## Ben Salisbury

Associate Professor
Department of Mathematics
Central Michigan University

Office: Pearce 206H
Phone: (989) 774-3086

Email: ben DOT salisbury AT cmich DOT edu

Curriculum Vitae

### Research

My research interests lie in combinatorial representation theory. More specifically, I study combinatorial crystal graphs and their applications.

Journal articles

 [14] PBW bases and marginally large tableaux in types B and C (with J. Criswell and P. Tingley), to appear in Canad. Math. Bull. [13] Counting Anosov graphs (with M. Mainkar and M. Plante), Ars Combin. 141 (2018), 29–51. [12] Virtual crystals and Nakajima monomials (with T. Scrimshaw), SIGMA 14 (2018), 103, 19 pages. [11] Rigged configurations and the $*$-involution (with T. Scrimshaw), Lett. Math. Phys. 108 (2018), no. 9, 1985–2007. [10] Combinatorial descriptions of the crystal structure on certain PBW bases (with A. Schultze and P. Tingley), Transform. Groups 23 (2018), no. 2, 501–525. [9] PBW bases and marginally large tableaux in type D (with A. Schultze and P. Tingley), J. Comb. 9 (2018), no. 3, 535–551. [8] The weight function for monomial crystals of affine type (with L. James), Comm. Alg. 46 (2018), no. 8, 3622–3641. [7] Rigged configurations for all symmetrizable types (with T. Scrimshaw), Electron. J. Combin. 24 (2017), no. 1, #P1.30. [6] Connecting marginally large tableaux and rigged configurations via crystals (with T. Scrimshaw), Algebr. Represent. Theory. 19 (2016), 523–546. [5] A rigged configuration model for $B(\infty)$ (with T. Scrimshaw), J. Combin. Theory Ser. A. 133 (2015), 29–57. [4] The flush statistic on semistandard Young tableaux, C. R. Math. Acad. Sci. Paris, Ser. I 352 (2014), 367–371. [3] Combinatorics of the Casselman–Shalika formula in type A (with K.-H. Lee and P. Lombardo), Proc. Amer. Math. Soc. 142 (2014), 2291–2301. [2] Young tableaux, canonical bases, and the Gindikin–Karpelevich formula (with K.-H. Lee), J. Korean Math. Soc. 51 (2014), no. 2, 289–309. [1] A combinatorial description of the Gindikin–Karpelevich formula in type A (with K.-H. Lee), J. Combin. Theory Ser. A. 119 (2012), 1081–1094.

Conference proceedings

 [5] PBW bases and marginally large tableaux in types B and C (extended abstract) (with J. Criswell and P. Tingley), Proceedings of the 30th International Conference on "Formal Power Series and Algebraic Combinatorics" (Hanover), Sém. Lothar. Combin. 80B (2018), Art. 35, 12 pp. [4] Description of crystals for generalized Kac–Moody algebras using rigged configurations (extended abstract) (with T. Scrimshaw), Proceedings of the 30th International Conference on "Formal Power Series and Algebraic Combinatorics" (Hanover), Sém. Lothar. Combin. 80B (2018), Art. 20, 12 pp. [3] Using rigged configurations to model $B(\infty)$ (extended abstract) (with T. Scrimshaw), Proceedings of the 29th International Conference on "Formal Power Series and Algebraic Combinatorics" (London), Sém. Lothar. Combin. 78B (2017), Art. 34, 12 pp. [2] A combinatorial description of the affine Gindikin–Karpelevich formula of type $A_n^{(1)}$ (with S.-J. Kang, K.-H. Lee, and H. Ryu), Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics, Proc. Sympos. Pure Math., vol. 92, Amer. Math. Soc., Providence, RI, 2016, pp. 145–165. [1] Combinatorial descriptions of the crystal structure on certain PBW bases (extended abstract) (with A. Schultze and P. Tingley), Proceedings of the 28th International Conference on "Formal Power Series and Algebraic Combinatorics" (Vancouver), DMTCS proc. BC (2016), 1063–1074.

### Contributions to SageMath

One may find my contributions to the Sage(-Combinat) project under the username bsalisbury1 on the Sage Trac server.

### Teaching

I have taught a wide range of mathematics courses at Central Michigan University. Detailed information about recent courses can be found on Blackboard (login required). A list of courses taught may be found on my Curriculum Vitae.

Before coming to Central Michigan University, I taught several classes as a graduate student at the University of Connecticut. For information about those courses, please select from the dropdown list below.