Curriculum Vita
Research Statement

ACCEPTED AND PUBLISHED PAPERS

• The Kontsevich integral and quantized Lie superalgebras.  Algebraic and Geometric Topology, 5 (2005), no. 45, 1111-1139.  Link to paper.
  
• The Etingof-Kazhdan quantization of Lie superbialgebras.  Advances of Mathematics, 207 (2006), no. 1, 1-38.  math.QA/0409563
• (with B. Patureau-Mirand)  Multivariable link invariants arising from sl(2|1) and the Alexander polynomial. Journal of Pure and Applied Algebra, 210 (2007),  no. 1, 283-298. math.GT/0601291
• Some remarks on quantized Lie superalgebras of classical type, Journal of Algebra, 314 (2007) no. 2, 565-580.  math.QA/0508440
• (with P. Etingof)  Monodromy of the trigonometric KZ equations, to appear in International Mathematics Research Notices. math.QA/0611003

SUBMITTED PUBLICATIONS

• (with B. Patureau-Mirand)  Multivariable link invariants arising from Lie superalgebras of type I, submitted. math.GT/0609034
• (with B. Enriquez)  Compatibility of quantization functors of Lie bialgebras with duality and doubling operations, submitted. arXiv:0707.2337
• (with B. Patureau-Mirand)  On the colored HOMFLY-PT, multivariable and Kashaev link invariants, submitted. arXiv:0711.4226
• (with B. Patureau-Mirand and V. Turaev)  Modified quantum dimensions and re-normalized link invariants, submitted. arXiv:0711.4229
• (with B. Patureau-Mirand)  An invariant trace for the category of representations of Lie superalgebras, submitted. arXiv:0711.4231

MANUSCRIPTS IN PREPARATION

• (with G. Karaali)  Quantization of super dynamical r-matrices.
  

RECENT INVITED CONFERENCE LECTURES

• Cascade Topology Seminar, Boise, Idaho, October 2007
  
• International Conference on Quantum Topology,  Ha-Noi, Vietnam, August 2007
• International Congress of Mathematicians, Short Communication, Madrid, Spain, August 2006
• Symposium about Pure Mathematics, University of Zurich, Switzerland, June 2006
• Special Session on Quantum Invariants of Knots and 3-Manifolds, AMS National Meeting, San Antonio, TX, January 2006
• Special Session on Quantum Knot Invariants, Joint Meeting of AMS, DMV, and MG, Mainz, Germany, June 2005
• Workshop on Representation Theory and Geometry, University of California, Berkeley, CA, May 2005
• Special Session on Quantum Topology, AMS National Meeting, Atlanta, GA, January 2005
• Special Session on Low-Dimensional Topology, AMS National Meeting, Phoenix, AZ, January 2004
• Knots in Poland 2003, Bedlewo, Poland, July 2003

RECENT INVITED COLLOQUIA AND SEMINAR LECTURES

• University of California, Riverside, Colloquium, Riverside, CA, November 2007
  
• Indiana University, Topology Seminar, Bloomington, IN, October 2007
  
• Georgia Institute of Technology, Geometry and Topology Seminar, Atlanta, GA, October 2007
• University of California, Berkeley, Subfactor Seminar, Berkeley, CA, October 2007
• University of California, Davis, Geometry/Topology Seminar, Davis, CA, October 2007
• University of California, Santa Cruz, Algebra and Number Theory Seminar, Santa Cruz, CA, October 2007
• University of Oregon, Basic Notions Seminar, Eugene, OR, October 2007
• Massachusetts Institute of Technology, Infinite-Dimensional Algebra Seminar, Boston, MA, September, 2007
• University of Wisconsin-Madison, Lie Theory Seminar, Madison, WI, September, 2007
  
• Universit de Bretagne Sud, Seminaire du LMAM, Vannes, France, July 2007
• Institut de Recherche Mathmatique Avance, Seminaire Quantique, Strasbourg, France, May 2007
• Georgia Institute of Technology, Geometry and Topology Seminar, Atlanta, GA, March 2007
• Boise State University, Colloquium, Boise, ID, March 2007
• University of Calgary, Colloquium, Calgary, Canada, March 2007
• Georgia Institute of Technology, Geometry and Topology Seminar, Atlanta, GA, October 2006
  
• University of Nantes, Topology Seminar, Nantes, France, April 2006
• Jussieu Institute of Mathematics (Paris VII), Topology Seminar, Paris, France, April 2006
• University of Oregon, Colloquium, Eugene, OR, March 2006
• Emory University, Topology Seminar, Atlanta, GA, February 2006
• University of Georgia, Topology/Geometry Seminar, Athens, GA, January 2006
  
• Institut de Recherche Mathematique Avancee, Seminaire Quantique, Strasbourg, France, June 2005
• Universite de Bretagne Sud, Seminaire du LMAM, Vannes, France, June 2005
• Massachusetts Institute of Technology, Infinite-Dimensional Algebra Seminar, Boston, MA, February 2005
• Georgia Institute of Technology, Geometry and Topology Seminar, Atlanta, GA, September 2004
  
• University of Georgia, Algebra Seminar, Athens, GA, September 2004
• Georgia Institute of Technology, Colloquium, Atlanta, GA, January 2004
• University of Oregon, Topology Seminar, Eugene, OR, January 2004
• University of Oregon, Algebra Seminar, Eugene, OR, June 2003