Research

Research Interests

• Quantum Groups, Hopf Algebras
• Super Representation Theory, Lie Superalgebras
• Combinatorial Representation Theory

Publications and Preprints

Research Papers (You can find preliminary versions / preprints of these papers on the arxiv):

• Spanning sets for Moebius vertex algebras satisfying arbitrary difference conditions; with Geoffrey Buhl
  J. Algebra 320 (2008), pp.3345--3364.


• On Hopf Algebras and Their Generalizations;
  to appear in Comm. Algebra.


• Dynamical Quantum Groups - The Super Story;
  Contemp. Math. 441 (2007), pp.19-52.
  MR2381534


• Super Solutions of the Dynamical Yang-Baxter Equation;
  Proc. Amer. Math. Soc. 134 (2006), pp.2521-2531.
  MR2262367


• A New Lie Bialgebra Structure on sl(2,1);
  Contemp. Math. 413 (2006), pp.101-122.
  MR2213729


• Constructing r-matrices on Simple Lie Superalgebras;
  J. Algebra 282 (2004), pp.83-102.
  MR2095573

Short Survey Articles (These were written at various times for various reasons and put here for whoever may find them interesting or useful):

• Deformation Quantization - A Brief Survey (PDF)


• (Kaehler-)Ricci Flow on (Kaehler) Manifolds (PDF)


• Basic Facts about Weakly Symmetric Spaces (PDF)


• Quantum Moment(um) Map(ping)s - A Hopf Algebra Approach (PDF)


• Flag Manifolds and Toric Geometry (PDF)

Presentations, Seminars and Conference Talks

Research Seminars and Conference Talks

• International Workshop on Lie Theory and Its Applications in Physics, Varna, Bulgaria;
  Title: On Hopf algebras and their generalizations;
  (June 2007)


• Workshop on Representation Theory and Geometry, Berkeley, CA;
  Title: On Generalizations of Hopf algebras;
  (May 2006)


• U.C. Riverside Lie Theory Seminar;
  Title: Super solutions of the Yang-Baxter equations;
  (February 2006)


• University of Arkansas Mathematics Colloquium, Fayetteville, AR;
  Title: Yang-Baxter equations and their super solutions;
  (February 2006)


• University of Hawaii Mathematics Colloquium;
  Title: Yang-Baxter equations and their super solutions;
  (February 2006)


• North Dakota State Mathematics Colloquium, Fargo, ND;
  Title: Yang-Baxter equations and their super solutions;
  (January 2006)


• AWM Workshop for Women Graduate Students and Recent Ph.D.'s, San Antonio, TX;
  Title: The Road to Super Quantum Groups;
  (January 2006)


• Georgia Tech Algebra-Geometry-Topology Seminar, Atlanta, GA;
  Title: Yang-Baxter Equations and Their Super Solutions;
  (November 2005)


• Southern California Algebra Conference, Los Angeles, CA;
  Title: What should a dynamical quantum super group be?;
  (November 2005)


• Bogazici University Mathematics Colloquium, Istanbul, Turkey;
  Title: The Road to Super Quantum Groups;
  (July 2005)


• Antalya Algebra Days - VII, Antalya, Turkey;
  Title: Dynamical Quantum Groups - The Super Story;
  (May 2005)


• Geometric Representation Theory, Tucson, AZ;
  Title: Super Solutions of the Dynamical Yang-Baxter Equation;
  (March 2005)


• U.C. Santa Barbara Algebra Seminar;
  Title: Super Lie Bialgebra Structures;
  (November 2004)


• AMS Special Session on Hopf Algebras at the Crossroads of Algebra, Category Theory, and Topology
  (AMS Sectional Meeting #1001), Evanston, IL;
  Title: A new Lie bialgebra structure on sl(2,1);
  (October 2004)


• AMS-IMS-SIAM Summer Research Conference on Representations of Algebraic Groups, Quantum Groups and Lie Algebras, Snowbird, UT;
  Title: How to construct an r-matrix on a Lie Superalgebra;
  (July 2004)


• U.C. Santa Barbara Algebra Seminar;
  Title: Constructing r-matrices on Lie Superalgebras;
  (February 2004)


• University of Southern California Algebra Seminar;
  Title: r-matrices on Lie Superalgebras;
  (October 2003)


• Workshop on Lie Groups, Lie Algebras and Their Representations, Santa Barbara, CA;
  Title: Constructing r-matrices on Lie Superalgebras;
  (October 2003)

