Research
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My interests

My mathematical interests include representation theory, combinatorics, centralizer algebras, Lie algebras and quantum groups, symmetric functions, partition algebras, Hecke algebras, BMW algebras, and other amazing quotients of braid algebras.

I work mainly in combinatorial representation theory. Specifically, I study how combinatorial objects (like partitions, tableaux, lattices, etc.) encode structure of algebras similar to the group algebra of the symmetric group, Brauer algebras, graded and affine Temperley-Lieb, Hecke, and Birman-Murakami-Wenzl algebras, etc.. My thesis work, completed in 2010 at the University of Wisconsin--Madison, began the study of two-boundary Hecke algebras.

My CV can be found here.

Publications

  1. Translation functors and Kazhdan-Lusztig multiplicities for the Lie superalgebra p(n), with Martina Balagovic, Inna Entova Aizenbud, Iva Halacheva, Johanna Hennig, Mee Seong Im, Gail Letzter, Emily Norton, Vera Serganova, Catharina Stroppel, preprint.

  2. Two boundary Hecke algebras and combinatorics of type C, with Arun Ram, preprint.

  3. Centralizers of the infinite symmetric group, with Peter Herbrich, DMTCS Proceedings for FPSAC 2014.

  4. Quasi-partition algebra, with Rosa Orellana, to appear in J. Algebra.

  5. Affine and degenerate affine BMW algebras: actions on tensor space, with Arun Ram and Rahbar Virk, Selecta Math., 19-2 (2013) 611--653.

  6. Affine and degenerate affine BMW algebras: The center, with Arun Ram and Rahbar Virk, to appear in to appear in Osaka J. Math., 51-1 (2014).

  7. Degenerate two-boundary centralizer algebras, Pacific J. Math., 258-1 (2012) 91--142.

  8. Degenerate two-boundary centralizer algebras, Dissertation (with corrections).

  9. Voting, the symmetric group, and representation theory, with A. K. Eustis, G. Minton, M. E. Orrison, American Mathematical Monthly 116 (2009), no. 8, 667--687.

  10. Integrality of Quotients of Wronskians of the Andrews-Gordon Series, Integers, 6 (2006).

  11. An Algebraic Approach to Voting Theory, Senior thesis, Harvey Mudd College (2005).

Talks

  1. Centralizers of the Lie superalgebra p(n) (where loops go to die), Representation Theory & Physics, University of Leeds, Leeds UK, July 2016. [Slides (.tex)] [Abstract]

  2. Representation theory and combinatorics of diagram algebras, 2nd Annual Graduate Student Conference in Algebra, Geometry, and Topology, Temple University, Philadelphia, PA, May 2016. [Slides (.tex)] [Abstract]

  3. Permutations, partitions, lattices, and some linear algebra: taste of combinatorial representation theory, 6th Annual York College Women In Mathematics Day, York College, New York, NY, April 2016. [Slides (.tex)] [Abstract]

  4. Diagrammatics and actions of the affine BMW algebra, University of Melbourne, Australia, July 2015.

  5. Representations of the two boundary Temperley-Lieb algebra, CUNY Representation Theory Seminar, New York, March 2015. [Slides] [Abstract]

  6. Representation theory and combinatorics of tensor power centralizer algebras, 8th Ausralia New Zealand Mathematics Convention, Melbourne, AU, December 2014. [Slides] [Abstract]

  7. Representations of the infinite symmetric group, Topology and Representation Theory at Kioloa, AU, November 2014. [Abstract]

  8. Tensor spaces, braid groups, and some remarkable quotients, AGT Seminar, The University of Melbourne, September 2014. [Slides] [Abstract]

  9. Representation theory of the two-boundary Temperley-Lieb algebra, Workshop on Diagram Algebras, University of Stuttgart, Germany, September 2014. [Slides] [Abstract]

  10. Central elements as parameters for centraliser algebras, Special program on Algebraic Lie theory and representation theory, ICMS, Edinburgh, September 2014. [Slides] [Abstract]

  11. Representations of the infinite symmetric group, Poster session, FPSAC, Chicago IL, July 2014. [Poster] [Abstract]

  12. Tensor spaces, braid groups, and some remarkable quotients, Colloquium, City College of NY, New York, NY, April 2014. [Slides] [Abstract]

  13. Tensor spaces, braid groups, and some remarkable quotients, Colloquium, University of Hawaii at Manoa, Honolulu HI, February 2014. [Slides] [Abstract]

  14. Centralizer Properties and Combinatorics of Affine Hecke Algebras of Type C, Lie Groups Seminar, Oklahoma State University, Stillwater OK, January 2014. [Slides]

  15. Tensor spaces, braid groups, and some remarkable quotients, Colloquium, Oklahoma State University, Stillwater OK, January 2014. [Slides] [Abstract]

  16. Centralizers of the infinite symmetric group, Algebra seminar, University of Oregon, Eugene OR, December 2013. [Slides (.tex)] [Abstract]

  17. The quasi-partition algebra, Combinatorics seminar, UC Davis, Davis CA, May 2013. [Slides (.tex)] [Abstract]

  18. Combinatorics of affine Hecke algebras of type C, Combinatorics seminar, University of Washington, Seattle WA, May 2013. [Slides (.tex)] [Abstract]

  19. Combinatorics of the two-boundary Hecke algebra, Postdoc and graduate student seminar, Semester Program on "Automorphic Forms, Combinatorial Representation Theory and Multiple Dirichlet Series", ICERM, April 2013. [Slides (.tex)]

