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
- Drew Armstrong (Coral Gables, Florida)
- David Bessis (Paris)
- Tom Brady (Dublin)
- Frédéric Chapoton (Lyon)
- Raquel Coelho Simões (Lisbon)
- Patrick Dehornoy (Caen)
- Matthew Dyer (Notre Dame, Indiana)
- Thomas Gobet (Amiens)
- Christian Krattenthaler (Vienna)
- Gus Lehrer (Sydney)
- Jean Michel (Paris)
- Dmitri Panyushev (Moscow)
- Nathan Reading (Raleigh, North Carolina)
- Claus Michael Ringel (Bielefeld)
- Roland Speicher (Saarbrücken)
- Hugh Thomas (Fredericton)
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
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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] | Generalized noncrossing partitions and combinatorics of Coxeter groups, Mem. Amer. Math. Soc. 202 (2006). | ,
[Bes03] | The dual braid monoid, Ann. Sci. Ecole Norm. Sup. 36 (2003). | ,
[BW02] | K(π,1)'s for Artin groups of finite type, Geom. Dedicata 94 (2002). | and ,
[IT09] | Noncrossing partitions and representations of quivers, Compositio Math. 145 (2009). | and ,
[Rea08] | Clusters, Coxeter-sortable elements and noncrossing partitions, Trans. Amer. Math. Soc. 359 (2007). | ,
[Kre72] | Sur les partitions non croisées d'un cycle, Discrete Math. 1 (1972). | ,