Education

Ph.D., Mathematics, University of Chicago, 1994, Advisor: Dr. J. L. Alperin
S.M., Mathematics, University of Chicago, 1991
B.S., Mathematics, Arizona State University, 1988

Awards and Fellowships

NSF Collaborative Research Grant (co-PI Anne Shepler, UNT), Sept. 2008-August 2011
Texas Advanced Research Program Grant (co-PI Anne Shepler, UNT), May 2008-May 2010
NSA Individual Research Grant, February 2007-February 2009
Humboldt Foundation Research Fellowship, August 2005-July 2006
NSF Individual Research Grant DMS0245082 (Amherst College), 0422506 (MSRI) and 0443476 (TAMU), July 2003-June 2006
NSA Individual Research Grant MDA904-01-1-0067, April 2001-October 2003
NSF Research Grant DMS9970119 (PI: Georgia Benkart), May 1999-June 2000
NSERC Individual Research Grant OGP0170281, April 1995-June 1998

Employment

Associate Professor, Texas A&M University, September 2006-present
Assistant Professor, Texas A&M University, July 2004-August 2006
Visiting Assistant Professor, Amherst College, July 2001-December 2003
Visiting Assistant Professor, University of Massachusetts, Amherst, Sept. 2000-August 2001
Van Vleck Assistant Professor, University of Wisconsin, Madison, January 1999-June 2000
General Member, Math. Sci. Res. Inst., 1996-1997, Fall 1998, and Spring 2004
Assistant Professor, University of Toronto, 1994-1998 (on leave 1996-1997)

Teaching Experience

Calculus, Finite Mathematics, Algebra, Structure of Mathematics, Texas A&M University, 2004-present (Math 166, 171, 172, 220, 365, 653, 654)
Calculus, Chaotic Dynamical Systems, and Topology, Amherst College, Spring 2001-Fall 2003
Calculus, Mount Holyoke College, Massachusetts, Spring 2001
Basic Mathematics Skills and Honors Calculus for the Life and Social Sciences, University of Massachusetts, Amherst, 2000-2001
Ring Theory, Finite Mathematics, and Linear Algebra, University of Wisconsin, Madison, 1999-2000
Abstract Algebra, Linear Algebra, and Calculus, University of Toronto, 1994-1996 and 1997-1998
Linear Algebra, Mills College, Oakland, CA, Fall 1996
Precalculus, University of Chicago, 1990-1993

