Profile
Profile

Prof. Dr. Catharina Stroppel

E-mail: stroppel(at)math.uni-bonn.de
Phone: +49 228 73 6838
Fax: +49 228 73 7916
Homepage: http://www.math.uni-bonn.de/people/stroppel/
Room: 4.007
Office hours: Wednesdays, 12-14
Location: Mathematics Center
Institute: Mathematical Institute
Research Areas: Former Research Area F (Leader)
Research Area F* (Leader)
Research Area C
Former Research Area E
Mathscinet-Number: 700232

Academic Career

1991 - 1998

Diploma and school teacher degree Mathematics / Theology, Freiburg

1994 - 2000

Scientific Assistant, University of Freiburg

1998 - 2001

PhD in Mathematics (supervisor: Prof. W. Soergel), University of Freiburg

2000 - 2001

Teaching Assistant, University of Freiburg

2001 - 2003

Research Associate in Pure Mathematics, University of Leicester, England, UK

2003 - 2004

Associate Professor (CAALT Postdoc), University of Aarhus, Denmark

2004 - 2005

Research Associate, University of Glasgow, Scotland, UK

2005 - 2007

Lecturer, University of Glasgow, Scotland, UK

2007 - 2008

Reader, University of Glasgow, Scotland, UK

2007 - 2008

Von-Neumann Fellow, Institute of Advanced Study, Princeton, NJ, USA

2008 - 2010

Professor (W2), University of Bonn

Since 2010

Professor (W3), University of Bonn

Research Profile

I am interested in geometric and combinatorial aspects of representation theory in particular in connection with topology and category theory.

Research Projects and Activities

DFG Priority Programme SPP 1388 “Representation theory”
Member

DFG Research Training Group GRK 1150 “Homotopy and Cohomology”
Member

DFG Collaborative Research Center SFB/TR 45 “Periods, moduli spaces and arithmetic of algebraic varieties”
Member

Contribution to Research Areas

Former Research Area E
One of my research interests is the interaction of geometry with representation theory and combinatorics. Schubert calculus is a classical representation theoretic tool to describe cohomology and representation rings in terms of symmetric functions. I am interested in modern aspects of this idea, of understanding integral structures, fusion algebras, canonical bases, and their connections to (topological) field theories. One of my recent contributions here is a combinatorial description of the affine {<br>rm sl}(n) Verlinde algebra with an explicit connection to quantum cohomology of Grassmannians [1]. In [2], we connect the cohomology theory of flag varieties and Springer fibers with the representation theory of Lie algebras and coherent sheaves related to nilpotent orbits in the Lie algebra {<br>rm gl}(n). Together with [3] this establishes a first concrete relationship between the geometric versions of Khovanov homology, the original algebraic-topological version and the Lie theoretic construction.
Former Research Area F
Representations of the symmetric group, more general Coxeter groups and their related Hecke algebras are an important topic in representation theory. They can be constructed geometrically in terms of convolution algebras of functions or sheaves on flag varieties or related varieties. Khovanov's categorification of the Jones polynomial and the important role played by Hecke algebras in knot theory leads to the question if these algebras, their representations and their representation categories can be categorified. This produces new interesting knot invariants, but also a more detailed description of the involved categories.
I categorified the complete Reshetikhin-Turaev quantum sl(2)-invariant for tangles and obtained a representation theoretic version of Khovanov homology [4], [5], [6]. In this context interesting braid group actions on derived categories play an important role. I used categorification techniques to establish unknown equivalences of categories.
In this way several problems about decomposition numbers or Jordan-Hoelder multiplicity formulas could be solved or refined, as for instance for generalized Verma modules in [7].
Research Area C
Research Area F*

