Phone: +49 521 106 5036
Office hours: Mondays, 14:00 - 16:00
I am a postdoc in the Bielefeld Representation Theory Research group (BIREP) under Professor Dr. Henning Krause at the Faculty of Mathematics at the University of Bielefeld.
I graduated from the University of Bonn, where I used to be a student of Professor Dr. Jan Schröer in the Algebra and Representation Theory Research group.
My field of interest is the representation theory of algebras. I am especially interested in quivers, cluster algebras, and quantum groups. My Ph.D. studies have focused on the connection between dual canonical bases and quantum cluster algebras. For an overview please look at two posters I have created for the annual poster exhibition of the Bonn International Graduate School in Mathematics (BIGS). More recently, I became interested in ring theoretic properties of cluster algebras. For an overview please loook at a slide I made for a five-minutes talk.
Here you can find a short curriculum vitae, and informations about my travels including selected talks.
Acyclic cluster algebras from a ring theoretic point of view, October 2012. Many authors have studied Fomin-Zelevinsky's cluster algebras combinatorially (what do Laurent coefficients count?), representation-theoretically (what triangulated categories are they a shadow of?) and linear algebraically (what are good bases?). We want to know: What is a cluster algebra as an algebra? We focus on two questions: When is a cluster algebra a unique factorization domain? What are irreducible elements? [arXiv]
Quantum cluster algebras and dual canonical bases, Oberwolfach Reports 8 (2011), no. 10, 564-565. A short survey about the connections between Lusztig's canonical basis and Fomin-Zelevinsky's cluster algebra. [Journal]
Quantum cluster algebras of type A and the dual canonical basis, to appear in Proceedings of the London Mathematical Society. The article concerns the subalgebra Uv(w) of the quantized universal enveloping algebra of the complex Lie algebra sln+1 associated with a particular Weyl group element of length 2n. We verify that Uv(w) can be endowed with the structure of a quantum cluster algebra of type An. To appear in Proceedings of the London Mathematical Society, [arXiv].
A quantum cluster algebra of Kronecker type and the dual canonical basis, International Mathematics Research Notices 2011 2011, no. 13, 2970-3005. The article studies the quantized cluster algebra structure induced by the dual canonical basis associated with a terminal module over the path algebra of the Kronecker quiver. [Journal], [arXiv]
Im Sommersemester 2012 biete ich zusammen mit Prof. Dr. Henning Krause und Dr. Nils Mahrt ein Proseminar: Einführung in Cluster-Algebren [eKVV] an; ferner leite ich eine Übung zur Vorlesung Lineare Algebra II bei Prof. Dr. Henning Krause. [eKVV], [Evaluation]
Mathe+ ist die Mathe-AG für Schülerinnen und Schüler in der Uni Bielefeld.
The BIREP group hosted the Workshop and International Conference on Representations of Algebras (ICRA 2012) in August 2012.
I was a coorganizer of the 16th NWDR Workshop which was held in Bielefeld on July 06, 2012.
Together with colleagues from Bielefeld I have organized a Summer School on Polynomial Representations of the General Linear Group which was held in August 2011 in Bad Driburg.
A selection of links that you might find interesting.
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