

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 


My main area of expertise is in geometric and combinatorial aspects of representation theory in particular in connection with topology and category theory.
My current and recent research is centered around a better and, if possible, an explicit understanding of categories with geometric origin which play important roles in representation theory. One family of examples are Fukaya categories arising from Kleinian singularities or from Springer theory, but also from convolution algebras obtained from moduli spaces of representations of quivers and from quiver flag varieties. Besides an explicit description the focus is on axiomatic definitions and the comparision of structural properties of the resulting categories.
A second focus of my research is on braid group actions on derived categories, in particular for braid groups of affine or hyperbolic type outside type A and their relevance in topology. In particular we expect here a connection with knot invariants in orbifolds which then should have a nice categorification using categories arising naturally in Lie theory. This would generalize Khovanov homology in a nontrivial way. The underlying analogue of a ReshethikinTuraev theory is hereby one of the main goal.
Another current research interest is the representation theory of super groups (like the orthosyplectic famiies, but also the socalled strange families) and make them accessible to more classical representation theoretic techniques, in particular with the goal to provide a geometric description of the involved categories of representations. These should also provide techniques which are also applicable to the representation theory of algebraic groups in positive characteristics.
Finally I am working on finite and affine Schur algebras and their generalizations, in particular I like to describe them using graded versions arising from Quiver Hecke algebras. Hereby general homological properties as well as decomposition numbers over fields of positive characteristics are important and of interest. The general results will be applied explicitly to the representation theory of the general linear padic groups and the local Langlands program as well as to the representation theory of the classical alternating groups over fields in positive characteristics. In both cases a good interplay between geometric and combinatorial tools will be used and hopefully further developed.


DFG Collaborative Research Center SFB/TR 45 “Periods, moduli spaces and arithmetic of algebraic varieties”
Principal Investigator
Series of Oberwolfach Workshops on “Interactions between Algebraic Geometry and Noncommutative Algebra”,
Organizer, 2014, 2018
Bonn International Graduate School of Mathematics”
Associate Director, since 2017
DFG Cluster of Excellence “Hausdorff Center for Mathematics”,
Principal Investigator
HIMJuniorTrimester, 2017
Organizer
MSRI Program Geometric Representation Theory 2014
Organizer
MSRI Program NonCommutative Geometry 2013
Organizer
HIMTrimester, 2011
Organizer


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, [1], [2], [3]. Fusion rings arising from quantum groups at roots of unities were studied from an integrable systems point of view in [4], from an algebraic point of view in [5] and where used to study the famous Brauer centralizer algebras in [6] , [7]. 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 [8], [9].  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 [10], [11] with its connections to the geometry of perverse sheaves on Grassmannians [12], Springer fibers [13] and its connections to algebras arising in classical invariant theory [14]. 


[ 1] Igor Frenkel, Catharina Stroppel, Joshua Sussan
Categorifying fractional Euler characteristics, JonesWenzl projectors and 3jsymbols Quantum Topol. , 3: (2): 181253 2012[ 2] Pramod N. Achar, Catharina Stroppel
Completions of Grothendieck groups Bull. Lond. Math. Soc. , 45: (1): 200212 2013[ 3] Catharina Stroppel, Joshua Sussan
Categorified JonesWenzl projectors: a comparison Perspectives in representation theory of Contemp. Math. : 333351 Publisher: Amer. Math. Soc., Providence, RI 2014[ 4] 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[ 5] Henning Haahr Andersen, Catharina Stroppel
Fusion rings for quantum groups Algebr. Represent. Theory , 17: (6): 18691888 2014[ 6] H. Haahr Andersen, C. Stroppel, D. Tubbenhauer
Cellular structures using \textbfU\_qtilting modules to appear in Pacific Journal of Math 2015[7] Henning Haahr Andersen, Catharina Stroppel, Daniel Tubbenhauer
Semisimplicity of Hecke and (walled) Brauer algebras J. Aust. Math. Soc. , 103: (1): 144 2017 [ 8] Michael Ehrig, Catharina Stroppel, Daniel Tubbenhauer
The BlanchetKhovanov algebras Categorification and higher representation theory of Contemp. Math. : 183226 Publisher: Amer. Math. Soc., Providence, RI 2017[ 9] M. Ehrig, C. Stroppel, D. Tubbenhauer
Generic \mathfrakgl\_2foams, web and arc algebras ArXiv eprints 2016[10] Antonio Sartori, Catharina Stroppel
Categorification of tensor product representations of {$\germ{sl}_k$} and category {$\Cal{O}$}} J. Algebra , 428: : 256291 2015 [ 11] Michael Ehrig, Catharina Stroppel
On the category of finitedimensional representations of {OSp(r2n)}: Part I Representation theorycurrent trends and perspectives EMS Ser. Congr. Rep. : 109170 Publisher: Eur. Math. Soc., Zürich 2017[ 12] Michael Ehrig, Catharina Stroppel
Diagrammatic description for the categories of perverse sheaves on isotropic Grassmannians Selecta Math. (N.S.) , 22: (3): 14551536 2016[ 13] Michael Ehrig, Catharina Stroppel
2row Springer fibres and Khovanov diagram algebras for type D Canad. J. Math. , 68: (6): 12851333 2016[ 14] Michael Ehrig, Catharina Stroppel
Koszul gradings on Brauer algebras Int. Math. Res. Not. IMRN (13): 39704011 2016[15] Catharina Stroppel
Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology Compos. Math. , 145: (4): 954992 2009 [ 16] Volodymyr Mazorchuk, Catharina Stroppel
Projectiveinjective modules, Serre functors and symmetric algebras J. Reine Angew. Math. , 616: : 131165 2008[ 17] 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[ 18] Catharina Stroppel
Categorification of the TemperleyLieb category, tangles, and cobordisms via projective functors Duke Math. J. , 126: (3): 547596 2005[ 19] 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




• Springer Lecture Notes (2011  2014)
• Algebra and Representation Theory (since 2016)


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  Professor Invité, Paris, France  2014  2015  “Hirzebruch Professor”, Max Planck Institute for Mathematics, Bonn  2017  Teaching Award, University of Bonn 


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  2016  Geometric Representation Theory and Beyond, Clay Research Workshop, Oxford, England, UK  2017  Springer Fibers and Fukaya categories, HIM, Bonn 


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


Olaf Schnuerer (2017), now in Muenster


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
Joanna Meinel (2016): “Affine nilTemperleyLieb Algebras and Generalized Weyl Algebras”,
now Telecom Bonn, parttime research
Arik Wlbert (2017): “Tworow Springer fibres, foams and arc algebras of type D”, now Postdoc in Melbourne, Australia


 Master theses: 17, currently 2
 Diplom theses: 7
 PhD theses: 7, currently 3


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