 20032005: Georgia Institute of Technology.

Graduate algebra, Undergraduate algebra.
 2005 : University of Utah.

Business algebra, Business calculus, Discrete mathematics, Complex variables, Foundations of algebra,
History of Mathematics, Number theory, Cryptography, Algebraic topology, Undergraduate algebra,
Graduate algebra, Commutative algebra, Invariant theory.
 Failure of Fpurity and Fregularity in certain rings of invariants,
Illinois Journal of Mathematics 42 (1998), 441448.
 A computation of tight closure in diagonal hypersurfaces,
Journal of Algebra 203 (1998), 579589.
 Tight closure in nonequidimensional rings,
Communications in Algebra 26 (1998), 39693983.
 Deformation of Fpurity and Fregularity,
Journal of Pure and Applied Algebra 140 (1999), 137148.
 Fregularity does not deform,
American Journal of Mathematics 121 (1999), 919929.
 Separable integral extensions and plus closure,
Manuscripta Mathematica 98 (1999), 497506.
 QGorenstein splinter rings of characteristic p are Fregular,
Mathematical Proceedings of the Cambridge Philosophical Society 127 (1999), 201205.
 Multisymbolic Rees algebras and strong Fregularity,
Mathematische Zeitschrift 235 (2000), 335344.
 Veronese subrings and tight closure,
Pacific Journal of Mathematics 192 (2000), 399413.
 Intersection multiplicities over Gorenstein rings, with Claudia Miller,
Mathematische Annalen 317 (2000), 155171.
 ptorsion elements in local cohomology modules,
Mathematical Research Letters 7 (2000), 165176.
 Relative test elements for tight closure,
Journal of Pure and Applied Algebra 158 (2001), 101109.
 ptorsion elements in local cohomology modules II, in: Local cohomology and its applications (Guanajuato, 1999),
Lecture Notes in Pure and Applied Mathematics 226 (2002), 155167.
 Todd classes of affine cones of Grassmannians, with Kazuhiko Kurano,
International Mathematics Research Notices 35 (2002), 18411855.
 Cyclic covers of rings with rational singularities,
Transactions of the American Mathematical Society 355 (2003), 10091024.
 Associated primes of local cohomology modules,
in: Proceedings of the 48th Algebra Symposium, Nagoya University (2003), 133145.
 Associated primes of local cohomology modules and of Frobenius powers, with Irena Swanson,
International Mathematics Research Notices 33 (2004), 17031733.
 The Fsignature of an affine semigroup ring,
Journal of Pure and Applied Algebra 196 (2005), 313321.
 On the arithmetic rank of certain Segre products, with Uli Walther,
Contemporary Mathematics 390 (2005), 147155.
 Twentyfour hours of local cohomology, with Srikanth Iyengar, Graham Leuschke, Anton Leykin,
Claudia Miller, Ezra Miller, and Uli Walther, AMS Graduate Studies in Mathematics 87, 2007.
 Annihilators of local cohomology in characteristic zero, with Paul Roberts and V. Srinivas,
Illinois Journal of Mathematics, Special Issue in Honor of Phil Griffith, 51 (2007), 237254.
 Local cohomology and pure morphisms, with Uli Walther,
Illinois Journal of Mathematics, Special Issue in Honor of Phil Griffith, 51 (2007), 287298.
 Divisor class groups of graded hypersurfaces, with Sandra Spiroff,
Contemporary Mathematics 448 (2007), 237243.
 A connectedness result in positive characteristic, with Uli Walther,
Transactions of the American Mathematical Society 360 (2008), 31073119.
 Tight closure: applications and questions, in: Proceedings of the 4th JapanVietnam Joint Seminar on
Commutative Algebra, February 1721, 2009, Meiji University (2009), 4563.
 Multigraded rings, rational singularities, and diagonal subalgebras, with Kazuhiko Kurano, Eiichi Sato, and Keiichi Watanabe,
Journal of Algebra, Special Issue in Honor of Paul Roberts, 322 (2009), 32483267.
 An algorithm for computing the integral closure, with Irena Swanson,
Algebra & Number Theory 3 (2009), 587595.
 Bockstein homomorphisms in local cohomology, with Uli Walther,
Journal für die reine und angewandte Mathematik 655 (2011), 147164.
 Reconciling RiemannRoch results, with Paul Roberts,
Contemporary Mathematics 555 (2011), 165172.
