Education

  • Graduate: University of Pennsylvania, Ph.D., 1991
  • Undergraduate: University of Pennsylvania, B.S., 1986



Academic Appointments

  • 7/12 - Present: Department Chairperson, Mathematics and Statistics, Loyola University Chicago
  • 9/03 - Present: Professor, Loyola University Chicago
  • 8/04 - 6/07: Department Chairperson, Mathematics and Statistics, Loyola University Chicago
  • 9/98 - 8/03: Associate Professor, Loyola University Chicago
  • 1/02 - 5/02: Visiting Associate Professor, University of Pennsylvania
  • 9/97 - 5/98: Visiting Associate Professor: Texas A&M University
  • 9/97 - 8/98: Associate Professor, Mississippi State University
  • 9/95 - 8/97: Assistant Professor, Mississippi State University
  • 9/91 - 8/95: Postdoctoral Assistant Professor: University of Michigan

Funded Research Grants

  • Problems in Lie theory and deformation theory, Co-Principal Investigator, National Security Agency, 2003-2005 
  • Construction of Nonstandard quantum groups, Principal Investigator, National Security Agency, 1998-2000
  • Deformation methods in quantum group and ring theory, Principal Investigator, National Security Agency, 1995-1998
  • Deformation of classical groups and polynomial rings, Principal Investigator, National Security Agency, 1992-1995

Publications

  • An explicit deformation formula with noncommuting derivations, Ring theory (Ramat Gan and Jerusalem, 1988/1989), 396–403, Israel Math. Conf. Proc., 1, Weizmann, Jerusalem, 1989.  (With V. Coll and M. Gerstenhaber)
  • Separable functors revisited. Comm. Algebra 18 (1990), no. 5, 1445–1459. (With F. Van Oystaeyen)
  • Quantization of tensor representations and deformation of matrix bialgebras. J. Pure Appl. Algebra 79 (1992), no. 2, 169–190.
  • Quantum symmetry. Quantum groups (Leningrad, 1990), 9–46, Lecture Notes in Math., 1510, Springer, Berlin, 1992. (With M. Gerstenhaber and S.D. Schack)
  • Quantum groups, cohomology, and preferred deformations. Proceedings of the XXth International Conference on Differential Geometric Methods in Theoretical Physics, Vol. 1, 2 (New York, 1991), 529–538, World Sci. Publ., River Edge, NJ, 1992.  (With M. Gerstenhaber and S.D. Schack)
  • Construction of quantum groups from Belavin-Drinfelʹd infinitesimals. Quantum deformations of algebras and their representations (Ramat-Gan, 1991/1992; Rehovot, 1991/1992), 45–64, Israel Math. Conf. Proc., 7, Bar-Ilan Univ., Ramat Gan, 1993.  (With M. Gerstenhaber and S.D. Schack)
  • Quantum Weyl algebras. J. Algebra 176 (1995), no. 3, 861–881. (With J.J. Zhang)
  • Boundary solutions of the classical Yang-Baxter equation. Lett. Math. Phys. 40 (1997), no. 4, 337–353. (With M. Gerstenhaber)
  • Nonstandard solutions of the Yang-Baxter equation. Lett. Math. Phys. 44 (1998), no. 1, 67–75. (With T. J. Hodges).
  • Bialgebra actions, twists, and universal deformation formulas. J. Pure Appl. Algebra 128 (1998), no. 2, 133–151. (With J.J. Zhang)
  • Boundary solutions of the quantum Yang-Baxter equation and solutions in three dimensions. Lett. Math. Phys. 44 (1998), no. 2, 131–141. (With M. Gerstenhaber)
  • Compatible deformations. Trends in the representation theory of finite-dimensional algebras (Seattle, WA, 1997), 159–168, Contemp. Math., 229, Amer. Math. Soc., Providence, RI, 1998. (With M. Gerstenhaber)
  • Generators and relations for Schur algebras. Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 54–62 (electronic). (With S. Doty)
  • The Donald-Flanigan problem for finite reflection groups. EuroConférence Moshé Flato 2000, Part I (Dijon). Lett. Math. Phys. 56 (2001), no. 1, 41–72. (With M. Gerstenhaber and M. Schaps)
  • Presenting Schur algebras. Int. Math. Res. Not. 2002, no. 36, 1907–1944. (With S. Doty)
  • Algebraic deformations arising from orbifolds with discrete torsion. J. Pure Appl. Algebra 187 (2004), no. 1-3, 51–70. (With A.  Căldăraru and S. Witherspoon)
  • Presenting Schur algebras as quotients of the universal enveloping algebra of gl(2). Algebr. Represent. Theory 7 (2004), no. 1, 1–17. (With S. Doty)
  • Quantum groups and deformation quantization: explicit approaches and implicit aspects. J. Math. Phys. 45 (2004), no. 10, 3703–3741. (With P. Bonneau, M. Gerstenhaber and D. Sternheimer)
  • Diagrams of Lie algebras. J. Pure Appl. Algebra 196 (2005), no. 2-3, 169–184. (With M. Gerstenhaber and S.D. Schack)
  • Presenting generalized Schur algebras in types B, C, and D. Adv. Math. 206 (2006), no. 2, 434–454. (With S. Doty and J. Sullivan)
  • On the defining relations for generalized q-Schur algebras. Adv. Math. 221 (2009), no. 3, 955–982. (With S. Doty and J. Sullivan)
  • The principal element of a Frobenius Lie algebra. Lett. Math. Phys. 88 (2009), no. 1-3, 333–341.
  • Topics in algebraic deformation theory. Higher Structures in Geometry and Physics,  1-24, Progress in Mathematics 287, Springer, New York, 2010.
  • Meander graphs and Frobenius seaweed algebras (with V. Coll and C. Magnant), Journal of Generalized Lie Theory, 5, (2011), 1 - 7 (With V. Coll and C. Magnant).
  • On the cohomology of the Weyl algebra, the quantum plane, and the q-Weyl algebra, Journal of Pure and Applied algebra 218 (2014), 879-887. (With M. Gerstenhaber)
  • Deformations associated with rigid algebras, Journal of Homotopy and Related Structures (2014), in press.

