Anurag K. Singh

Professional Experience

• 2011–present: Professor, University of Utah.
• Spring 2024: Chern Professor, Simons Laufer Mathematical Sciences Institute, Berkeley.
• June 2017: Visiting Professor, Indian Institute of Technology Bombay.
• 2012-2013: Program Organizer, Mathematical Sciences Research Institute, Berkeley.
• July 2011: Visiting Associate Professor, Indian Institute of Technology Bombay.
• 2005-2011: Associate Professor, University of Utah.
• 2002-2006: Assistant Professor, Georgia Institute of Technology.
• 2002-2003: Postdoctoral Fellow/Member, Mathematical Sciences Research Institute, Berkeley.
• 1999-2002: Instructor/Wylie-Scott Assistant Professor, University of Utah.
• 1998-1999: Visiting Assistant Professor, University of Illinois at Urbana-Champaign.
• 1992–1998: University of Michigan. M.S. Mathematics (1994); Ph.D. Mathematics (1998).
  Thesis advisor:Professor Melvin Hochster
  Thesis:F-regularity, F-rationality and F-purity
• 1987-1992: Indian Institute of Technology Kanpur. B.S. equivalent in Mathematics (1992).

Awards and Grants

• National Board of Higher Mathematics (India) Scholarship, 1990-92.
• Copeland-Glover Fellowship, University of Michigan, 1992-94.
• Rackham Predoctoral Fellowship, University of Michigan, 1996-97.
• NSF Grant DMS 0070268, Studies in commutative algebra, 2000-03.
• Outstanding Instructor Award, University of Utah, 2001.
• NSF Grant DMS 0300600, Questions in commutative algebra, 2003-06.
• NSF Grant DMS 0600819, Tight closure, local cohomology, and related questions, 2006-09.
• NSF Grant DMS 0856044, Studies in commutative algebra, 2009-12.
• Faculty Undergraduate Teaching Award, University of Utah, 2012.
• NSF Grant DMS 1162585, Local cohomology, tight closure, and related questions, 2012-15.
• NSF Grant DMS 1500613, Questions on local cohomology and tight closure theory, 2015-18.
• Simons Visiting Professorship, Università di Genova, Italy, December 2016.
• NSF Grant DMS 1801285, Determinantal rings, local cohomology, and tight closure, 2018-21.
• NSF Grant DMS 2101671, Local cohomology, differential operators, and determinantal rings, 2021-24.
• Faculty Undergraduate Teaching Award, University of Utah, 2022.
• Fellow of the American Mathematical Society, 2023.
• NSF Grant DMS 2349623, Invariant rings, Frobenius, and differential operators, 2024-27.

Teaching Experience

• University of Michigan (1992-1998)
  Calculus, Business calculus.
• University of Illinois at Urbana-Champaign (1998-1999)
  Calculus, Linear algebra.
• University of Utah (1999-2002)
  Business algebra, Business calculus, Abstract algebra, Local cohomology, Intersection multiplicities.
• Georgia Institute of Technology. (2003–2005)
  Graduate algebra, Undergraduate algebra.
• University of Utah (2005–present)
  Business algebra, Business calculus, Business mathematics, Discrete mathematics, Complex variables,
  Foundations of algebra, History of Mathematics, Number theory, Cryptography, Algebraic topology,
  Undergraduate algebra, Graduate algebra, Commutative algebra, Invariant theory.

Publications

The research was supported in part by grants from the National Science Foundation.