  20. The quasi-partition algebra, Discrete Math Day, WPI, Worcester MA, April 2013. [Slides (.tex)] [Abstract]

  21. Combinatorics of affine Hecke algebras of type C, Special Session on Combinatorial Avenues in Representation Theory, AMS meeting, Boulder CO, April 2013. [Slides (.tex)] [Abstract]

  22. The quasi-partition algebra, Discrete math seminar, Brown College, Providence RI, March 2013. [Slides (.tex)] [Abstract]

  23. A taste of combinatorial representation theory, Center for Women in Math at Smith College, March 2013. [Slides (.tex)] [Abstract]

  24. 10-min introduction, ICERM Semester Program on "Automorphic Forms, Combinatorial Representation Theory and Multiple Dirichlet Series", January 2013. [Slides (.tex)]

  25. Two boundary Hecke algebra and the affine Hecke algebra of type C, Special session on Algebraic Combinatorics and Representation Theory, Joint Math Meetings, January 2013. [Slides (.tex)] [Abstract]

  26. The quasi-partition algebra, Algebra and combinatorics seminar, Loyola University, Chicago, December 2012. [Slides (.tex)] [Abstract]

  27. The quasi-partition algebra, Combinatorics seminar, University of Wisconsin, December 2012. [Slides] [Abstract]

  28. Universal parameters for centralizer algebras, Representation theory seminar, Northeastern University, April 2012. [Abstract]

  29. The two-boundary braid group and its amazing quotients, colloquium, Dartmouth College, March 2012. [Slides (.tex)] [Abstract]

  30. Type C symmetry of two-boundary Hecke algebras, AGC Seminar, San Francisco State University, March 2012. [Slides] [Abstract]

  31. The affine BMW algebra and its degenerate version, Algebra, Geometry, and Topology Seminar, University of Melbourne, December 2011. [Abstract]

  32. Type C symmetry in type A representation theory, Combinatorics Seminar, Dartmouth College, November 2011.
  33. The degenerate affine BMW algebra and its center, Special Session on Combinatorial Representation Theory, AMS Spring Eastern Section Meeting, April 2011. [Abstract]

  34. Permutations, braids, partitions, and tableaux: finding the center of the affine BMW algebra, Research Seminar, St. Olaf Mathematics Dept, April 2011. [Abstract]

  35. Centers of the affine BMW algebra and its degenerate version, Special Session on Geometric Commutative Algebra and Applications, AMS Spring Central Section Meeting, March 2011. [Slides] [Abstract]

  36. Two-boundary Hecke algebras and the graded Hecke algebra of type C, Algebraic Lie Theory Seminar, University of Colorado at Boulder, March 2011. [Slides] [Abstract]

  37. The centers of the affine BMW algebra and its degenerate version, Representation Theory seminar, Oklahoma University, January 2011. [Slides] [Abstract]

  38. The degenerate two-boundary Hecke algebra, Algebra, Geometry, and Topology Seminar, University of Melbourne, August 2010. [Abstract]

  39. Two-boundary centralizer algebras, Dissertation defense, University of Wisconsin, May 2010.[Slides]

  40. Degenerate two-boundary centralizer algebras, Algebraic Geometry Seminar, University of Iowa, April 16, 2010.[Abstract]

  41. The degenerate two-boundary Hecke algebra, Special Session on Combinatorial Representation Theory, 2010 Spring Central Sectional Meeting, April 11, 2010. [Abstract]

  42. Combinatorics of Centralizer Algebras, Colloquium, Swarthmore, April, 2010.

  43. Combinatorics of Centralizer Algebras, Colloquium, Vassar College, March 30, 2010.

  44. Algebra and Voting Theory, St. Olaf College, March 22, 2010.

  45. Degenerate Two-boundary Centralizer Algebras, Lie Group/Quantum Mathematics Seminar, Rutgers University, January 22, 2010. [Slides]

  46. Two-Boundary Graded Centralizer Algebras, Special Session on Representation Theory, 2009 Fall Western Section Meeting, November 8, 2009. [Slides]

  47. Building two-boundary graded diagram algebras, Special Session on Lie Groups, Lie Algebras, and Representations, Fall Central Section Meeting, October 16, 2009. [Slides] [Abstract]

  48. Two boundary centralizer algebras, Lie theory seminar, University of Wisconsin -- Madison, October 5, 2009. [Abstract]

  49. Combinatorics and the representation theory of centralizer algebras, Pure maths student seminars, University of Melbourne, August 14, 2009. [Abstract]

  50. Two boundary graded centralizer algebras, Algebra Seminar, University of Sydney, August 7, 2009. [Abstract]

  51. Two boundary graded centralizer algebras, Tuesday seminar at Department of Mathematics and Statistics, University of Melbourne, August 4, 2009.

  52. Building my favorite centralizer algebras, Combinatorics seminar, University of Wisconsin -- Madison, March 2009.

  53. Centralizers and the combinatorics of diagram algebras, Graduate Student Combinatorics Conference, University of California, Davis, April 12, 2008.

  54. Graded diagram algebras, Representation Theory seminar, University of Wisconsin -- Madison, December 7, 2007. [Abstract]

  55. Introduction to affine and graded BMW algebras, Representation Theory seminar, University of Wisconsin -- Madison, April 18, 2007.

  56. An Algebraic Approach to Voting Theory, Presentation days, Harvey Mudd College, May 2005 (an expansion of a talk given in a special session at the AMS/MAA Joint Meetings, Atlanta, Jan. 2005). [Slides] [Abstract]