Refereed Publications

1. The ring of equivariant vector bundles on finite sets, J. Algebra 175 (1995), 274-286.
2. The representation ring of the quantum double of a finite group, J. Algebra 179 (1996), 305-329.
3. The representation ring of the twisted quantum double of a finite group, Canad. J. Math. 48 (1996), 1324-1338.
4. Irreducible representations of crossed products (with Susan Montgomery), J. Pure Appl. Algebra 129 (1998), 315-326.
5. The Hochschild cohomology ring of a group algebra (with Stephen F. Siegel), Proc. London Math. Soc. 79 (1999), 131-157.
6. The representation ring and the centre of a Hopf algebra, Canad. J. Math. 51 (1999), 881-896.
7. Clifford correspondence for finite-dimensional Hopf algebras, J. Algebra 218 (1999), 608-620.
8. A module-theoretic approach to Clifford theory for blocks, Proc. Amer. Math. Soc. 128 (2000), 661-670.
9. The Hochschild cohomology ring of a cyclic block (with Stephen F. Siegel), Proc. Amer. Math. Soc. 128 (2000), 1263-1268.
10. A Hopf structure for down-up algebras (with Georgia Benkart), Math. Z. 238 (2001), 523-553.
11. Clifford correspondence for algebras, J. Algebra 256 (2002), 518-530.
12. Hochschild cohomology and Linckelmann cohomology for blocks of finite groups (with Jonathan Pakianathan), J. Pure Appl. Algebra 178 (2003), 87-100.
13. Algebraic deformations arising from orbifolds with discrete torsion (with A. Caldararu and A. Giaquinto), J. Pure Appl. Algebra 187 (2004), no. 1-3, 51-70.
14. Representations of two-parameter quantum groups and Schur-Weyl duality (with G. Benkart), Hopf algebras, 65-92, Lecture Notes in Pure and Appl. Math., 237, Dekker, New York, 2004.
15. Restricted two-parameter quantum groups (with G. Benkart), Representations of finite dimensional algebras and related topics in Lie theory and geometry, 293-318, Fields Inst. Commun. 40 , Amer. Math. Soc., Providence, RI, 2004.
16. Products in Hochschild cohomology and Grothendieck rings of group crossed products, Adv. Math. 185 (2004), no. 1, 136-158.
17. Two-parameter quantum groups and Drinfel'd doubles (with G. Benkart), Algebras and Representation Theory 7 (2004), 261-286.
18. Quillen stratification for Hochschild cohomology of blocks (with J. Pakianathan and an appendix by S. Siegel), Trans. Amer. Math. Soc. 358 (2006), no. 7, 2897-2916.
19. Skew derivations and deformations of a family of group crossed products, Comm. Algebra 34 (2006), no. 11, 4187-4206.
20. Quantum group actions, twisting elements, and deformations of algebras (with G. Benkart), J. Pure Appl. Algebra 208 (2007), 371-389.
21. Twisted graded Hecke algebras, J. Algebra 317 (2007), 30-42.
22. Hochschild cohomology of smash products and rank one Hopf algebras (with Sebastian Burciu), Biblioteca de la Revista Matematica Iberoamericana Actas del "XVI Coloquio Latinoamericano de Algebra" (Colonia, Uruguay, 2005), 2007, 153-170.
23. Braid group representations from twisted quantum doubles of finite groups (with Pavel Etingof and Eric Rowell), Pacific J. Math. 234 (2008), no. 1, 33-41.
24. Hochschild cohomology and graded Hecke algebras (with Anne V. Shepler), Trans. Amer. Math. Soc. 360 (2008), no. 8, 3975-4005.
25. Bialgebra cohomology, pointed Hopf algebras, and deformations (with Mitja Mastnak), J. Pure Appl. Algebra 213 (2009), 1399-1417.
26. Varieties for modules of quantum elementary abelian groups (with Julia Pevtsova), to appear in Algebras and Rep. Th.
27. Hopf quivers and Nichols algebras in positive characteristic (with Claude Cibils and Aaron Lauve), to appear in Proc. Amer. Math. Soc.
28. Fusion subcategories of representation categories of twisted quantum doubles of finite groups (with Deepak Naidu and Dmitri Nikshych), to appear in Int. Math. Res. Not.
29. Cohomology of finite dimensional pointed Hopf algebras (with Mitja Mastnak, Julia Pevtsova, and Peter Schauenburg), to appear in Proc. London Math. Soc.

Departmental Service

Graduate Students:
• Mariana Pereira, Ph.D. December 2006
• Current: Piyush Shroff, Jeanette Shakalli

Postdocs Supervised:
• Aaron Lauve (current, with Marcelo Aguiar and Frank Sottile)
• Deepak Naidu (current, with Marcelo Aguiar and Eric Rowell)

Committees:
• Member, Graduate Committee, Fall 2006-present, and Mentoring Subcommittee, December 2008-present
• Member, Maxson Lectures Committee, Spring 2007
• Member, Mathematics Awareness Month Committee, Spring 2007 (Co-organized the Integral Bee, April 16, 2007)
• Member, Subcommittee T, Spring 2009-present

Miscellaneous:
• Organizer, Working Algebra Seminar, Fall 2008
• SEE Math: gave 3 lectures to middle school students, July 21 and 22, 2008

Professional Service

Professional Societies:
• AMS-MAA-SIAM Committee on Employment Opportunities, February 2006-January 2009 (Chair February 2008-January 2009)
• Member-at-Large of the AMS Council, February 2008-January 2011
• AMS Committee on Education, February 2008-January 2011
  
