

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 Program 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]. 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 [6].  Research Area C Fusion rings and categorification questions are of interest for mathematicians and physicists. In particular allows categorification the interpretation of inverted quantum numbers and formal power series in q as as Euler characteristics of infinite complexes of graded vector spaces. We used this to categorify parts of the ReshethikinTuraevViro invariants for 3manifolds, [7], [8], [9]. Fusion rings arising from quantum groups at roots of unities were studied from an integrable systems point of view in [1], from an algebraic point of view in [10] and where used to study the famous Brauer centralizer algebras in [11] , [12]. One of the first successful categorifications was the famous Khovanov homology of links. It categorifies the Jones polynomial and lifts to an invariant of cobordisms of tangles up to signs. We addressed these sign issues in two papers describing a slightly twisted version of Khovanov homology which is functorial, see [13], [14].  Research Area F* One of my research interests is the interaction of geometry with representation theory and combinatorics. I studied in particular categories of representations of Lie superalgebras [15], [16] with its connections to the geometry of perverse sheaves on Grassmannians [17], Springer fibers [18] and its connections to algebras arising in classical invariant theory [19]. 


[ 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 DOI: 10.1016/j.aim.2010.02.021[ 2] Catharina Stroppel, Ben Webster
2block Springer fibers: convolution algebras and coherent sheaves Comment. Math. Helv. , 87: (2): 477520 2012 DOI: 10.4171/CMH/261[ 3] Catharina Stroppel
Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology Compos. Math. , 145: (4): 954992 2009 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 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 DOI: 10.1007/s000290070031y[ 6] Volodymyr Mazorchuk, Catharina Stroppel
Categorification of (induced) cell modules and the rough structure of generalised Verma modules Adv. Math. , 219: (4): 13631426 2008 DOI: 10.1016/j.aim.2008.06.019[ 7] Igor Frenkel, Catharina Stroppel, Joshua Sussan
Categorifying fractional Euler characteristics, JonesWenzl projectors and 3jsymbols Quantum Topol. , 3: (2): 181253 2012 DOI: 10.4171/QT/28[ 8] Pramod N. Achar, Catharina Stroppel
Completions of Grothendieck groups Bull. Lond. Math. Soc. , 45: (1): 200212 2013 DOI: 10.1112/blms/bds079[ 9] Catharina Stroppel, Joshua Sussan
Categorified JonesWenzl projectors: a comparison Perspectives in representation theory of Contemp. Math. : 333351 Publisher: Amer. Math. Soc., Providence, RI 2014 DOI: 10.1090/conm/610/12194[ 10] Henning Haahr Andersen, Catharina Stroppel
Fusion rings for quantum groups Algebr. Represent. Theory , 17: (6): 18691888 2014[ 11] H. Haahr Andersen, C. Stroppel, D. Tubbenhauer
Cellular structures using \textbfU\_qtilting modules to appear in Pacific Journal of Math 2015[12] H. Haahr Andersen, C. Stroppel, D. Tubbenhauer
Semisimplicity of Hecke and (walled) Brauer algebras to appear in the Journal of the Australian Mathematical Society 2015 [13] M. Ehrig, C. Stroppel, D. Tubbenhauer
The BlanchetKhovanov algebras to appear in Perpectives in Categorification in Algebra, Geometry and Physics 2015 [14] M. Ehrig, C. Stroppel, D. Tubbenhauer
Generic \mathfrakgl\_2foams, web and arc algebras ArXiv eprints 2016 [15] Antonio Sartori, Catharina Stroppel
Categorification of tensor product representations of {\germsl_k} and category {\CalO} J. Algebra , 428: : 256291 2015 DOI: 10.1016/j.jalgebra.2014.12.043 [ 16] M. Ehrig, C. Stroppel
On the category of finitedimensional representations of \operatornameOSp(r2n): Part I Representation TheoryCurrent Trends and Perspectives of EMS Series of Congress Reports : 109170 2017[ 17] Michael Ehrig, Catharina Stroppel
Diagrammatic description for the categories of perverse sheaves on isotropic Grassmannians Selecta Math. (N.S.) , 22: (3): 14551536 2016 DOI: 10.1007/s0002901502159[ 18] Michael Ehrig, Catharina Stroppel
2row Springer fibres and Khovanov diagram algebras for type D Canad. J. Math. , 68: (6): 12851333 2016 DOI: 10.4153/CJM20150514[ 19] Michael Ehrig, Catharina Stroppel
Koszul gradings on Brauer algebras Int. Math. Res. Not. IMRN (13): 39704011 2016 DOI: 10.1093/imrn/rnv267[20] Jonathan Brundan, Catharina Stroppel
Highest weight categories arising from Khovanov's diagram algebra IV: the general linear supergroup J. Eur. Math. Soc. (JEMS) , 14: (2): 373419 2012 DOI: 10.4171/JEMS/306 [ 21] Volodymyr Mazorchuk, Catharina Stroppel
Projectiveinjective modules, Serre functors and symmetric algebras J. Reine Angew. Math. , 616: : 131165 2008 DOI: 10.1515/CRELLE.2008.020



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 on representation theory and combinatorics, Beijing, China  2009  Lecture series on structures on Lie representation theory, Bremen  2009  Summer school on link homology, Paris, France  2010  Oporto Meeting on Geometry, Topology and Physics, Faro, Portugal  2010  Lectures on categorification, Aarhus, Denmark  2010  International Congress of Mathematicians, invited speaker, Hyderabad, India  2011  Lecture series on Lie superalgebras, Cargese, France  2012  Lecture series on Springer fibers, Northeastern University, Boston, MA, USA  2012  Lecture series on categorification, Luminy, France  2013  Lecture series on categorified invariants of manifolds, MPI, Bonn  2013  Summer school on Category O, Freiburg  2014  Lecture series on Khovanov algebras (Program Math. Structures and Computations), Lyon, France  2014  Lecture series on categorification (Program on Algebraic Lie Theory), Glasgow, Scotland, UK  2016  Lecture series on representation theory of Lie superalgebras and categorification, Workshop, Bonn 


2007  University of WisconsinMadison, WI, USA  2009  University of Vienna, Austria  2010  University of Chicago, IL, USA  2013  University of Glasgow, Scotland, UK 


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
Hanno Becker (2015): “HomotopyTheoretic Studies of KhovanovRozansky Homology”
Joanna Meinel (2016): “Affine nilTemperleyLieb Algebras and Generalized Weyl Algebras”,
now Postdoc, University of Stuttgart


 Master theses: 7, currently 5
 Diplom theses: 8
 PhD theses: 6, currently 4


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