Edited Books



Invited Conference Talks

  • August 1988, Summer program in Brauer groups and module theory, Scuola Normale di Pisa, Cortona, Italy.
  • July 1989, Microprogram on noncommutative ring theory, Mathematical Sciences Research Institute, Berkeley, CA.
  • June 1990, Deformation theory of algebras and quantization with applications to physics, University of Massachusetts, Amherst, MA.
  • July 1991, Summer Institute on algebraic groups and their representations, Pennsylvania State University, State College, PA.
  • September 1991,  Mid-Atlantic conference on developments in algebra related to quantum groups, Wake Forest University, Winston Salem, NC
  • January 1992, U.S.-Israel Binational Science Foundation conference on quantum deformations of algebras and their representations, Bar Ilan University, Ramat Gan, Israel
  • November 1995, Polish Academy of Science conference on quantum groups and quantum spaces, Stefan Banach International Mathematical Center, Warsaw, Poland.
  • May 1996, Benelux Mathematical Congress special session on recent trends in algebra, University of Antwerp, Antwerp, Belgium.
  • June 1996 ETH conference on deformation theory, quantization, and symplectic geometry, Eidgenossiche Techniche Hochschule, Ascona, Switzerland.
  • June 1997, Ring theory and noncommutative projective geometry, Seattle, WA.
  • July 1999, London Mathematical Society workshop on quantum groups, University of Durham, Durham, UK.
  • March 2000, Interactions between noncommutative algebra and algebraic geometry, Mathematical Sciences Research Institute, Berkeley, CA.
  • February 2001, Miniworkshop on Schur Algebras, Mathematisches Forschungsinstitut Oberwolfach, Germany
  • March 2001, Journee Groupes Quantiques, Ecole Normale Superiore, Paris, France.
  • July 2001, American Mathematical Society--Mathematical Society of France Joint Meeting, Ecole Normale Superiore, Lyon, France.
  • October 2001, Midwest Algebra Conference, DePaul University, Chicago, IL.
  • November 2003, Journee Groupes Quantiques, Ecole Normale Superiore, Paris, France.
  • January 2007, Higher Structures in Geometry and Physics, Institute Henri Poincare, Paris, France.
  • July 2009, Hopf-in-Lux School-Conference on Hopf Algebras, University of Luxembourg, Luxembourg.
  • April 2010, Seminaire Sophus Lie, Universite de Haute Alsace, Mulhouse, France.
  • September 2010, Deformation methods in mathematics and physics, Oberwolfach workshop 2010-43, Mathematisches Forschungsinstitut Oberwolfach, Germany.
  • May 2011, NSF/CBMS Conference on deformation theory of algebras and modules, Raleigh, NC.
  • March, 2014, Plenary Speaker, Illinois Section of the MAA, Southern Illinois University, Edwardsville, IL. 
  • December 2014, Algebras, Deformations and Quantum Groups Centre International de Recontres Mathematiques, Luminy, France.