  Organization:
• Organizing Committee, AMS-IMS-SIAM Joint Summer Research Conference on Groups, Representations, and Cohomology, Mount Holyoke College, Massachusetts, June 7-13,2002
• Co-organizer, Special Session on Hopf Algebras and Quantum Groups at the AMS Sectional Meeting in New York City, April 12-13, 2003
• Co-organizer, Banff International Research Station Workshop on Hochschild Cohomology of Algebras: Structure and Applications, Banff, Alberta, Canada, September 2-7, 2007


Refereeing and Reviewing:
• Reviewer, Math Reviews, Fall 2004-present
• Referee, NSA and NSF
• Referee, Adv. Math., Algebra Colloq., Algebras and Rep. Th., Commun. Algebra, IMRN, J. Algebra, J. Math. Phys., J. Pure Appl. Algebra, Math. Proc. Royal Irish Acad., Proc. AMS, Rocky Mtn. Math. J.


Miscellaneous:
• Project NExT Panel, Expanding One's Reseach Horizons After the Ph.D., New Orleans, January 7, 2007
• AWM Workshop Mentor, January 7-8, 2007


Conference Talks:
• The quantum double of a finite group, NATO ASI on Finite and Locally Finite Groups, Istanbul, August 26, 1994.
• A module-theoretic approach to Clifford theory for blocks, AMS Special Session, Kent, Ohio, November 4, 1995 (20 minute invited talk).
• Irreducible representations of crossed products, AMS Summer Research Institute on Cohomology, Representations, and Actions of Finite Groups, Seattle, July 17, 1996.
• Irreducible representations of crossed products, AMS Special Session on Hopf Algebras and Their Representations, Caltech, November 17, 1996 (20 minute invited talk).
• Clifford theory for Hopf algebras, Southern California Algebra Conference, UCLA, April 12, 1997 (one hour invited talk).
• The Hochschild cohomology ring of a finite group, Colloque de Luminy, Methodes Homologiques et Representations de Groupes, Luminy, France, July 3, 1997 (one hour invited talk).
• The Hochschild cohomology ring of a group algebra: Connections with the quantum double, AMS Special Session on Representations of Finite Groups , Baltimore, January 9, 1998 (20 minute invited talk).
• A Hopf structure for down-up algebras, MSRI Hopf Algebras Workshop, Berkeley, October 27, 1999.
• Down-up algebras and two-parameter quantum groups, AMS-CMS Special Session on Representations of Infinite Dimensional Lie Algebras, Toronto, September 23, 2000 (20 minute invited talk).
• Hochschild cohomology and Linckelmann cohomology for blocks of finite groups, AMS Special Session, New Orleans, January 12, 2001 (20 minute invited talk).
• Clifford correspondence for Hopf algebras, International Hopf Algebras Conference, DePaul University, Chicago, February 1, 2002 (35 minute invited talk).
• Hochschild cohomology and representations of crossed products, AMS Special Session on Ring Theory, Madison, Wisconsin, October 12, 2002 (20 minute invited talk).
• Algebraic deformations arising from an orbifold with discrete torsion, AMS Special Session on Algebras, Actions, and Algorithms, Baltimore, January 15, 2003 (20 minute invited talk).
• Hochschild cohomology of crossed products, Workshop on Representation Theory, Australian National University, June 30, 2003.
• Ring structures of Hochschild and orbifold cohomology, AMS Special Session on Group Cohomology and Related Topics, Lawrenceville, New Jersey, April 17, 2004 (20 minute invited talk).
• Algebraic deformations arising from quantum group actions, Lie Groups, Lie Algebras, and their Representations Workshop, University of California, Santa Cruz, April 24, 2004 (one hour invited talk).
• Deformations arising from quantum group actions on algebras, CMS Session on Hopf Algebras and Related Topics, Halifax, June 14, 2004 (20 minute invited talk).
• Quantum group actions, R-matrices, and deformations of algebras, AMS Special Session on Algebraic Representations and Deformations, Evanston, IL, October 24, 2004 (20 minute invited talk).
• Deformations of crossed products and graded Hecke algebras, Red Raider Mini-Symposium on Invariant Theory in Perspective, Texas Tech, November 12, 2004 (one hour invited talk).
• Varieties for modules of noncocommutative Hopf algebras, AMS Special Session on Hopf Algebras and Related Topics, Bowling Green, Kentucky, March 19, 2005 (20 minute invited talk).
• Skew derivations and deformations of algebras, AMS-DMV-OMV Special Session on Hopf Algebras and Quantum Groups, Mainz, Germany, June 17, 2005 (25 minute invited talk).
• Graded Hecke algebras and Hochschild cohomology, Session on Homological Methods and Representation Theory at the XVI Coloquio Latinoamericano de Algebra, Colonia, Uruguay, August 4, 2005 (40 minute invited talk).
• Varieties for modules of quantum elementary abelian groups, AMS Special Session on Cohomology and Representation Theory, New Orleans, January 5, 2007 (20 minute invited talk).
• Braid group representations from twisted quantum doubles of finite groups, AMS Special Session on Hopf Algebras and Related Areas, Chicago, October 6, 2007 (20 minute invited talk).
• Quantum groups and pointed Hopf algebras, University of California Lie Theory Workshop in Honor of Georgia Benkart, San Diego, February 18, 2008 (50 minute invited talk).
• Cohomology of finite dimensional pointed Hopf algebras, AMS Special Session on Hopf Algebras and Quantum Groups, Claremont, California, May 4, 2008 (20 minute invited talk).
• Cohomology of pointed Hopf algebras, Rencontre Mathematique, Homologie des algebres: structures et applications, CIRM Luminy, France, December 2, 2008 (1 hour invited talk).
• Nichols algebras in positive characteristic, AMS Special Session on Noncommutative Algebra, Washington, DC, January 6, 2009 (20 minute invited talk).
  
