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| 1997 | Dr. math., University of Bielefeld (advisor: C.M. Ringel) | | 1997 - 1998 | Research Fellow, University of Bielefeld | | 1998 - 1999 | DAAD Postdoctoral Fellow, National Autonomous University of Mexico, Mexico City, Mexico | | 1999 - 2000 | Research Fellow, University of Bielefeld | | 2000 - 2005 | Lecturer/Reader, University of Leeds, England, UK (Temporary leave: 2003-2004) | | 2003 - 2004 | DFG Research Fellow, University of Leeds, England, UK | | Since 2005 | Professor (W2), University of Bonn |
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My research area is the representation theory of finite-dimensional algebras and quivers. I focus particularly on the numerous deep connections to the representation theory of Kac-Moody Lie algebras. Various crucial geometric constructions (Nakajima quiver varieties, Kashiwara-Saito's geometric crystal graphs, semicanonical bases for enveloping algebras, generic bases for cluster algebras) can only be realized for symmetric Kac-Moody Lie algebras. In an extensive project with Geiss and Leclerc, we are currently developing a general framework for all of the above (using quivers with loops and relations) which covers all symmetrizable, non-symmetric cases. This should also trigger a new research field inside the classical representation theory of finite-dimensional algebras, namely the study of generalized modulated graphs. I'm also interested in classical homological conjectures for finite-dimensional algebras.
The project described above will keep us busy for several years. A related topic of future investigation is the representation theory of wild quivers or more generally of wild algebras. Roughly speaking these are finite-dimensional algebras whose module category contains all module categories of all finite-dimensional algebras via suitable embedding functors. This fractal behaviour of module categories is quite common and should also occur in many other areas of mathematics. As a research group we would like to “start again from zero” and develop a vision for the future of this research area. The methods will include Schofield induction, Kerner bijections and Auslander-Reiten Theory.
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DFG Collaborative Research Center Transregio SFB/TR 45 “Periods, Moduli Spaces and Arithmetic of Algebraic Varieties”
Principal Investigator
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[ 1] Christof Geiss, Bernard Leclerc, Jan Schröer
Quivers with relations for symmetrizable Cartan matrices III: Convolution algebras
Represent. Theory , 20: : 375--413
2016
DOI: 10.1090/ert/487[ 2] Christof Geiss, Bernard Leclerc, Jan Schröer
Quivers with relations for symmetrizable Cartan matrices I: Foundations
Invent. Math. , 209: (1): 61--158
2017
DOI: 10.1007/s00222-016-0705-1[ 3] Christof Geiss, Daniel Labardini-Fragoso, Jan Schröer
The representation type of Jacobian algebras
Adv. Math. , 290: : 364--452
2016
DOI: 10.1016/j.aim.2015.09.038[ 4] C. Geiss, B. Leclerc, J. Schröer
Cluster structures on quantum coordinate rings
Selecta Math. (N.S.) , 19: (2): 337--397
2013
DOI: 10.1007/s00029-012-0099-x[ 5] Christof Geiss, Bernard Leclerc, Jan Schröer
Generic bases for cluster algebras and the Chamber ansatz
J. Amer. Math. Soc. , 25: (1): 21--76
2012
DOI: 10.1090/S0894-0347-2011-00715-7[ 6] Christof Geiss, Bernard Leclerc, Jan Schröer
Kac-Moody groups and cluster algebras
Adv. Math. , 228: (1): 329--433
2011
DOI: 10.1016/j.aim.2011.05.011[ 7] Christof Geiss, Bernard Leclerc, Jan Schröer
Rigid modules over preprojective algebras
Invent. Math. , 165: (3): 589--632
2006
DOI: 10.1007/s00222-006-0507-y[ 8] Christof Geiss, Bernard Leclerc, Jan Schröer
Semicanonical bases and preprojective algebras
Annales Scientifiques de l’École Normale Supérieure (4) , 38: (2): 193--253
2005
DOI: 10.1016/j.ansens.2004.12.001[ 9] William Crawley-Boevey, Jan Schröer
Irreducible components of varieties of modules
J. Reine Angew. Math. , 553: : 201--220
2002
DOI: 10.1515/crll.2002.100[ 10] Jan Schröer
On the infinite radical of a module category
Proc. London Math. Soc. (3) , 81: (3): 651--674
2000
DOI: 10.1112/S0024611500012600 |
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| 2000 | Plenary lecture at the ICRA, Beijing, China | | 2002 | Plenary lecture at the ICRA, Toronto, ON, Canada | | 2004 | Plenary lecture at the ICRA, Pátzcuaro, Mexico | | 2005 | Morning Speaker at the British Mathematical Colloquium, Liverpool, England, UK | | 2011 | Lecture at the Abel Symposium, Balestrand, Norway | | 2013 | Mathematisches Kolloquium, Bern, Switzerland | | 2014 | Lecture series at the ICRA, Sanya, China | | 2015 | Lecture at the Mittag-Leffler Institute, Stockholm, Sweden |
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| 2008 | University of Dortmund (W3) | | 2009 | University of Bielefeld (W3) |
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Jan Geuenich (January/February 2017): “Quiver Mutations and Potentials”,
afterwards Postdoc, University of Bielefeld
Sondre Kvamme (October 2017): “Comonads and Gorenstein Homological Algebra”,
now Postdoc, Département de Mathématiques d’Orsay
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- Master theses: 29, currently 7
- Diplom theses: 16
- PhD theses: 7, currently 2
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