 Galois extensions, plus closure, and maps on local cohomology, with Akiyoshi Sannai,
Advances in Mathematics 229 (2012), 18471861.
 A note on Bockstein homomorphisms in local cohomology, with Uli Walther,

Advanced Studies in Pure Mathematics 62 (2012), 513521.
 Rings of Frobenius operators, with Mordechai Katzman, Karl Schwede, and Wenliang Zhang,
Mathematical Proceedings of the Cambridge Philosophical Society 157 (2014), 151167.
 Local cohomology modules of a smooth Zalgebra have finitely many associated primes, with Bhargav Bhatt, Manuel Blickle,
Gennady Lyubeznik, and Wenliang Zhang, Inventiones Mathematicae, 197 (2014) 509519.
 Appendix, with Karl Schwede, to Deformation of Finjectivity and local cohomology, by Jun Horiuchi, Lance E. Miller,
and Kazuma Shimomoto, Indiana University Mathematics Journal 63 (2014), 11391157.
 The Fpure threshold of a determinantal ideal, with Lance E. Miller and Matteo Varbaro,
Bulletin of the Brazilian Mathematical Society 45 (2014), 767775.
 The Fpure threshold of a CalabiYau hypersurface, with Bhargav Bhatt,
Mathematische Annalen 362 (2015) 551567.
 Local cohomology supported at determinantal ideals, with Gennady Lyubeznik and Uli Walther,
Journal of the European Mathematical Society 18 (2016), 25452578.
 A Gorenstein criterion for strongly Fregular and log terminal singularities, with Matteo Varbaro and Shunsuke Takagi,
International Mathematics Research Notices 21 (2017), 64846522.
 Positive characteristic methods in commutative algebra,
GIAN lecture notes, 2017.
 A polynomial identity via differential operators, in: Homological and computational methods in commutative algebra
(Cortona, 2016), Springer INdAM Series 20 (2017), 239247.
 Hankel determinantal rings have rational singularities,
with Aldo Conca, Maral Mostafazadehfard, and Matteo Varbaro, Advances in Mathematics 335 (2018), 111129.
 Stabilization of the cohomology of thickenings, with Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, and Wenliang Zhang,
American Journal of Mathematics 141 (2019), 531561.
 On a conjecture of Lynch, with Uli Walther,
Communications in Algebra 48 (2020), 26812682.
 Homogeneous prime elements in normal twodimensional graded rings,, with Ryo Takahashi and
Keiichi Watanabe,
Journal of Algebra, Special Issue in Honor of Craig Huneke, 571 (2021), 339349.
 Koszul and local cohomology, and a question of Dutta, with Linquan Ma and Uli Walther,
Mathematische Zeitschrift 298 (2021), 697711.
 An asymptotic vanishing theorem for the cohomology of thickenings, with Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik,
and Wenliang Zhang, Mathematische Annalen 380 (2021), 161173.
 Differential operators on classical invariant rings do not lift modulo p, with Jack Jeffries,
Preprint.
 Commutative algebra and interactions with algebraic geometry and combinatorics, June 2004,
International Centre for Theoretical Physics (ICTP), Trieste, Italy. (Four lectures)
 Summer school in commutative algebra: Local cohomology and its interactions with algebra, geometry, and analysis,
June 2005, Snowbird, Utah. (Three lectures)
 Fourth JapanVietnam Joint Seminar on Commutative Algebra, February 2009, Meiji University, Tokyo, Japan. (Five lectures)
 CIMPATUBITAK school on commutative algebra and applications to combinatorics and algebraic geometry,
September 2010, Feza Gürsey Institute, Istanbul, Turkey. (Five lectures.)
 Workshop on local cohomology, July 2011, Indian Institute of Technology, Bombay, India. (Five lectures)
 Pragmatic: Research school in algebraic geometry and commutative algebra, JuneJuly 2014, Catania, Italy. (Five lectures)
 Dmodules in commutative algebra, August 2015, Guanajuato, Mexico. (Three lectures)
 Advanced Instructional School on invariant theory, December 2015January 2016,
Chennai Mathematical Institute, India. (Five 90minute lectures)
 Minicourse on invariants of finite groups, August 2016, Universidad de Costa Rica, San José, Costa Rica. (Six 3hour lectures)
 GIAN lecture series on positive characteristic methods in commutative algebra, June 2017,
Indian Institute of Technology, Bombay, India. (Ten 90minute lectures)
 Advanced Instructional School on Gröbner bases and their applications, December 2017,
Indraprastha Institute of Information Technology, Delhi, India. (Two 90minute lectures)
 Advanced Instructional School on commutative algebra and algebraic geometry in positive characteristics, December 2018,
Indian Institute of Technology, Bombay, India. (Six 75minute lectures)
 American Mathematical Society Mathfest, August 1996, Seattle, Washington.
