Workshop "Non-crossing partitions in representation theory"

Thursday, 12 June to Saturday, 14 June 2014

Location: Bielefeld University. All talks will be given in the main university building (UHG), for detailed information please see the workshop programme. Maps are available on the university's travel information page.

Schedule: Talks start Thursday morning and finish Saturday in the late afternoon.

Organisers: Barbara Baumeister, Andrew Hubery, Henning Krause, Christian Stump

Support: DFG CRC 701 "Spectral Structures and Topological Methods in Mathematics", DFG SPP 1388 "Representation Theory", EPSRC Network Grant "Anglo-Franco-German Representation Theory", GDRI 571 "French-British-German network in Representation theory" and DFG SPP 1489 "Computer Algebra".

Registration: If you would like to attend the workshop, please register using the webform.

Workshop speakers

Titles of talks and abstracts are available on a separate page. For some of the talks, slides are available, too. Please see the programme page.

Workshop participants

Picture of the pariticipants of the Workshop 'Non-crossing partitions in representation theory'

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The Topic

The systematic study of noncrossing partitions goes back to G. Kreweras in the 1970s where he considered set partitions on {1,...,n} with noncrossing blocks when drawn on a circle [Kre]. Among other beautiful properties, such noncrossing set partitions are counted by the famous Catalan numbers and they form a lattice under the refinement order.

More than 30 years later, D. Bessis and, independently, T. Brady and C. Watt provided an algebraic framework to generalize noncrossing partitions to finite Coxeter groups in a very natural and beautiful way [Bes03, BW02]. These developments opened the new combinatorial field of "Coxeter-Catalan combinatorics", see [Arm06] for further background and references. The final link to representations of quivers arose shortly after from the connection between noncrossing partitions and cluster algebras [Rea08] and their categorification via cluster categories [IT09].

This workshop is devoted to all aspects of this exciting development with the objective to bring together specialists interested in noncrossing partitions, in particular those from algebraic combinatorics and from quiver representation theory.

[Arm06] D. Armstrong, Generalized noncrossing partitions and combinatorics of Coxeter groups, Mem. Amer. Math. Soc. 202 (2006).
[Bes03] D. Bessis, The dual braid monoid, Ann. Sci. Ecole Norm. Sup. 36 (2003).
[BW02] T. Brady and C. Watt, K(π,1)'s for Artin groups of finite type, Geom. Dedicata 94 (2002).
[IT09] C. Ingalls and H. Thomas, Noncrossing partitions and representations of quivers, Compositio Math. 145 (2009).
[Rea08] N. Reading, Clusters, Coxeter-sortable elements and noncrossing partitions, Trans. Amer. Math. Soc. 359 (2007).
[Kre72] G. Kreweras, Sur les partitions non croisées d'un cycle, Discrete Math. 1 (1972).