• A computation of tight closure in diagonal hypersurfaces
  Journal of Algebra 203 (1998), 579–589.
• Failure of F-purity and F-regularity in certain rings of invariants,
  Illinois Journal of Mathematics 42 (1998), 441-448.
• Tight closure in non-equidimensional rings,
  Communications in Algebra 26 (1998), 3969-3983.
• Separable integral extensions and plus closure,
  Manuscripta Mathematica 98 (1999), 497-506.
• Deformation of F-purity and F-regularity,
  Journal of Pure and Applied Algebra 140 (1999), 137-148.
• F-regularity does not deform,
  American Journal of Mathematics 121 (1999), 919-929.
• Q-Gorenstein splinter rings of characteristic p are F-regular,
  Mathematical Proceedings of the Cambridge Philosophical Society 127 (1999), 201-205.
• Veronese subrings and tight closure,
  Pacific Journal of Mathematics 192 (2000), 399-413.
• Intersection multiplicities over Gorenstein rings, with Claudia Miller,
  Mathematische Annalen 317 (2000), 155-171.
• p-torsion elements in local cohomology modules,
  Mathematical Research Letters 7 (2000), 165-176.
• Multi-symbolic Rees algebras and strong F-regularity,
  Mathematische Zeitschrift 235 (2000), 335-344.
• Relative test elements for tight closure,
  Journal of Pure and Applied Algebra 158 (2001), 101-109.
• p-torsion elements in local cohomology modules II, in: Local cohomology and its applications (Guanajuato, 1999),
  Lecture Notes in Pure and Applied Mathematics 226 (2002), 155-167.
• Todd classes of affine cones of Grassmannians, with Kazuhiko Kurano,
  International Mathematics Research Notices 35 (2002), 1841-1855.
• Cyclic covers of rings with rational singularities,
  Transactions of the American Mathematical Society 355 (2003), 1009-1024.
• Associated primes of local cohomology modules,
  in: Proceedings of the 48th Algebra Symposium, Nagoya University (2003), 133-145.
• Associated primes of local cohomology modules and of Frobenius powers, with Irena Swanson,
  International Mathematics Research Notices 33 (2004), 1703-1733.
• The F-signature of an affine semigroup ring,
  Journal of Pure and Applied Algebra 196 (2005), 313-321.
• On the arithmetic rank of certain Segre products, with Uli Walther,
  Contemporary Mathematics 390 (2005), 147-155.
• Annihilators of local cohomology in characteristic zero, with Paul Roberts and V. Srinivas,
  Illinois Journal of Mathematics, special volume in honor of Phil Griffith, 51 (2007), 237-254.
• Local cohomology and pure morphisms, with Uli Walther,
  Illinois Journal of Mathematics, special volume in honor of Phil Griffith, 51 (2007), 287-298.
• Twenty-four 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.
• Divisor class groups of graded hypersurfaces, with Sandra Spiroff,
  Contemporary Mathematics 448 (2007), 237-243.
• A connectedness result in positive characteristic, with Uli Walther,
  Transactions of the American Mathematical Society 360 (2008), 3107-3119.
• Tight closure: applications and questions, in: Proceedings of the 4th Japan-Vietnam Joint Seminar on
  Commutative Algebra, February 17-21, 2009, Meiji University (2009), 45-63.
• Multigraded rings, rational singularities, and diagonal subalgebras, with Kazuhiko Kurano, Ei-ichi Sato, and Kei-ichi Watanabe,
  Journal of Algebra, special volume in honor of Paul Roberts, 322 (2009), 3248-3267.
• An algorithm for computing the integral closure, with Irena Swanson,
  Algebra & Number Theory 3 (2009), 587-595.
• Bockstein homomorphisms in local cohomology, with Uli Walther,
  Journal für die reine und angewandte Mathematik 655 (2011), 147-164.
• Reconciling Riemann-Roch results, with Paul Roberts,
  Contemporary Mathematics 555 (2011), 165-172.
• Galois extensions, plus closure, and maps on local cohomology, with Akiyoshi Sannai,
  Advances in Mathematics 229 (2012), 1847-1861.
• A note on Bockstein homomorphisms in local cohomology, with Uli Walther,
  Advanced Studies in Pure Mathematics 62 (2012), 513-521.
• Rings of Frobenius operators, with Mordechai Katzman, Karl Schwede, and Wenliang Zhang,
  Mathematical Proceedings of the Cambridge Philosophical Society 157 (2014), 151-167.
• Local cohomology modules of a smooth Z-algebra have finitely many associated primes, with Bhargav Bhatt, Manuel Blickle,