 American Mathematical Society Meeting, November 1996, Columbia, Missouri.
 American Mathematical Society Meeting, January 1998, Baltimore, Maryland.
 Second Annual Missouri Algebra Weekend, October 1998, Columbia, Missouri.
 American Mathematical Society Meeting, March 1999, Urbana, Illinois.
 American Mathematical Society Meeting, September 1999, Salt Lake City, Utah.
 Conference on local cohomology, NovemberDecember 1999,
Centro de Investigación en Matemáticas (CIMAT), Guanajuato, Mexico.
 American Mathematical Society Meeting, April 2000, Notre Dame, Indiana.
 Commutative algebra seminar, August 2000, University of Minnesota.
 American Mathematical Society Meeting, March 2001, Lawrence, Kansas.
 Colloquium, January 2002, Georgia Institute of Technology.
 Colloquium, January 2002, University of Illinois at UrbanaChampaign.
 Colloquium, February 2002, University of Kentucky.
 Colloquium, February 2002, Syracuse University.
 Special lecture, February 2002, University of Minnesota.
 Workshop on commutative algebra: local and birational theory,
Mathematical Sciences Research Institute (MSRI), December 2002, Berkeley, California.
 Algebra seminar, April 2003, University of Kansas.
 Ellis B. Stouffer Colloquium, April 2003, University of Kansas.
 American Mathematical Society Meeting, May 2003, San Francisco, California.
 Algèbre commutative et ses interactions avec la géométrie algébrique,
Centre International de Rencontres Mathématiques (CIRM), June 2003, Luminy, France.
 Singularities seminar, July 2003, Nihon University, Japan.
 Algebra seminar, July 2003, Shinshu University, Japan.
 Commutative algebra seminar, August 2003, Meiji University, Japan.
 48th Algebra Symposium, August 2003, Nagoya University, Japan.
 Joint International Meeting of the American Mathematical Society and
the Indian Mathematical Society, December 2003, Bangalore, India.
 Algebra seminar, February 2004, University of Texas at Austin.
 Commutative algebra: homological and birational theory,
Banff International Research Station (BIRS), September 2004, Banff, Canada.
 Algebra seminar, October 2004, University of Georgia.
 American Mathematical Society Meeting, October 2004, Nashville, Tennessee.
 Colloquium, January 2005, University of Notre Dame.
 Colloquium, January 2005, University of Utah.
 Colloquium, February 2005, University of Kansas.
 Colloquium, February 2005, Purdue University.
 Conference on commutative algebra: recent developments in tight closure, April 2005,
University of Arkansas.
 Workshop on Kommutative Algebra, April 2005, Oberwolfach, Germany.
 CIMPA international conference on commutative algebra, January 2006, Hanoi, Vietnam.
 American Mathematical Society Meeting, April 2006, Notre Dame, Indiana.
 American Mathematical Society Meeting, April 2006, San Francisco, California.
 Homological conjectures in commutative algebra: a conference in honor of Paul Roberts,
May 2006, Snowbird, Utah.
 Algebra seminar, February 2007, University of Nebraska.
 Colloquium, February 2007, University of Nebraska.
 Hilbert functions and syzygies in commutative algebra and combinatorics:
a conference in honor of Jürgen Herzog, September 2007, Cortona, Italy.
 Georgia State UniversityUniversity of South Carolina joint seminar, November 2007, Columbia.
 Macaulay2 conference, March 2008, Cornell University.
 Algèbre commutative et ses interactions avec la géométrie algébrique,
Centre International de Rencontres Mathématiques (CIRM), October 2008, Luminy, France.
 Workshop on Kommutative Algebra, April 2009, Oberwolfach, Germany.
 First Pacific Rim Mathematical Association (PRIMA) Congress, July 2009, Sydney, Australia.
 Commutative algebra and its connections to geometry,
PASI conference honoring Wolmer Vasconcelos, August 2009, Olinda, Brazil.
 Frobenius splittings in algebraic geometry, commutative algebra, and representation theory,
May 2010, University of Michigan.
 Local rings and local study of algebraic varieties,
International Centre for Theoretical Physics (ICTP), June 2010, Trieste, Italy.
