Office: Mathematical Institute, room 210
Mailing address: Mathematisches Institut, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
E-mail:delaporte(at)math.uni-koeln(dot)de
Research: My research focuses around the theory of crystal graphs, an important tool in the study of representation
of complex algebraic groups. This theory has a lot of – natural and surprising – connections to polyhedral and
tropical geometry, algebraic geometry, combinatorics and homological algebra. The mathematical problems I
enjoy the most are the ones building bridges between different areas with a particular stress on explicit formulas
and computations. Here my list of publications and preprints:
- Bea Schumann. Homological description of crystal structures on quiver varieties.
Dissertation (2015).
- Bea Schumann. Homological description of crystal structures on Lusztig's quiver varieties, Int.
Math. Res. Not. IMRN (2017), no. 12, 3684-3725, doi:10.1093/imrn/rnw117.
- Bea Schumann. Combinatorics of canonical bases and cluster duality. Oberwolfach Reports 21/2017, Mathematisches Forschungsinstitut Oberwolfach.
- Bea Schumann, Jacinta Torres. A non-Levi branching rule in terms of Littelmann paths. Proc. Lond.
Math. Soc.117 (2018), no. 5, 1077-1100, doi:10.1112/plms.12175.
- Volker Genz, Gleb Koshevoy, Bea Schumann. Polyhedral parametrizations of canonical bases & cluster duality, Adv. Math. 369 (2020), 107178, 41 pp., doi:10.1016/j.aim.2020.107178.
- Volker Genz, Gleb Koshevoy, Bea Schumann. Combinatorics of canonical bases revisited: Type A. Selecta Math. 27 (2021), no. 4, 45 pp., doi:10.1007/s00029-021-00658-x.
- Bea Schumann. Optimality of string cone inequalities and potential functions. Oberwolfach Reports 20/2021, Mathematisches Forschungsinstitut Oberwolfach.
- Bea Schumann. String cones and cluster varieties. Oberwolfach Reports 52/2021, Mathematisches Forschungsinstitut Oberwolfach.
- Deniz Kus , Bea Schumann. Nakajima quiver varieties, affine crystals and combinatorics of Auslander-Reiten quivers, Algebra Discrete Math. 34 (2022), no. 2, 244-272, doi:10.48550/arXiv.1910.07411.
- Volker Genz, Gleb Koshevoy, Bea Schumann. Combinatorics of canonical bases revisited: string data
in type A, Transform. Groups 27 (2022), no. 3, 867-895, doi:10.1007/s00031-021-09668-7.
- Gleb Koshevoy, Bea Schumann, Redundancy in string cone inequalities and multiplicities in
potential functions on cluster varieties, J. Algebraic Combin. 56 (2022), no. 4, 1031-1053,
doi:10.1007/s10801-022-01144-z.>
- Daniel Labardini-Fragoso, Bea de Laporte. Landau-Ginzburg potentials via projective representations, arXiv preprint, arXiv.2208.00028.