  Gennady Lyubeznik, and Wenliang Zhang, Inventiones Mathematicae, 197 (2014) 509-519.
• Appendix, with Karl Schwede, to Deformation of F-injectivity and local cohomology, by Jun Horiuchi, Lance E. Miller,
  and Kazuma Shimomoto, Indiana University Mathematics Journal 63 (2014), 1139-1157.
• The F-pure threshold of a determinantal ideal, with Lance E. Miller and Matteo Varbaro,
  Bulletin of the Brazilian Mathematical Society 45 (2014), 767-775.
• The F-pure threshold of a Calabi-Yau hypersurface, with Bhargav Bhatt,
  Mathematische Annalen 362 (2015), 551-567.
• Local cohomology supported at determinantal ideals, with Gennady Lyubeznik and Uli Walther,
  Journal of the European Mathematical Society 18 (2016), 2545-2578.
• A Gorenstein criterion for strongly F-regular and log terminal singularities, with Matteo Varbaro and Shunsuke Takagi,
  International Mathematics Research Notices 21 (2017), 6484-6522.
• 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), 239-247.
• Hankel determinantal rings have rational singularities,
  with Aldo Conca, Maral Mostafazadehfard, and Matteo Varbaro, Advances in Mathematics 335 (2018), 111-129.
• Stabilization of the cohomology of thickenings, with Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, and Wenliang Zhang,
  American Journal of Mathematics 141 (2019), 531-561.
• On a conjecture of Lynch, with Uli Walther,
  Communications in Algebra 48 (2020), 2681-2682.
• Homogeneous prime elements in normal two-dimensional graded rings,, with Ryo Takahashi and Kei-ichi Watanabe,
  Journal of Algebra, special volume in honor of Craig Huneke, 571 (2021), 339-349.
• Koszul and local cohomology, and a question of Dutta, with Linquan Ma and Uli Walther,
  Mathematische Zeitschrift 298 (2021), 697-711.
• An asymptotic vanishing theorem for the cohomology of thickenings, with Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik,
  and Wenliang Zhang, Mathematische Annalen 380 (2021), 161-173.
• When are the natural embeddings of classical invariant rings pure? with Mel Hochster, Jack Jeffries, and Vaibhav Pandey,
  Forum of Mathematics, Sigma 11 (2023), paper no. e67, 43 pp.
• Differential operators on classical invariant rings do not lift modulo p, with Jack Jeffries,
  Advances in Mathematics 432 (2023), paper no. 109276, 53 pp.
• On an example of Nagarajan, with Annie Giokas,
  Journal of Algebra 638 (2024), 931-936.
• Frobenius on the cohomology of thickenings, with Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, and Wenliang Zhang,
  International Mathematics Research Notices 10 (2024), 8557-8567.
• On Segre products, F-regularity, and finite Frobenius representation type, with Kei-ichi Watanabe,
  Acta Mathematica Vietnamica, special volume in honor of Ngo Viet Trung, 49 (2024), 129-138.
• Flat morphisms with regular fibers do not preserve F-rationality, with Eamon Quinlan-Gallego and Austyn Simpson,
  Revista Matemática Iberoamericana 40 (2024), 1989–2001.
• Frobenius representation type for invariant rings of finite groups, with Mitsuyasu Hashimoto,
  Advances in Mathematics 458 (2024), paper no. 109978, 17 pp.
• Ideals generated by power sums, with Aldo Conca and Kannan Soundararajan,
  Revue Roumaine de Mathématiques Pures et Appliquées, special volume in honor of Lucian Bădescu, 70 (2025), 49–71.
• Applications of perverse sheaves in commutative algebra, with Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, and Wenliang Zhang,
  Journal für die reine und angewandte Mathematik 825 (2025), 81–128.
• Invariant rings of the special orthogonal group have nonunimodal h-vectors, with Aldo Conca and Matteo Varbaro,
  Journal of Algebra and its Applications, special volume in honor of Sudhir Ghorpade, 24 (2025), paper no. 2540001, 10pp.
• Local cohomology of modular invariant rings, with Kriti Goel and Jack Jeffries,
  Transformation groups, to appear.
• Abelian extensions of equicharacteristic regular rings need not be Cohen-Macaulay,
  with Aryaman Maithani and Prashanth Sridhar, preprint.
• The arithmetic rank of determinantal nullcones, with Jack Jeffries, Vaibhav Pandey, and Uli Walther, preprint.

