# Travis Scrimshaw's homepage

## Background

I received my Ph.D. in Mathematics from University of California, Davis in 2015 under the guidance of Anne Schilling. From 2015 to 2017, I an RTG Postdoctoral Associate as part of the combinatorics group at the University of Minnesota, specifically under the mentorship of Pavlo Pylyavskyy. I am currently a Postdoctoral Research Fellow at the University of Queensland under the mentorship of Ole Warnaar.

My primary research interests are in combinatorics and representation theory, specifically in the area of crystals and (Kac--Moody) Lie algebras. My research focuses on a specific class of finite crystals for affine Lie algebras called *Kirillov-Reshetikhin (KR) crystals* and combinatorial objects called *rigged configurations*. The (conjectural) bijection between tensor products of KR crystals and rigged configurations of objects arose from statistical mechanics and has led to applications in soliton cellular automata, a generalization of the box-ball system. Characters of tensor products of KR crystals also have deep connections with other areas of mathematics, including Macdonald symmetric functions and Q-systems. Ben Salisbury and I have also generalized rigged configurations to be a model for highest weight crystals, where they appear to be a very natural model.

Recently I have become interested in generalizations of crystals; specifically in geometric crystals, a rational lifting of crystals, and crystals for Kac-Moody superalgebras and Borcherds algebras. I have additional interests in combinatorial Hopf algebras, which includes symmetric functions, Coxeter and Artin groups, and Hecke algebras.

I have also been a developer for the open-source mathematical software SageMath since 2010 and have been programming in various languages since 2001.

Email: tcscrims {a} gmail.com

## Publications

- Cara Monical, Oliver Pechenik, and T. Scrimshaw: Crystal structures for symmetric Grothendieck polynomials. Preprint, (2018). arXiv version.
- Se-jin Oh and T. Scrimshaw:
*Identities from representation theory*. Preprint, (2018). arXiv version. - Se-jin Oh and T. Scrimshaw:
*Categorical relations between Langlands dual quantum affine algebras: Exceptional cases*. Preprint, (2018). arXiv version. - Jia Huang, Brendon Rhoades, and T. Scrimshaw: Hall-Littlewood polynomials and a Hecke action on ordered set partitions. Proc. Amer. Math. Soc., to appear (2018). arXiv version.
- Ben Salisbury and T. Scrimshaw:
*Virtual crystals and Nakajima monomials*. Preprint, (2017). arXiv version. - Masato Okado, Anne Schilling and T. Scrimshaw:
*Rigged configuration bijection and the proof of the $X = M$ conjecture for nonexceptional affine types*. Preprint, (2017). arXiv version. - Xuan Liu and T. Scrimshaw:
*A uniform approach to soliton cellular automata using rigged configurations*. Preprint, (2017). arXiv version. SageMath code. - T. Scrimshaw:
*Uniform description of the rigged configuration bijection*. Preprint, (2017). arXiv version. - Arthur Lubovsky and T. Scrimshaw:
*Alcove path model for $B(\infty)$*. Preprint, (2016). arXiv version. - Emily Gunawan and T. Scrimshaw:
*Kirillov--Reshetikhin crystals $B^{1,s}$ using Nakajima monomials for $\widehat{\mathfrak{sl}}_n$*. Preprint, (2016). arXiv version. - T. Scrimshaw:
*Rigged configurations as tropicalizations of loop Schur functions*. J. Integrable Syst., {\bf 2}(1) (2017) pp. 1--24. DOI: 10.1093/integr/xyw015, arXiv version. - Masato Okado, Reiho Sakamoto, Anne Schilling and T. Scrimshaw:
*Type $D_n^{(1)}$ rigged configuration bijection*. J. Algebraic Combin., {\bf 46}(2) (2017) pp. 341--401. arXiv version. - Ben Salisbury and T. Scrimshaw:
*Rigged configurations and the $\ast$-involution*. Lett. Math. Phys., to appear (2018). DOI: 10.1007/s11005-018-1063-2, arXiv version. - Jianping Pan and T. Scrimshaw:
*Virtualization map for the Littelmann path model*. Transform. Groups, to appear (2017). DOI: 10.1007/s00031-017-9456-3, arXiv version. - Ben Salisbury and T. Scrimshaw:
*Rigged configurations for all symmetrizable types*. Electron. J. Combin., {\bf 24}(1) (2017) \#P1.30. arXiv version. - Ben Salisbury and T. Scrimshaw:
*Connecting marginally large tableaux and rigged configurations via crystals.*Algebras and Repr. Theory, {\bf 19}(3) (2016) pp. 523--546. DOI: 10.1007/s10468-015-9587-y, arXiv version. - T. Scrimshaw:
*A crystal to rigged configuration bijection for type $D_4^{(3)}$*. J. Algebra, {\bf 448C} (2016), pp. 294--349. DOI: 10.1016/j.jalgebra.2015.09.047, arXiv version. - Anne Schilling and T. Scrimshaw:
*Crystal structure on rigged configurations and the filling map*. Electron. J. Combin., {\bf 22}(1) (2015) \#P1.73. arXiv version. - Ben Salisbury and T. Scrimshaw:
*A rigged configuration model for $B(\infty)$*. J. Combin. Theory Ser. A, {\bf 133} (2015) pp. 29--57. DOI 10.1016/j.jcta.2015.01.008, arXiv version. - Paul Prue and T. Scrimshaw:
*Abrams's stable equivalence for graph braid groups*. Topology Appl., {\bf 178} (2014) pp. 136--145. DOI: 10.1016/j.topol.2014.09.009, arXiv version. - Chris Berg, Viviane Pons, T. Scrimshaw, Jessica Striker, and Christian Stump:
*FindStat - the combinatorial statistics database*. (2014) arXiv version.