Other Talks

  • October 1992, AMS special session on quantum groups and regular algebras, Dayton, OH.
  • October 1993, AMS special session on representation theory and geometry of noncommutative algebras, College Station, TX.
  • March 1994, Colloquium, SUNY Buffalo, Buffalo, NY.
  • April 1994, Geometry, Physics, and Symmetry seminar, Yale University, New Haven, CT.
  • January 1995,  AMS special session on noncommutative ring theory, San Francisco, CA.
  • March 1995, AMS special session on Hopf algebras and quantum groups, Chicago, IL.
  • February 1997, Colloquium, Emory University, Atlanta, GA. 
  • March 1997, Colloquium, Kent State University, Ken, OH.
  • April 1997, AMS special session on rings and representations, Philadelphia, PA.
  • October 1997, AMS special session on quantum groups and Hopf algebras, Milwaukee, WI.
  • March 1998, Colloquium, California State University Northridge, Northridge, CA.
  • March 1998, Algebra seminar, University of Southern California, Los Angeles, CA.
  • October 1998, AMS special session on symplectic geometry, State College, PA.
  • March 1999, GAP (geometry, algebra, physics) seminar, Pennsylvania State University, State College, PA.
  • February 2000, Deformation theory seminar, University of Pennsylvania, Philadelphia, PA. 
  • March 2000, Physically inspired seminar, University of North Carolina, Chapel Hill, NC.
  • April 2000, Algebra seminar, Virginia Polytechnic University, Blacksburg, VA.
  • May 2000, Colloquium, DePaul University, Chicago, IL.
  • January 2002, Algebra seminar, Temple University, Philadelphia, PA.
  • April 2002, Representation theory seminar, University of Massachusetts, Amherst, MA.
  • March 2003, AMS special session on Hopf algebras and quantum groups, New York, NY.
  • March 2003, Colloquium, University of Glasgow, Glasgow, Scotland.
  • November 2003, Quantum groups seminar, Universite de Bourgogne, Bourgogne, France.
  • April 2004, Deformation theory seminar, University of Pennsylvania, Philadelphia, PA. 
  • April 2004, AMS special session on noncommutative algebra and algebraic geometry, Los Angeles, CA.
  • April 2005, Algebra seminar, Notre Dame Universtiy, South Bend, IN.
  • April 2005, AMS special session on representations of finite dimensional algebras, Santa Barbara, CA.
  • June 2005,  Deformation theory seminar, University of Pennsylvania, Philadelphia, PA. 
  • June 2006, Deformation theory seminar, University of Pennsylvania, Philadelphia, PA. 
  • April 2007, Algebra seminar, Illinois State University, Bloomington, IL.
  • July 2007, Deformation theory seminar, University of Pennsylvania, Philadelphia, PA. 
  • October 2009, AMS special session on noncommutative algebra, Vancouver, British Columbia, CA.
  • March 2010, Lie algebra seminar, Rutgers University, New Brunswick, NJ
  • April 2010, AMS special session on noncommutative geometry and algebra, Lexington, KY.
  • August 2011, Deformation theory seminar, University of Pennsylvania, Philadelphia, PA.
  • October 2011, Algebra/Combinatorics seminar, Texas A & M University, College Station, TX.
  • March 2012, DePaul University colloquium, DePaul University, Chicago, IL.
  • April 2012, Northern Illinois University colloquium, De Kalb, IL.
  • August 2012, Deformation theory seminar, University of Pennsylvania, Philadelphia, PA.
  • July 2013, Deformation theory seminar, University of Pennsylvania, Philadelphia, PA.
  • April 2014, AMS spession on non-commutative algebra, deformations, and Hochschild cohomology, Lubbock, TX.
  • August 2012, Deformation theory seminar, University of Pennsylvania, Philadelphia, PA.

Teaching Experience

  • Mentor of several undergraduate students in research projects concerning Frobenius Lie algebras and quantum groups.
  • Courses taught include honors science and society, honors calculus, calculus, precalculus, linear algebra, advanced linear algebra, statistics, real analysis, abstract algebra, advanced abstract algebra, graduate algebra, geometry, differential equations, and chaos theory.
  • Experienced in teaching calculus using mathematical software such as Maple, Mathematica and WebWork.
  • Co-directed the calculus reform program at the University of Michigan from 1993-1995.

Selected Departmental, University and Other Service

  • Department of Mathematics and Statistics Chairperson, effective July 1, 2012.
  • University Rank and Tenure Committee, September 2011 - May 2012.
  • Coordinator of Departmental Tenure-Track and Non-Tenure Track Hiring Committees, September 2011 - May 2012.
  • College of Arts and Sciences Teaching Committee, September 2011 - May 2012.
  • College of Arts and Sciences Rank, Tenure, and Leave Committee, September 2008 - June 2011. Committee chairperson for academic year 2010-11.
  • Department Hiring Committee - September 2009 - June 2011.
  • Keynote speaker at Chicago high school math teachers' association annual meeting, January 2009.
  • Organized the "Solving for Why" meeting held at Loyola University Chicago between 200 high school and university algebra teachers, April 2008.
  • Department of Mathematics and Statistics Chairperson, August 2004 - June 2007.
  • Co-Organized special session on Representation and Deformation Theory
    at the AMS meeting in Evanston, 2004.
  • Departmental Hiring Committee - September 2003 - May 2004.
  • Computer software and lab needs committee, January, 2003 - August 2004.
  • Faculty status committee, September, 2003 - August 2004.
  • Committee on the Calculus sequence, September, 2003 - August 2004.
  • Graduate Program Director, September 2001 - August 2004.
  • Graduate Council, September 2001 - August 2004.
  • Academic Council, College of Arts and Sciences, September, 2000 - August 2004.
  • Mission, goals and assessment committee, September, 1999 - August 2004.
  • Departmental representative to the core curriculum committee, October, 1999 - 2001.
  • Graduate math committee, September, 1998 - August 2004.
  • Math club advisor, September, 1998 - December, 2001.
  • Taught in the program Michigan mathematics scholars high school program at the University of Michigan for the summers of 1997 and 1998.
  • Referee for Journal of Algebra, Journal of Pure and Applied Algebra, Proceedings of London Mathematical Society, Journal of Lie Theory, Communications in Algebra. 

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