Research

Research Interests:

• Vertex operator algebras

• Kac-Moody Lie algebras

• Relations to q-series, partitions, combinatorics, and number theory

Publications and Preprints:

• Ghost series and a motivated proof of the Bressoud-Göllnitz-Gordon identities, joint work with J. Layne*, S. Marshall*, and E. Shambaugh*, The Ramanujan Journal, to appear. https://arxiv.org/abs/2311.01992  

• Principal subspaces of basic modules for twisted affine Lie algebras, q-series multisums, and Nandi's identities, joint work with K. Baker*, S. Kanade, and M.C. Russell, Algebraic Combinatorics, Volume 6 (2023) no. 6, 1533-1556. Link.

• Weight-one elements of vertex operator algebras and automorphisms of categories of generalized twisted modules, joint work with Y.-Z. Huang, Journal of Algebra, Vol. 628 (2023) 452-485. https://arxiv.org/abs/2211.05334 

• S_3-permutation orbifolds of Virasoro vertex algebras, joint work with A. Milas and M. Penn, Journal of Pure and Applied Algebra 227 (2023).  https://arxiv.org/abs/2209.13341 

• Permutation orbifolds of Virasoro vertex algebras and W-algebras, joint work with A. Milas and M. Penn, Journal of Algebra, Vol. 570 (2021) 267-296. arXiv:2005.08398

• Principal subspaces of twisted modules for lattice vertex operator algebras, joint work with M. Penn and G. Webb*, International Journal of Mathematics, Vol. 30, No. 10, 1950048 (2019). arXiv:1804.09230

• Combinatorial bases of principal subspaces of modules for twisted affine Lie algebras of type $A_{2l-1}^{(2)}, D_l^{(2)}, E_6^{(2)}, and D_4^{(3)}$, joint work with M. Butorac, New York J. Math 25 (2019) 71-106. Link.

• Presentations of principal subspaces of higher level standard $A_2^{(2)}$-modules, joint work with C. Calinescu and M. Penn, Algebras and Representation Theory, 22 (2019), 1457-1478. Link. arXiv:1806.01634

• Vertex-algebraic structure of principal subspaces of basic modules for twisted affine Kac-Moody Lie algebras of type $A_{2n+1}^{(2)}, D_n^{(2)}, E_6^{(2)}$, joint work with M. Penn, Journal of Algebra, Vol. 496 (2018), 242-291. arXiv:1603.02737

• Vertex-algebraic structure of principal subspaces of basic $D_4^{(3)}$-modules, joint work with M. Penn, The Ramanujan Journal, 43:4 (2017), 571-617. Link

• A motivated proof of the Gollnitz-Gordon-Andrews identities, joint work with B. Coulson, S. Kanade, J. Lepowsky, R. McRae, F. Qi, and M.C. Russell, The Ramanujan Journal, 42:1 (2017), 97-129. arXiv:1411.2044

• Principal subspaces of standard sl(n)^-modules, International Journal of Mathematics, Vol. 26, No. 08, 1550063 (2015). arXiv:1406.0095

• Presentations of the principal subspaces of the higher level sl(3)^-modules, Journal of Pure and Applied Algebra, 219 (2015) 2300-2345. arXiv:1312.6412

• On a symmetry of the category of integrable modules, joint work with William J. Cook  New York J. Math. 15 (2009) 133-160. Related Maple code can be found here. arXiv:0901.4791

*Indicates undergraduate co-author

Dissertation: 

• On the structure of principal subspaces of standard modules for affine Lie algebras of type A, Ph.D. dissertation, Rutgers University, May 2014, under the direction of Yi-Zhi Huang and James Lepowsky, Link. 

Conference Organizing:

• Vertex Operator Algebras and Related Topics, virtual, April 9-10, 2021.

• AMS Fall Eastern Section Meeting: Special Session on Representations of Lie Algebras, Vertex Operators, and Related Topics, Binghamton University, October 12-13, 2019.