Poster Presentations

• CRM Workshop on Combinatorial Hopf Algebras and Macdonald Polynomials, Montreal, Quebec;
  Title: On Hopf Algebras and Their Generalizations;
  (May, 2007)


• Project NExT/Young Mathematician's Network Poster Session, New Orleans, LA;
  Title: On Hopf Algebras and Their Generalizations;
  (January 2007)


• AWM Workshop for Women Graduate Students and Recent Ph.D.'s, Phoenix, AZ;
  Title: r-matrices on Lie Superalgebras;
  (January 2004)

Expository Talks

• California State Polytechnic University Mathematics Collloquium, Pomona, CA;
  Title: Yang-Baxter equations and quantum groups;
  (May 2008)


• California State University San Bernardino Mathematics Collloquium, San Bernardino, CA;
  Title: Algebra for the Quantum World;
  (May 2007)


• Southeastern Louisiana University Algebra Seminar, Hammond, LA;
  Title: A Beginner's Guide to Hopf Algebras;
  (April 2007)


• Southeastern Louisiana University Mathematics Collloquium, Hammond, LA;
  Title: Algebra for the Quantum World;
  (April 2007)


• California State University Dominguez Hills Mathematics Collloquium, Carson, CA;
  Title: Algebra for the Quantum World;
  (March 2007)


• Claremont Colleges Algebra/Combinatorics Seminar, Claremont, CA;
  Title: A Beginner's Guide to Hopf Algebras;
  (February 2007)


• California State University Los Angeles Mathematics Collloquium, Los Angeles, CA;
  Title: Algebra for the Quantum World;
  (January 2007)


• University of Southern California Math Talks for Women in Mathematics, Los Angeles, CA;
  Title: Yang-Baxter equations and quantum groups;
  (April 2006)


• Pomona College Undergraduate Mathematics Talk, Claremont, CA;
  Title: Algebra for the Quantum World;
  (February 2006)


• Vassar College Mathematics Colloqium, Poughkeepsie, NY;
  Title: Algebra for the Quantum World;
  (February 2006)


• Colby College Mathematics Colloqium, Waterville, ME;
  Title: Algebra for the Quantum World;
  (December 2005)


• Mathematics Graduate Seminar - CSU Channel Islands, Camarillo, CA;
  Title: Algebra for the Quantum World - A Basic Introduction to Quantum Groups;
  (September 2005)


• U.C. Santa Barbara Undergraduate Linear Algebra Seminar;
  Title: Symmetries and Matrices - An Elementary Introduction to Representation Theory;
  (May 2005)


• U.C. Santa Barbara Algebra Seminar;
  Title: On the Classification of Finite-Type Cluster Algebras;
  (February 2005)


• U.C. Santa Barbara Combinatorics and Discrete Geometry Seminar;
  Title: Combinatorics in Representation Theory - series of two lectures;
  (December 2004 and February 2005)


• U.C. Berkeley Seminar on Representations of Lie Groups;
  Title: A Short Course on Poisson-Lie Groups - series of four lectures with Milen Yakimov;
  (April 2001)

Talks about Teaching Mathematics, Pedagody and Mathematics Education

• MathFEST 2008 - Contributed Paper Session on Incorporating Humanities and the Arts into the Mathematics Classroom (and Vice Versa), Madison, WI;
  Title: An "Unreasonable" Reading Component to a Reasonable Course: Readings for a Transitional Class;
  (August 2008)


• MAA Southern California/Nevada Section Spring 2007 Meeting, Claremont, CA;
  Title: Math Digital Libraries a presentation with Robert Baker;
  (March 2007)


• Third International Conference on the Teaching of Mathematics (ICTM3), Istanbul, Turkey;
  Title: What does that mean? Helping Upper Division Students Understand Concepts;
  (June 2006)


• MathFEST 2005 - General Contributed Paper Session, Albuquerque, NM;
  Title: Word Problems and Quantitative Literacy;
  (August 2005)

Other Conferences, Minicourses and Workshops Attended

Research Conferences and Workshops

• Special Session on Hopf Algebras and Quantum Groups, 2008 Spring Western Section Meeting of the American Mathematical Society (Meeting #1039) ,
  Claremont, CA; (May 3-4, 2008)
  Co-organizer of the session, with Susan Montgomery (USC) and Serban Raianu (Cal State Domnguez Hills)