  Colloquium Talks:
• From groups to Hopf algebras, University of Saskatchewan, Canada, November 29, 1996.
• Kaplansky's conjectures on Hopf algebras, University of California, Santa Cruz, February 11, 1997.
• Kaplansky's conjectures on Hopf algebras, New Mexico State University, March 10, 1997.
• Finite groups and Mackey functors, University of Southern California, April 9, 1997.
• Applications of finite group representation theory, Texas A&M University, February 2, 1998.
• Representations of finite groups and Hopf algebras, Loyola University Chicago, March 19, 1998.
• Group cohomology and Hochschild cohomology, University of California, Santa Cruz, November 10, 1998.
• Representations of finite groups and Hopf algebras, Northern Illinois University, De Kalb, November 12, 1999.
• From groups to Hopf algebras, University of Wisconsin, Parkside, May 5, 2000.
• Knots and the Jones polynomial, Amherst College, February 15, 2001.
• Knots and the Jones polynomial, Mount Holyoke College, April 9, 2001.
• Cohomology in Algebra, North Carolina State University, January 31, 2003.
• Cohomology in Algebra, University of Colorado, February 2003.
• Cohomology in Algebra, Texas A&M University, February 24, 2003.
• Algebraic Deformation Theory, University of Saskatchewan, March 18, 2003.
• Cohomology in Algebra, Virginia Tech, October 17, 2003.
• Cohomology and deformations of algebras, Texas A&M University, April 26, 2005.
• Graded Hecke algebras and deformations of crossed products, Bristol-Leicester-Oxford Colloquium, University of Oxford, UK, May 30, 2006.
• Dynkin diagrams in algebra: The old and the new, Sam Houston University, April 4, 2007.
• Dynkin diagrams in algebra, University of South Alabama, September 18, 2008.
  
