Profile
Profile

Prof. Dr. Jan Schröer

E-Mail: schroer(at)math.uni-bonn.de
Telefon: +49 228 73 7786
Homepage: http://www.math.uni-bonn.de/~schroer/
Raum: 3.006
Standort: Mathematics Center
Institute: Mathematical Institute
Forschungsbereiche: Research Area DE (Leader)
Research Area C (until 10/2012)
Former Research Area E
Geburtsdatum: 04.May 1971

Academic Career

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

Research Profile

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.

Research Projects and Activities

DFG Collaborative Research Center Transregio SFB/TR 45 “Periods, Moduli Spaces and Arithmetic of Algebraic Varieties”
Principal Investigator

Selected Publications

[1] Christof Geiß, Bernard Leclerc, Jan Schröer
Quivers with relations for symmetrizable Cartan matrices III: Convolution algebras
Represent. Theory , 20: : 375--413
2016
[2] Christof Geiss, Bernard Leclerc, Jan Schröer
Quivers with relations for symmetrizable Cartan matrices I: foundations
Invent. Math. , 209: (1): 61--158
2017
[3] Christof Geiß, Daniel Labardini-Fragoso, Jan Schröer
The representation type of Jacobian algebras
Adv. Math. , 290: : 364--452
2016
[4] C. Geiß, B. Leclerc, J. Schröer
Cluster structures on quantum coordinate rings
Selecta Math. (N.S.) , 19: (2): 337--397
2013
[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
[6] Christof Geiß, Bernard Leclerc, Jan Schröer
Kac-Moody groups and cluster algebras
Adv. Math. , 228: (1): 329--433
2011
[7] Christof Geiß, Bernard Leclerc, Jan Schröer
Rigid modules over preprojective algebras
Invent. Math. , 165: (3): 589--632
2006
[8] Christof Geiss, Bernard Leclerc, Jan Schröer
Semicanonical bases and preprojective algebras
Ann. Sci. École Norm. Sup. (4) , 38: (2): 193--253
2005
[9] William Crawley-Boevey, Jan Schröer
Irreducible components of varieties of modules
J. Reine Angew. Math. , 553: : 201--220
2002
[10] Jan Schröer
On the infinite radical of a module category
Proc. London Math. Soc. (3) , 81: (3): 651--674
2000

Publication List

MathSciNet Publication List (external link)

Selected Invited Lectures

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

Offers

2008

University of Dortmund (W3)

2009

University of Bielefeld (W3)

Selected PhD students

Philipp Lampe (2010): “Quantum cluster algebras and the dual canonical basis”,
now Postdoc, University of Bielefeld

Jan Geuenich (January/February 2017): “Quiver Mutations and Potentials”,
afterwards Postdoc, University of Bielefeld

Supervised Theses

  • Master theses: 29, currently 7
  • Diplom theses: 16
  • PhD theses: 7, currently 2
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