Lecture Series

• 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 Japan-Vietnam Joint Seminar on Commutative Algebra, February 2009, Meiji University, Tokyo, Japan. (Five lectures)
• CIMPA-TUBITAK 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, June-July 2014, Catania, Italy. (Five lectures)
• D-modules in commutative algebra, August 2015, Guanajuato, Mexico. (Three lectures)
• Advanced Instructional School on invariant theory, December 2015-January 2016,
  Chennai Mathematical Institute, India. (Five 90-minute lectures)
• Mini-course on invariants of finite groups, August 2016, Universidad de Costa Rica, San José, Costa Rica. (Six 3-hour lectures)
• GIAN lecture series on positive characteristic methods in commutative algebra, June 2017,
  Indian Institute of Technology Bombay, India. (Ten 90-minute lectures)
• Advanced Instructional School on Gröbner bases and their applications, December 2017,
  Indraprastha Institute of Information Technology Delhi, India. (Two 90-minute lectures)
• Advanced Instructional School on commutative algebra and algebraic geometry in positive characteristics, December 2018,
  Indian Institute of Technolog, Bombay, India. (Six 75-minute lectures)
• Commutative algebra and its interaction with algebraic geometry, May-June 2023,
  MSRI/SLMath Summer Graduate School, University of Notre Dame. (Five lectures)
• Advanced Instructional School on recent trends in commutative algebra, June 2024,
  Indian Institute of Technology Bombay, India. (Three lectures)

Selected Talks

• 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, November-December 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 Urbana-Champaign.
• 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 University-University 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 University-University 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 Kei-ichi Watanabe,
  July-August 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, May-June 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.
• D-modules, group actions, and Frobenius: computing on singularities, August 2021,
  Institute for Computational and Experimental Research in Mathematics (ICERM), Brown University.
• Seminar, November 2022, Osaka Metropolitan University, Japan.
• 43rd Japan Symposium on Commutative Algebra, November 2022, Osaka University, Japan.
• Algebraic/arithmetic geometry seminar, December 2022, Technische Universität München, Germany.
• Géométrie écrite: algèbre commutative, January 2023,
  Centre International de Rencontres Mathématiques (CIRM), Luminy, France.
• Commutative algebra and algebraic geometry seminar, March 2023, University of California, Berkeley.
• Colloquium, April 2023, Georgia State University.
• Colloquium, April 2024, Simons Laufer Mathematical Sciences Institute, Berkeley.
• International conference on local rings and singularities,
  in honor of Jugal Verma, June 2024, Indian Institute of Technology Bombay, India.
• Seminar, September 2024, Osaka Metropolitan University, Japan.
• Symmetries and singularities in Texas, February 2025, Texas A&M University.
• Colloquium, February 2025, Arizona State University.
• Southwest Local Algebra Meeting (SLAM), March 2025, Arizona State University.
• Commutative algebra in mixed characteristic, March 2025, University of Nebraska-Lincoln.
• Symbolic Computation Seminar, April 2025, North Carolina State University.
• Modules & Rings: recent developments in commutative algebra,
  in honor of Marilina Rossi, June 2025, Università di Genova, Italy.

Professional Activities

• 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. Sather-Wagstaff, 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 AMS-IMS-SIAM 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 2012-May 2013, Berkeley, California.
• Organizer (with B. Bhatt, S. B. Iyengar, and W. Niziol), The homological conjectures, Hot Topics workshop,
  Mathematical Sciences Research Institute (MSRI), March 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.
• Organizer (with S. B. Iyengar, C. Miller, and C. Polini), Introductory workshop: Commutative algebra,
  January 2024, MSRI/SLMath, Berkeley.
• Organizer (with M. Hashimoto, R. Kanda and S. Takagi), Commutative algebra and singularity theory, in honor of the 80th birthday of Kei-ichi Watanabe,
  September 2024, Osaka Metropolitan University, Osaka, Japan.
• Organizer (with A. Hariharan and S. K. Masuti), Recent developments in commutative algebra,
  June 2025, Indian Institute of Technology Dharwad, India.
• Organizer (with S. B. Iyengar, M. Kummini, and K. Hanumanthu), Algebra and geometry conference, in honor of Dale Cutkosky and Hema Srinivasan,
  December 2026, Chennai Mathematical Institute, Chennai, India.
• Moderator for the arXiv since 2007.
• Editorial Board of Communications in Algebra, 2006-2011.
• 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.
• Editorial Board of the Journal of the Ramanujan Mathematical Society, since 2023.
• Referee for various journals and conference proceedings.
• Reviewer for Mathematical Reviews. Papers reviewed