 Workshop on integral closure, July 2010, Mathematical Sciences Research Institute (MSRI), Berkeley.
 Georgia State UniversityUniversity of South Carolina joint seminar, September 2010, Atlanta.
 Algèbre commutative et ses interactions avec la géométrie algébrique,
Centre International de Rencontres Mathématiques (CIRM), November 2010, Luminy, France.
 Colloquium, May 2011, University of California, Riverside.
 Midwest commutative algebra and geometry conference, May 2011, Purdue University.
 Seminar, July 2011, Chennai Mathematics Institute, Chennai, India.
 Relating test ideals and multiplier ideals, August 2011, American Institute of Mathematics (AIM), Palo Alto.
 American Mathematical Society Meeting, October 2011, Lincoln, Nebraska.
 Algebra and number theory seminar, February 2012, Penn State University.
 Colloquium, February 2012, Penn State University.
 Computational workshop on Frobenius singularities and invariants, May 2012, University of Michigan.
 12th ALGA Meeting, Instituto Nacional de Matemática Pura e Aplicada (IMPA),
August 2012, Rio de Janeiro, Brasil.
 Commutative algebra and algebraic geometry seminar, October 2012, University of California, Berkeley.
 Singularity categories in algebraic geometry and commutative algebra, January 2013,
Indian Institute of Technology, Madras, India.
 Joint International Meeting of the American Mathematical Society and the
Romanian Mathematical Society, June 2013, Alba Iulia, Romania.
 Combinatorial structures in algebra and topology, July 2013, Osnabrück, German.
 Algèbre commutative et ses interactions avec la géométrie algébrique,
Centre International de Rencontres Mathématiques (CIRM), July 2013, Luminy, France.
 International conference on commutative algebra and its interaction to algebraic geometry and combinatorics,
December 2013, Hanoi, Vietnam.
 Colloquium, March 2014, University of Arkansas.
 American Mathematical Society Meeting, April 2014, Albuquerque, New Mexico.
 Seminari geometria algebraica, June 2014, Universitat de Barcelona, Spain.
 Commutative algebra and singularity theory, a conference in honor of Keiichi Watanabe,
JulyAugust 2014, Tateyama, Japan.
 Commutative algebra seminar, August 2014, Meiji University, Japan.
 MOCCA: Meeting on combinatorial commutative algebra, September 2014, Trento, Italy.
 American Mathematical Society Meeting, October 2014, San Francisco, California.
 Recent developments in positive characteristic techniques in commutative algebra:
Frobenius operators and Cartier algebras, March 2015, Georgia State University.
 Joint International Meeting of the American Mathematical Society, European Mathematical Society, and
Sociedade Portuguesa de Matemática, June 2015, Porto, Portugal.
 Midwest commutative algebra conference, August 2015, Purdue University.
 Syzygies in algebra and geometry, August 2015, Haeundae, South Korea.
 KUMUNU conference, October 2015, University of Missouri.
 Commutative algebra and algebraic geometry seminar, January 2016, Indian Institute of Technology, Bombay, India.
 American Mathematical Society Meeting, March 2016, Athens, Georgia.
 Homological and computational methods in commutative algebra,
a conference in honor of Winfried Bruns, MayJune 2016, Cortona, Italy.
 Commutative algebra and its interactions with algebraic geometry: tight closure, linkage, and syzygies,
a conference in honor of Craig Huneke, July 2016, University of Michigan.
 Algebra and geometry seminar, December 2016, Università di Genova, Italy.
 Colloquium, February 2017, Reed College.
 Commutative algebra seminar, April 2017, University of Michigan.
 Colloquium, June 2017, International Centre for Theoretical Sciences (ICTS), Bengaluru, India.
 Local cohomology in commutative algebra and algebraic geometry,
a conference in honor of Gennady Lyubeznik, August 2017, University of Minnesota.
 Colloquium, October 2017, University of Notre Dame.
 Algebraic geometry and commutative algebra seminar, October 2017, University of Notre Dame.
 39th Japan Symposium on Commutative Algebra, November 2017,
Research Institute for Mathematical Sciences (RIMS), Kyoto, Japan.
 Algebraic geometry and number theory conference, December 2017, Indian Statistical Institute, Bengaluru, India.
 Colloquium, October 2018, Georgia State University.
 Algebra seminar, October 2018, Georgia State University.
 Singularities and homological aspects of commutative algebra, February 2019, Oberwolfach, Germany.
