Research

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.

- The affine VW supercategory, with Martina Balagovic, Zajj Daugherty, Inna Entova-Aizenbud, Iva
Halacheva, Johanna Hennig, Mee Seong Im, Gail Letzter, Emily Norton, Vera Serganova, and Catharina Stroppel, preprint.
- Quasisymmetric Power Sums, with Cristina Ballantine, Angela Hicks, Sarah Mason, and Elizabeth Niese, preprint.
- 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.
- Two boundary Hecke algebras and combinatorics of type C, with Arun Ram, preprint.
- Centralizers of the infinite symmetric group, with Peter Herbrich, DMTCS Proceedings for FPSAC 2014.
- Quasi-partition algebra, with Rosa Orellana, J. Algebra, Vol 404 (2014), 124--151
- Affine and degenerate affine BMW algebras: actions on tensor space, with Arun Ram and Rahbar Virk, Selecta Math., 19-2 (2013) 611--653.
- Affine and degenerate affine BMW algebras: The center, with Arun Ram and Rahbar Virk, Osaka J. Math.,
Volume 51, Number 1 (2014), 257--285.
- Degenerate two-boundary centralizer algebras, Pacific J. Math., 258-1 (2012) 91--142.
- Degenerate two-boundary centralizer algebras, Dissertation.
- 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. - Integrality of Quotients of Wronskians of the Andrews-Gordon Series,
*Integers*,**6**(2006). - An Algebraic Approach to Voting Theory, Senior thesis, Harvey Mudd College (2005).

