Anurag Singh's Curriculum Vitae
Professional Experience:
1998–1999: Visiting Assistant Professor, University of Illinois at Urbana-Champaign.
1999–2002: Instructor/Wylie-Scott Assistant Professor, University of Utah.
2002–2003: Postdoctoral Fellow/Member, Mathematical Sciences Research Institute, Berkeley.
2002–2006: Assistant Professor, Georgia Institute of Technology.
2005–2011: Associate Professor, University of Utah.
2011–present: Professor, University of Utah.
Education:
1987–1992: Indian Institute of Technology, Kanpur.
B.S. equivalent in Mathematics, May 1992.
1992–1998: University of Michigan.
M.S. in Mathematics, December 1994.
Ph.D. in Mathematics, May 1998.
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.
Teaching Experience:
1992–1998: University of Michigan.
Instructor for various Calculus courses; organized self-study courses and workshops.
1998–1999: University of Illinois at Urbana-Champaign.
Instructor for Calculus and Linear Algebra courses.
1999–2002: University of Utah.
Instructor for courses in Business Algebra, Business Calculus, Abstract Algebra,
Local Cohomology, and Intersection Multiplicities.
2003–2005: Georgia Institute of Technology.
Instructor for Graduate Algebra and Undergraduate Algebra courses.
2005– : University of Utah.
Instructor for Business Algebra, Abstract Algebra, Commutative Algebra, Algebraic Topology,
Graduate Algebra, Undergraduate Algebra, Business Calculus, Discrete Mathematics,
Complex Variables, Number Theory, and Cryptography and Codes.
Publications:
The research was supported in part by grants from the National Science Foundation.
Failure of F-purity and F-regularity in certain rings of invariants,
Illinois Journal of Mathematics 42 (1998) 441–448.
A computation of tight closure in diagonal hypersurfaces,
Journal of Algebra 203 (1998) 579–589.
Tight closure in non-equidimensional rings,
Communications in Algebra 26 (1998) 3969–3983.
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.
Separable integral extensions and plus closure,
manuscripta mathematica 98 (1999) 497–506.
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, ed. G. Lyubeznik, Marcel Dekker (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.
Characteristic p methods and tight closure,
Four lectures at the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy.
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.
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.
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) 237–254.
Local cohomology and pure morphisms, with Uli Walther,
Illinois Journal of Mathematics, Special Issue in Honor of Phil Griffith, 51 (2007) 287–298.
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.
Multigraded rings, rational singularities, and diagonal subalgebras,with Kazuhiko Kurano, Ei-ichi Sato,
and Kei-ichi Watanabe, Journal of Algebra, Special Issue 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.
Splinters: splitting questions for finite ring extensions, in preparation.
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, 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, 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.
Algébre commutative et ses interactions avec la géométrie algébrique,
Centre International de Rencontres Mathématiques, 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, December 2003, Bangalore, India.
Algebra seminar, February 2004, University of Texas at Austin.
School on commutative algebra and interactions with algebraic geometry and combinatorics,
Abdus Salam International Centre for Theoretical Physics, June 2004, Trieste, Italy.
Commutative algebra: homological and birational theory,
Banff International Research Station, 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.
Commutative algebra and its interactions with algebraic geometry,
Centre International de Rencontres Mathématiques, October 2008, Luminy, France.
Fourth Japan-Vietnam joint conference on commutative algebra,
February 2009, Meiji University, Japan.
Workshop on Kommutative Algebra, April 2009, Oberwolfach, Germany.
First 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,
University of Michigan, May 2010, Ann Arbor, Michigan.
Local rings and local study of algebraic varieties,
Abdus Salam International Centre for Theoretical Physics, June 2010, Trieste, Italy.
School on commutative algebra and applications to combinatorics and algebraic geometry,
Feza Gürsey Institute, September 2010, Istanbul, Turkey.
Georgia State University-University of South Carolina joint seminar, September 2010, Atlanta.
Commutative algebra and its interactions with algebraic geometry,
Centre International de Rencontres Mathématiques, November 2010, Luminy, France.
Colloquium, May 2011, University of California, Riverside.
Midwest commutative algebra and geometry conference, May 2011, Purdue University.
Workshop on local cohomology, July 2011, IIT Bombay, India.
American Mathematical Society Meeting, October 2011, Lincoln, Nebraska.
Algebra and number theory seminar, February 2012, Penn State University.
Colloquium, February 2012, Penn State University.
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. Iyengar, S. Sather-Wagstaff, and C. Yackel), Special session on commutative algebra,
Joint Mathematics Meeting, January 2005, Atlanta, Georgia.
Organizer (with U. Walther), Summer school in commutative algebra for graduate students:
Local cohomology and its interactions with algebra, geometry, and analysis,
Joint AMS-IMS-SIAM Summer Research Conference, June 2005, Snowbird, Utah.
Organizer (with S. 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. Iyengar and J. Verma), Workshop and conference on local cohomology,
July 2011, IIT 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. Iyengar, E. Miller, and K. E. Smith), Commutative algebra program,
Mathematical Sciences Research Institute, August 2012–May 2013, Berkeley, California.
Moderator for the Commutative Algebra section of the arXiv.
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.
Referee for various journals and conference proceedings.
Reviewer for Mathematical Reviews. Papers reviewed
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