 American Mathematical Society Meeting, March 2019, Auburn, Alabama.
 Colloquium, April 2019, Purdue University.
 Conference on commutative algebra and its interaction with algebraic geometry,
in honor of Bernd Ulrich, June 2019, University of Notre Dame.
 Commutative algebra seminar, September 2019, University of Illinois at Chicago.
 Colloquium, October 2019, University of Minnesota.
 Commutative algebra seminar, February 2020, University of Michigan.
 Fellowship of the ring zoom seminar, April 2020, Mathematical Sciences Research Institute (MSRI), Berkeley, California.
 Virtual commutative algebra seminar, June 2020, Indian Institute of Technology, Bombay, India.
 Organizer (with P. Roberts), Special session on commutative algebra and algebraic geometry,
Joint Mathematics Meeting, January 2002, San Diego, California.
 Organizer (with F. Enescu and K. E. Smith), Special session on commutative algebra,
American Mathematical Society Meeting, March 2002, Ann Arbor, Michigan.
 Organizer (with S. B. Iyengar, S. SatherWagstaff, and C. Yackel), Special session on commutative algebra,
Joint Mathematics Meeting, January 2005, Atlanta, Georgia.
 Organizer (with U. Walther), Local cohomology and its interactions with algebra, geometry, and analysis,
Joint AMSIMSSIAM Summer Research Conference, June 2005, Snowbird, Utah.
 Organizer (with S. B. Iyengar, G. Leuschke, and C. Miller), Minnowbrook workshop on commutative algebra,
Minnowrook Adirondack Conference Center, August 2005, Syracuse, New York.
 Organizer (with A. Kustin, M. Miller, and S. Spiroff), Commutative algebra conference honoring the contributions of Phillip Griffith,
University of Illinois, September 2005, Urbana, Illinois.
 Organizer (with P. Roberts and O. Veliche), Special session on commutative algebra,
American Mathematical Society Meeting, October 2006, Salt Lake City, Utah.
 Organizer (with P. Roberts and O. Veliche), Special session on commutative algebra and algebraic geometry,
Joint Mathematics Meeting, January 2007, New Orleans, Louisiana.
 Organizer (with C. Huneke and K. E. Smith), Commutative algebra and its interactions, a conference in honor of Mel Hochster
University of Michigan, August 2008, Ann Arbor, Michigan.
 Organizer (with D. Eisenbud and K.i. Watanabe), Special session on commutative algebra,
Pacific Rim Mathematical Association (PRIMA) Congress, July 2009, Sydney, Australia.
 Organizer (with P. Roberts and S. Spiroff), Special session on local commutative algebra,
Joint Mathematics Meeting, January 2011, New Orleans, Louisiana.
 Organizer (with S. B. Iyengar and J. Verma), Workshop and conference on local cohomology,
July 2011, Indian Institute of Technology, Bombay, India.
 Organizer (with C.Y. Chan and L. Miller), Special session on commutative algebra,
American Mathematical Society Meeting, October 2011, Salt Lake City, Utah.
 Organizer (with D. Eisenbud, S. B. Iyengar, E. Miller, and K. E. Smith), Commutative algebra program year,
Mathematical Sciences Research Institute (MSRI), August 2012May 2013, Berkeley, California.
 Organizer (with B. Bhatt, S. B. Iyengar, and W. Niziol), The homological conjectures, Hot Topics workshop,
Mathematical Sciences Research Institute (MSRI), Spring 2018, Berkeley.
 Organizer (with S. B. Iyengar), Topics in commutative algebra, May 2018, RTG workshop, University of Utah.
 Organizer (with A. Conca and S. B. Iyengar), Recent developments in commutative algebra,
Centro Internazionale Matematico Estivo (CIME), July 2019, Trento, Italy.
 Moderator for the arXiv.
 Editorial Board of Communications in Algebra, 20062011.
 Editor (with K. E. Smith) special volume of the Michigan Mathematical Journal in honor of Mel Hochster, Volume 57, 2008.
 Editor (with D. Eisenbud, S. B. Iyengar, J. T. Stafford, and M. Van den Bergh), Commutative Algebra and Noncommutative Algebraic Geometry,
Volume I: Expository Articles, 67, and Volume II: Research Articles, 68, MSRI Publications, Cambridge University Press, 2015.
 Referee for various journals and conference proceedings.
 Reviewer for Mathematical Reviews. Papers reviewed