Selected Publications

[1] Christian Korff, Catharina Stroppel
The {\widehat{\germsl}(n)_k}-WZNW fusion ring: a combinatorial construction and a realisation as quotient of quantum cohomology
Adv. Math. , 225: (1): 200--268
2010
ISSN: 0001-8708
DOI: 10.1016/j.aim.2010.02.021
[3] Catharina Stroppel
Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology
Compos. Math. , 145: (4): 954--992
2009
ISSN: 0010-437X
DOI: 10.1112/S0010437X09004035
[4] Catharina Stroppel
Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors
Duke Math. J. , 126: (3): 547--596
2005
ISSN: 0012-7094
DOI: 10.1215/S0012-7094-04-12634-X
[5] Igor Frenkel, Mikhail Khovanov, Catharina Stroppel
A categorification of finite-dimensional irreducible representations of quantum {\germsl_2} and their tensor products
Selecta Math. (N.S.) , 12: (3-4): 379--431
2006
ISSN: 1022-1824
DOI: 10.1007/s00029-007-0031-y
[6] Volodymyr Mazorchuk, Catharina Stroppel
A combinatorial approach to functorial quantum {\germsl_k} knot invariants
Amer. J. Math. , 131: (6): 1679--1713
2009
ISSN: 0002-9327
DOI: 10.1353/ajm.0.0082
[7] Volodymyr Mazorchuk, Catharina Stroppel
Categorification of (induced) cell modules and the rough structure of generalised Verma modules
Adv. Math. , 219: (4): 1363--1426
2008
ISSN: 0001-8708
DOI: 10.1016/j.aim.2008.06.019
[8] Jonathan Brundan, Catharina Stroppel
Highest weight categories arising from Khovanov's diagram algebra IV: The super case.
JEMS : 44
2009
[9] Jonathan Brundan, Catharina Stroppel
Highest weight categories arising from Khovanov's diagram algebra. I. cellularity
to appear in Mosc. Math. Journal
0
[10] Volodymyr Mazorchuk, Catharina Stroppel
Projective-injective modules, Serre functors and symmetric algebras
J. Reine Angew. Math.
,
616: : 131--165
2008
ISSN: 0075-4102
DOI: 10.1515/CRELLE.2008.020
[11] Jonathan Brundan, Catharina Stroppel
Highest weight categories arising from Khovanov's diagram algebra. II. Koszulity
Transform. Groups , 15: (1): 1--45
2010
ISSN: 1083-4362
DOI: 10.1007/s00031-010-9079-4
[12] Volodymyr Mazorchuk, Serge Ovsienko, Catharina Stroppel
Quadratic duals, Koszul dual functors, and applications
Trans. Amer. Math. Soc. , 361: (3): 1129--1172
2009
ISSN: 0002-9947
DOI: 10.1090/S0002-9947-08-04539-X

Publication List

Awards

1998

Ferdinand-von-Lindeman Prize for the best diploma thesis at the faculty, University of Freiburg

2007

Whitehead Prize, London Mathematical Society

2007

Von-Neumann Award, Institute of Advanced Study

Selected Invited Lectures

2009

Lecture Series Representation theory and Combinatorics, Beijing, China

2009

Lecture series Structures on Lie representation theory, Bremen

2009

Lecture series Summer school on link homology, Paris, France

2010

Lecture series Oporto Meeting on Geometry, Topology and Physics, Faro, Portugal

2010

Lectures on categorification, Aarhus, Denmark

2010

ICM, invited speaker, Hyderabad, India

2011

(planed) Lecture series on Lie superalgebras, Cargese, France

Offers

2007

University of Wisconsin-Madison, WI, USA

2009

University of Vienna, Austria

2010

University of Chicago, IL, USA

Selected PhD students

Hoel Queffelec (2013): “Sur la catégorification des invariants quantiques sln : étude algébrique et diagrammatique”,
now Chargé de recherche CNRS, Institut Montpelliérain Alexander Grothendieck, University of Montpellier, France

Antonio Sartori (2014): “Categorification of tensor powers of the vector representation of Uq(gl(1|1))”,
now Research Assistant, University of Freiburg

Gisa Schäfer (2014): “Categorified Uq(sl2) theory using Bar-Natan's approach”

Hanno Becker (2015): “Homotopy-Theoretic Studies of Khovanov-Rozansky Homology”

Supervised Theses

  • Master theses: 1
  • Diplom theses: 8, currently 3
  • PhD theses: 5, currently 4
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