

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  VonNeumann Fellow, Institute of Advanced Study, Princeton, NJ, USA  2008  2010  Professor (W2), University of Bonn  Since 2010  Professor (W3), University of Bonn 


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


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


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 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 . Together with [3] this establishes a first concrete relationship between the geometric versions of Khovanov homology, the original algebraictopological 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 ReshetikhinTuraev 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 JordanHoelder multiplicity formulas could be solved or refined, as for instance for generalized Verma modules in [7].  Research Area C
 Research Area F*



[ 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): 200268 2010 ISSN: 00018708 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): 954992 2009 ISSN: 0010437X DOI: 10.1112/S0010437X09004035[ 4] Catharina Stroppel
Categorification of the TemperleyLieb category, tangles, and cobordisms via projective functors Duke Math. J. , 126: (3): 547596 2005 ISSN: 00127094 DOI: 10.1215/S001270940412634X[ 5] Igor Frenkel, Mikhail Khovanov, Catharina Stroppel
A categorification of finitedimensional irreducible representations of quantum {\germsl_2} and their tensor products Selecta Math. (N.S.) , 12: (34): 379431 2006 ISSN: 10221824 DOI: 10.1007/s000290070031y[ 6] Volodymyr Mazorchuk, Catharina Stroppel
A combinatorial approach to functorial quantum {\germsl_k} knot invariants Amer. J. Math. , 131: (6): 16791713 2009 ISSN: 00029327 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): 13631426 2008 ISSN: 00018708 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
Projectiveinjective modules, Serre functors and symmetric algebras J. Reine Angew. Math. , 616: : 131165 2008 ISSN: 00754102 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): 145 2010 ISSN: 10834362 DOI: 10.1007/s0003101090794[ 12] Volodymyr Mazorchuk, Serge Ovsienko, Catharina Stroppel
Quadratic duals, Koszul dual functors, and applications Trans. Amer. Math. Soc. , 361: (3): 11291172 2009 ISSN: 00029947 DOI: 10.1090/S000299470804539X



1998  FerdinandvonLindeman Prize for the best diploma thesis at the faculty, University of Freiburg  2007  Whitehead Prize, London Mathematical Society  2007  VonNeumann Award, Institute of Advanced Study 


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 


2007  University of WisconsinMadison, WI, USA  2009  University of Vienna, Austria  2010  University of Chicago, IL, USA 


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(11))”,
now Research Assistant, University of Freiburg
Gisa Schäfer (2014): “Categorified Uq(sl2) theory using BarNatan's approach”
Hanno Becker (2015): “HomotopyTheoretic Studies of KhovanovRozansky Homology”


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


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