• MSRI Workshop on Topics in Combinatorial Representation Theory,
  Berkeley, CA; (March 17-21, 2008)


• Southern California Algebra Conference,
  Los Angeles, CA; (February 23, 2008)


• MSRI Connections for Women workshop on Combinatorial Representation Theory and Representations of Finite Groups,
  Berkeley, CA; (January 16-18, 2008)


• CRM Workshop on Combinatorial Hopf Algebras and Macdonald Polynomials,
  Montreal, Quebec; (May 7-11, 2007)


• AIM Workshop on Buildings and combinatorial representation theory,
  Palo Alto, CA; (March 26-30, 2007)


• Southern California Algebra Conference,
  Los Angeles, CA; (November 18, 2006)


• NSF-CBMS Regional Conference on Cluster Algebras and Applications,
  Raleigh, NC; (June 13-17, 2006)


• Geometry and Representation Theory, A Conference in Honor of George Lusztig,
  Cambridge, MA; (May 30 - June 3, 2006)


• Geometric Group Theory, University of Arkansas Spring Lecture Series 2006
  Fayetteville, AR; (April 5-8, 2006)


• Workshop on Lie Groups, Lie Algebras and Their Representations,
  Eugene, OR; (October 8-9, 2005)


• Southern California Algebra Conference,
  Los Angeles, CA; (February 26, 2005)


• Southern California Algebra Conference,
  Los Angeles, CA; (November 6, 2004)


• Interactions between Representation Theories, Knot Theory, Topology, Quantum Field Theory, Category Theory, and Mathematical Physics,
  Potsdam, NY; (June 2-6, 2003)


• Workshop on Lie Groups, Lie Algebras and Their Representations,
  Riverside, CA; (March 9-10, 2002)


• Workshop on Representation of Loop Groups,
  Institute for Pure and Applied Mathematics, Los Angeles, CA; (November 12-16, 2001)

Scholarship of Teaching and Learning, Pedagody and Mathematics Education

• MAA Minicourse on Teaching a Proof-Based Course as the Gateway to the Mathematics Major,
  MathFEST 2008, Madison, WI; (July 31-August 2, 2008)


• Boot Camp for Profs 2008,
  Leadville, CO; (July 19-25, 2008)


• Pomona College TLC Workshop: Team Teaching Interdisciplinary Courses,
  Claremont, CA; (April 15, 2008)


• IME (Institute for Mathematics and Education) Workshop for Mathematicians in Mathematics Education (MIME),
  Tucson, AZ; (March 20-22, 2008)


• MAA Minicourse on Evaluating Student Presentations in Mathematics,
  Joint Mathematics Meeting, San Diego, CA; (January 7-9, 2008)


• MAA Minicourse on Directing Undergraduate Research,
  Joint Mathematics Meeting, San Diego, CA; (January 6-8, 2008)


• MAA Minicourse on Using History of Calculus to Enhance Its Teaching,
  MathFEST 2007, San Jose, CA; (August 3-5, 2007)


• Pomona College Writing Center Workshop: Responding to Student Writing - How can we help student writing improve through comments on a single paper?,
  Claremont, CA; (February 22, 2007)


• NITLE Workshop on Emerging Technologies and the Liberal Arts Campus,
  Claremont, CA; (January 11, 2007)


• MAA Minicourse on Scholarship of Teaching and Learning,
  Joint Mathematics Meetings 2007, New Orleans, LA; (January 6-8, 2007)

Miscellaneous Topics

• MAA Minicourse on A Game Theory Path to Quantitative Literacy,
  MathFEST 2008, Madison, WI; (July 31-August 2, 2008)


• MAA Short Course: Game-theoretic Modeling: Techniques and Applications,
  MathFEST 2008, Madison, WI; (July 29-30, 2008)


• MAA Short Course: Combinatorics: Past, Present, and Future,
  Joint Mathematics Meeting 2008, San Diego, CA; (January 4-5, 2008)


• MAA Digital Library Workshop,
  Washington, DC; (October 6-8, 2006)


• MAA Minicourse on Mathematical Finance,
  MathFEST 2005, Albuquerque, NM; (August 4-5, 2005)


• MAA PREP - MSRI Workshop on Geometric Combinatorics,
  Mathematical Sciences Research Institute, Berkeley, CA; (June 6-9, 2005)