  Seminar Talks and Other Talks:
• Representations of symmetric groups, Pizza Seminar, University of Chicago, May 10, 1991.
• Simple Lie algebras and groups of Lie type, Junior Seminar on Groups and Geometries, University of Chicago, April 17, 1991.
• The quantum double of a group algebra, Group Theory Seminar, Michigan State University, March 23, 1993.
• The quantum double of a group algebra, Group Theory Seminar, University of Chicago, May 20, 1993.
• Hopf algebras and quantum groups, Pizza Seminar, University of Chicago, June 4, 1993.
• Representations of the quantum double of a finite group, Algebra Seminar, Northwestern University, Evanston, Illinois, November 2, 1993.
• Kaplansky's 10 conjectures on Hopf algebras, Pizza Seminar, University of Chicago, December 3, 1993.
• Quantum doubles and Mackey functors, Group Theory Seminar, University of Chicago, May 12, 1994.
• The quantum double of a finite group, Algebra Seminar, Purdue University, May 27, 1994.
• Projective representations of the quantum double of a finite group, Princeton-Rutgers Group Theory Seminar, Princeton University, February 14, 1995.
• Characters and representations, Applied Group Representations Seminar, University of Toronto, April 4, 1995.
• The representation ring of the twisted quantum double of a finite group, Algebra Seminar, University of Southern California, September 5, 1995.
• Representations of crossed products, Algebra Seminar, McMaster University, Canada, November 15, 1995.
• Representations of Hopf algebras, Lie Groups Seminar, University of Toronto, November 24, 1995.
• Error-detecting and error-correcting codes, Mathematical Science Day, lecture to high school students, University of Toronto, April 27, 1996.
• A conjecture of Kaplansky for finite dimensional Hopf algebras, Quantum Groups Seminar, University of Waterloo, Canada, May 28, 1996.
• A conjecture of Kaplansky for finite dimensional Hopf algebras, Seminar, Mount Allison University, Canada, June 26, 1996.
• A conjecture of Kaplansky for finite dimensional Hopf algebras, Conformal Field Theory Seminar, University of California, Santa Cruz, October 22, 1996.
• Irreducible representations of crossed products, Lie Theory Seminar, University of Saskatchewan, Canada, November 30, 1996.
• Kaplansky's conjectures on Hopf algebras, Seminar, Texas A&M University, March 5, 1997.
• Kaplansky's conjectures on Hopf algebras, Area III Seminar, MSRI, Berkeley, April 2, 1997.
• Clifford theory for Hopf algebras, Commutative Algebra Seminar, University of Illinois, Urbana-Champaign, May 1, 1997.
• The twisted quantum double of a finite group, Quantum Topology Seminar, MSRI, Berkeley, May 9, 1997.
• The Hochschild cohomology ring of a finite group, Algebra Seminar, University of California, Santa Cruz, May 30, 1997.
• Clifford correspondence for Hopf algebras, Oberseminar Hopfalgebren, Universitaet Muenchen, July 22, 1997.
• The Hochschild cohomology ring of a group algebra, Ring Theory Seminar, University of Wisconsin, Madison, February 18, 1998.
• Hopf algebras and Kaplansky's conjecture, Noetherian Ring Seminar, University of Wisconsin, Madison, February 19, 1998.
• Clifford theory, Ring Theory Seminar, University of Wisconsin, Madison, March 31 and April 7, 1999.
• Alperin's weight conjecture, Group Theory Seminar, University of Wisconsin, Madison, November 8 and 15, 1999.
• Mackey functors, Hochschild cohomology, and quantum doubles, Learning Topology Seminar, University of Wisconsin, Madison, November 8 and 15, 1999.
• A Hopf structure for down-up algebras, Ring Theory Seminar, University of Wisconsin, Madison, February 9 and 16, 2000.
• Introduction to quantum groups, Representation Theory Seminar, University of Massachusetts, Amherst, September 18, 2000.
• Two-parameter quantum groups, Hecke algebra representations, and Schur-Weyl duality, Representation Theory Seminar, University of Massachusetts, Amherst, September 25, 2000.
