I am a postdoc in the working group of Prof. Peter Littelmann in Cologne working in the project C3 Momentum polytopes, string polytopes and generalizations of the CRC/TRR 191 Symplectic Structures in Geometry, Algebra and Dynamics. I defended my PhD thesis in October 2014.

**Office:** Mathematical Institute, room 210

**Mailing address:** Mathematisches Institut, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany

**E-mail:**bschumann(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:

- Homological description of crystal structures on quiver varieties. Dissertation (2015).
- with Jacinta Torres. A non-Levi branching rule in terms of Littelmann paths. Preprint (2016). Submitted.
- with Volker Genz and Gleb Koshevoy, Combinatorics of canonical bases revisited: Type A. Preprint (2016), Submitted.
- Combinatorics of canonical bases and cluster duality. Oberwolfach Reports 21/2017, Mathematisches Forschungsinstitut Oberwolfach.
- Homological description of crystal structures on Lusztig's quiver varieties. Int. Math. Res. Notices. 2017 (12):3684--3725. Arxiv version.
- with Volker Genz and Gleb Koshevoy. Polyhedral parametrizations of canonical bases & cluster duality. Preprint (2017). Submitted.

**Notes and slides:**

- with Volker Genz and Gleb Koshevoy, Convex orderings on positive roots, Kashiwara crystals and string cones, notes written for my talk at the workshop Algebraic Lie Theory and Represetation Theory in Sugadaira, Japan, 2016.
- slides for a talk I gave in Hannover in 2016 with the title 'Combinatorics of canonical bases revisited'
- slides for a talk I gave at the workshop Lie Theory and Representation Theory in August 2016 with the title 'Crystal structures on PBW – type bases via Rhombic tilings'

**Teaching:**

- This semester I am teaching a seminar on logic (Goedel's incompleteness theorems) Thursdays at 16:00 in room 314.
- Here are notes of my cluster algebra class (in German) written by Dario Antweiler.