Profile
Profile

Prof. Dr. Catharina Stroppel

Associate Director of Graduate Studies

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

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

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 Reshethikin-Turaev 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 p-adic 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.

Research Projects and Activities

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 Non-commutative Algebra”,
Organizer, 2014, 2018

Bonn International Graduate School of Mathematics”
Associate Director, since 2017

DFG Cluster of Excellence “Hausdorff Center for Mathematics”,
Principal Investigator

HIM-Junior-Trimester, 2017
Organizer

MSRI Program Geometric Representation Theory 2014
Organizer

MSRI Program Non-Commutative Geometry 2013
Organizer

HIM-Trimester, 2011
Organizer

Contribution to Research Areas

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 Reshethikin-Turaev-Viro invariants for 3-manifolds, [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].

Selected Publications

[1] Igor Frenkel, Catharina Stroppel, Joshua Sussan
Categorifying fractional Euler characteristics, Jones-Wenzl projectors and 3j-symbols
Quantum Topol. , 3: (2): 181--253
2012
[2] Pramod N. Achar, Catharina Stroppel
Completions of Grothendieck groups
Bull. Lond. Math. Soc. , 45: (1): 200--212
2013
[3] Catharina Stroppel, Joshua Sussan
Categorified Jones-Wenzl projectors: a comparison
Perspectives in representation theory
of Contemp. Math. : 333--351
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): 200--268
2010
[5] Henning Haahr Andersen, Catharina Stroppel
Fusion rings for quantum groups
Algebr. Represent. Theory , 17: (6): 1869--1888
2014
[6] H. Haahr Andersen, C. Stroppel, D. Tubbenhauer
Cellular structures using \textbfU\_q-tilting 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): 1--44
2017
[8] Michael Ehrig, Catharina Stroppel, Daniel Tubbenhauer
The Blanchet-Khovanov algebras
Categorification and higher representation theory
of Contemp. Math. : 183--226
Publisher: Amer. Math. Soc., Providence, RI
2017
[9] M. Ehrig, C. Stroppel, D. Tubbenhauer
Generic \mathfrakgl\_2-foams, web and arc algebras
ArXiv e-prints
2016
[10] Antonio Sartori, Catharina Stroppel
Categorification of tensor product representations of {$\germ{sl}_k$} and category {$\Cal{O}$}}
J. Algebra
, 428: : 256--291
2015
[11] Michael Ehrig, Catharina Stroppel
On the category of finite-dimensional representations of {OSp(r|2n)}: Part I
Representation theory---current trends and perspectives
EMS Ser. Congr. Rep. : 109--170
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): 1455--1536
2016
[13] Michael Ehrig, Catharina Stroppel
2-row Springer fibres and Khovanov diagram algebras for type D
Canad. J. Math. , 68: (6): 1285--1333
2016
[14] Michael Ehrig, Catharina Stroppel
Koszul gradings on Brauer algebras
Int. Math. Res. Not. IMRN (13): 3970--4011
2016
[15] Catharina Stroppel
Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology
Compos. Math.
, 145: (4): 954--992
2009
[16] Volodymyr Mazorchuk, Catharina Stroppel
Projective-injective modules, Serre functors and symmetric algebras
J. Reine Angew. Math. , 616: : 131--165
2008
[17] 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
[18] Catharina Stroppel
Categorification of the Temperley-Lieb category, tangles, and cobordisms via projective functors
Duke Math. J. , 126: (3): 547--596
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): 373--419
2012

Publication List

MathSciNet Publication List (external link)

Editorships

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

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

2009

Professor Invité, Paris, France

2014 - 2015

“Hirzebruch Professor”, Max Planck Institute for Mathematics, Bonn

2017

Teaching Award, University of Bonn

Selected Invited Lectures

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

Offers

2007

University of Wisconsin-Madison, WI, USA

2009

University of Vienna, Austria

2010

University of Chicago, IL, USA

2013

University of Glasgow, Scotland, UK

Habilitations

Olaf Schnuerer (2017), now in Muenster

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

Joanna Meinel (2016): “Affine nilTemperley-Lieb Algebras and Generalized Weyl Algebras”,
now Telecom Bonn, part-time research

Arik Wlbert (2017): “Two-row Springer fibres, foams and arc algebras of type D”, now Postdoc in Melbourne, Australia

Supervised Theses

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