• Quantum groups, Drinfel'd doubles, and down-up algebras, Lie Theory Seminar, University of Wisconsin, Madison, March 20, 2001.
• Clifford correspondence, Number Theory Seminar, Amherst College, October 2, 2001.
• Down-up algebras, quantum groups, and Schur-Weyl duality, Group Theory Seminar, University of Chicago, January 31, 2002.
• Algebraic deformations arising from orbifolds with discrete torsion, Lie Theory Seminar, University of Wisconsin, Madison, October 15, 2002.
• What is (co)homology?, The "What Is . . . ?" Graduate Seminar, University of Massachusetts, Amherst, November 20, 2002.
• Algebraic deformations arising from orbifolds, Valley Geometry Seminar, University of Massachusetts, Amherst, November 22, 2002.
• Hochschild cohomology and orbifolds, Group Theory Seminar, Ohio State University, January 23, 2003.
• Hochschild cohomology and representations of crossed products, Algebra and Logic Seminar, University of Saskatchewan, March 20, 2003.
• Hochschild cohomology and deformations of crossed products, Deformation Theory Seminar, University of Pennsylvania, September 24, 2003.
• Cohomology and deformations of crossed products, Representation Theory Seminar, University of Massachusetts, November 10, 2003.
• Representations of the symmetric groups and cohomology, Discrete Mathematics and Representation Theory Seminar, University of California, Davis, March 5, 2004.
• Algebraic deformations arising from quantum group actions, Algebra Seminar, University of Oregon, April 27, 2004.
• Graded Hecke algebras and deformations of crossed products, Lie Theory Seminar, University of Wisconsin, Madison, October 26, 2004.
• Reflection groups and graded Hecke algebras, Groups and Dynamics Seminar, Texas A&M University, November 3, 2004.
• Quantum groups and deformations of algebras, Graduate Student Organization Seminar, Texas A&M University, November 4, 2004.
• Representations of the symmetric groups and cohomology, Algebra and Combinatorics Seminar, Texas A&M University, February 18, 2005.
• Graded Hecke algebras and deformations of crossed products, Algebra Seminar, University of Texas, Austin, May 3, 2005.
• Twisted graded Hecke algebras, Group Theory Seminar, University of Chicago, May 12, 2005.
• Graded Hecke algebras and deformations of crossed products, Algebra Seminar, DePaul University, Chicago, May 13, 2005.
• Hochschild cohomology, graded Hecke algebras, and Hopf algebra actions, Oberseminar Hopfalgebren, Universitaet Muenchen, December 5 and 9, 2005.
• Hochschild cohomology and graded Hecke algebras, Geometry, Topology, and Algebra Seminar, Universite de Montpellier II, France, March 30, 2006.
• Varieties for modules of finite groups and Hopf algebras, Oberseminar Hopfalgebren, Universitaet Muenchen, Germany, May 4 and 11, 2006.
• Quantum groups and pointed Hopf algebras, Algebra and Combinatorics Seminar, Texas A&M University, September 15, 2006.
• Quantum groups and pointed Hopf algebras, Algebra and Algebraic Geometry Seminar, University of Washington, May 15, 2007.
• Graded Hecke algebras and Hochschild cohomology, I and II, Algebraic Representation Theory Seminar, University of Minnesota, June 14 and 21, 2007.
• When is cohomology finitely generated? Algebra and Combinatorics Seminar, Texas A&M University, November 26, 2007.
• Cohomology of pointed Hopf algebras, Algebra Seminar, University of South Alabama, September 19, 2008.
• Algebras in tensor categories, Working Algebra Seminar, Texas A&M University, September 24 and October 1, 2008.
• Hopf algebras in braided monoidal categories, Working Algebra Seminar, Texas A&M University, November 5, 2008.
• Quantum symmetric algebras, Algebra and Combinatorics Seminar, Texas A&M University, November 7, 2008.
• The bilax structure of the chain complex functor, Working Algebra Seminar, April 10, 2009.
• Knots and the Jones Polynomial, Undergraduate Math Club Meeting, Texas A&M University, April 20, 2009.