*Quasisymmetric power sums*, Formal Power Series and Algebraic Combinatorics, Dartmouth College, July 2018. [Slides (.tex)] [Abstract]*The affine signed Brauer algebra*, Special Session on Combinatorial Representation Theory, Spring Eastern Sectional Meeting, Northeastern University, April 2018. [Slides (.tex)] [Abstract]*Quasisymmetric power sums*, New York Combinatorics Seminar, CUNY Graduate Center, March 2018. [Abstract]*Representations of the periplectic Lie superalgebra*, 3rd meeting of the US-Mexico Conference on Representation Theory, Categorification, and Noncommutative Algebra, Mexico City, MX, November 2017. [Slides (.tex)] [Abstract]*Quasisymmetric power sums*, Discrete Math Day at Queens College, Queens NY, October 2017. [Slides (.tex)] [Abstract]*Two-boundary diagram algebras*, Colloquium, Bronx Community College, Bronx NY, October 2017. [Slides (.tex)] [Abstract]*Representation theory and combinatorics of two-boundary Temperley-Lieb algebras*, Mathematical Physics Seminar, Centre de recherches mathematiques, Montreal, April 2017. [Abstract]*Brauer algebras and their generalizations*, Colloquium, New York City College of Technology, Brooklyn, NY, March 2017. [Abstract]*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]*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]*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]*Diagrammatics and actions of the affine BMW algebra*, University of Melbourne, Australia, July 2015.*Representations of the two boundary Temperley-Lieb algebra*, CUNY Representation Theory Seminar, New York, March 2015. [Slides] [Abstract]*Representation theory and combinatorics of tensor power centralizer algebras*, 8th Ausralia New Zealand Mathematics Convention, Melbourne, AU, December 2014. [Slides] [Abstract]*Representations of the infinite symmetric group*, Topology and Representation Theory at Kioloa, AU, November 2014. [Abstract]*Tensor spaces, braid groups, and some remarkable quotients*, AGT Seminar, The University of Melbourne, September 2014. [Slides] [Abstract]*Representation theory of the two-boundary Temperley-Lieb algebra*, Workshop on Diagram Algebras, University of Stuttgart, Germany, September 2014. [Slides] [Abstract]*Central elements as parameters for centraliser algebras*, Special program on Algebraic Lie theory and representation theory, ICMS, Edinburgh, September 2014. [Slides] [Abstract]*Representations of the infinite symmetric group*, Poster session, FPSAC, Chicago IL, July 2014. [Poster] [Abstract]*Tensor spaces, braid groups, and some remarkable quotients*, Colloquium, City College of NY, New York, NY, April 2014. [Slides] [Abstract]*Tensor spaces, braid groups, and some remarkable quotients*, Colloquium, University of Hawaii at Manoa, Honolulu HI, February 2014. [Slides] [Abstract]*Centralizer Properties and Combinatorics of Affine Hecke Algebras of Type C*, Lie Groups Seminar, Oklahoma State University, Stillwater OK, January 2014. [Slides]*Tensor spaces, braid groups, and some remarkable quotients*, Colloquium, Oklahoma State University, Stillwater OK, January 2014. [Slides] [Abstract]*Centralizers of the infinite symmetric group*, Algebra seminar, University of Oregon, Eugene OR, December 2013. [Slides (.tex)] [Abstract]*The quasi-partition algebra*, Combinatorics seminar, UC Davis, Davis CA, May 2013. [Slides (.tex)] [Abstract]*Combinatorics of affine Hecke algebras of type C*, Combinatorics seminar, University of Washington, Seattle WA, May 2013. [Slides (.tex)] [Abstract]*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)]*The quasi-partition algebra*, Discrete Math Day, WPI, Worcester MA, April 2013. [Slides (.tex)] [Abstract]*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]*The quasi-partition algebra*, Discrete math seminar, Brown College, Providence RI, March 2013. [Slides (.tex)] [Abstract]*A taste of combinatorial representation theory*, Center for Women in Math at Smith College, March 2013. [Slides (.tex)] [Abstract]*10-min introduction*, ICERM Semester Program on "Automorphic Forms, Combinatorial Representation Theory and Multiple Dirichlet Series", January 2013. [Slides (.tex)]*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]-
*The quasi-partition algebra*, Algebra and combinatorics seminar, Loyola University, Chicago, December 2012. [Slides (.tex)] [Abstract] -
*The quasi-partition algebra*, Combinatorics seminar, University of Wisconsin, December 2012. [Slides] [Abstract] -
*Universal parameters for centralizer algebras*, Representation theory seminar, Northeastern University, April 2012. [Abstract] -
*The two-boundary braid group and its amazing quotients*, colloquium, Dartmouth College, March 2012. [Slides (.tex)] [Abstract] -
*Type C symmetry of two-boundary Hecke algebras*, AGC Seminar, San Francisco State University, March 2012. [Slides] [Abstract] -
*The affine BMW algebra and its degenerate version*, Algebra, Geometry, and Topology Seminar, University of Melbourne, December 2011. [Abstract] -
*Type C symmetry in type A representation theory*, Combinatorics Seminar, Dartmouth College, November 2011. -
*The degenerate affine BMW algebra and its center*, Special Session on Combinatorial Representation Theory, AMS Spring Eastern Section Meeting, April 2011. [Abstract] -
*Permutations, braids, partitions, and tableaux: finding the center of the affine BMW algebra*, Research Seminar, St. Olaf Mathematics Dept, April 2011. [Abstract] *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]-
*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] *The centers of the affine BMW algebra and its degenerate version*, Representation Theory seminar, Oklahoma University, January 2011. [Slides] [Abstract]*The degenerate two-boundary Hecke algebra*, Algebra, Geometry, and Topology Seminar, University of Melbourne, August 2010. [Abstract]*Two-boundary centralizer algebras*, Dissertation defense, University of Wisconsin, May 2010.[Slides]*Degenerate two-boundary centralizer algebras*, Algebraic Geometry Seminar, University of Iowa, April 16, 2010.[Abstract]*The degenerate two-boundary Hecke algebra*, Special Session on Combinatorial Representation Theory, 2010 Spring Central Sectional Meeting, April 11, 2010. [Abstract]*Combinatorics of Centralizer Algebras*, Colloquium, Swarthmore, April, 2010.*Combinatorics of Centralizer Algebras*, Colloquium, Vassar College, March 30, 2010.*Algebra and Voting Theory*, St. Olaf College, March 22, 2010.*Degenerate Two-boundary Centralizer Algebras*, Lie Group/Quantum Mathematics Seminar, Rutgers University, January 22, 2010. [Slides]*Two-Boundary Graded Centralizer Algebras*, Special Session on Representation Theory, 2009 Fall Western Section Meeting, November 8, 2009. [Slides]*Building two-boundary graded diagram algebras*, Special Session on Lie Groups, Lie Algebras, and Representations, Fall Central Section Meeting, October 16, 2009. [Slides] [Abstract]*Two boundary centralizer algebras*, Lie theory seminar, University of Wisconsin -- Madison, October 5, 2009. [Abstract]*Combinatorics and the representation theory of centralizer algebras*, Pure maths student seminars, University of Melbourne, August 14, 2009. [Abstract]*Two boundary graded centralizer algebras*, Algebra Seminar, University of Sydney, August 7, 2009. [Abstract]*Two boundary graded centralizer algebras*, Tuesday seminar at Department of Mathematics and Statistics, University of Melbourne, August 4, 2009.*Building my favorite centralizer algebras*, Combinatorics seminar, University of Wisconsin -- Madison, March 2009.*Centralizers and the combinatorics of diagram algebras*, Graduate Student Combinatorics Conference, University of California, Davis, April 12, 2008.*Graded diagram algebras*, Representation Theory seminar, University of Wisconsin -- Madison, December 7, 2007. [Abstract]*Introduction to affine and graded BMW algebras*, Representation Theory seminar, University of Wisconsin -- Madison, April 18, 2007.*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]