Prof. Dr. Henning Krause

Professor

Faculty of Mathematics
Bielefeld University
PO Box 100 131
D-33501 Bielefeld

Tel: +49 521 106-5020 (office)
Tel: +49 521 106-4991 or 5021 (secretary)
Tel: +49 5251 2078378 (home)
Fax: +49 521 106-6482
Email: hkrause

Office: V5-222

Office hours: Wednesday 15:00 - 16:00 or by appointment (via email).

About myself

I am professor of mathematics at Bielefeld University since 2010 and member of the Bielefeld Representation Theory Group (BIREP). Previous appointments were at Paderborn (2003 - 2010) and Leeds (2002 - 2003). For more details see my CV.

Research in representation theory at Bielefeld is currently funded through DFG TRR 358"Integral Structures in Geometry and Representation Theory". Before that, I was involved in two major research projects:

I am an editorial board member for these journals:

I am a Fellow of the American Mathematical Society and a member of The Royal Norwegian Society of Sciences and Letters.

Book project

Here is a completed book manuscript; it is published by Cambridge University Press in the series Cambridge Studies in Advanced Mathematics:

Homological theory of representations (September 2021)

The book has an own website. An illustrated short note explains what the book is about.

Teaching

SS 2022: Lineare Algebra II (Vorlesung) [ekkv]
WS 2021/22: Lineare Algebra I (Vorlesung) [ekkv]
SS 2021: Elementare Zahlentheorie (Vorlesung) [ekkv]
SS 2021: Darstellungen von Gruppen (Proseminar) [ekkv]
WS 2020/21: Funktionentheorie (Vorlesung) [ekkv]
SS 2020: Masterkurs Darstellungstheorie von Algebren, II (Vorlesung) [ekkv]
WS 2019/20: Masterkurs Darstellungstheorie von Algebren, I (Vorlesung) [ekkv]
WS 2018/19: Diskrete Mathematik (Vorlesung) [ekkv]
WS 2018/19: Algebra (Bachelorseminar) [ekkv]
SS 2018: Algebra II (Vorlesung) [ekkv]
WS 2017/18: Algebra I (Vorlesung) [ekkv]
SS 2017: Lineare Algebra II (Vorlesung) [ekkv]
SS 2017: Selected Topics in Representation Theory (Vorlesung) [ekkv]
WS 2016/17: Lineare Algebra I (Vorlesung) [ekkv]
SS 2016: Ausgewählte Kapitel der Zahlentheorie (Vorlesung) [ekkv]
WS 2015/16: Darstellungstheorie von Algebren III (Vorlesung) [ekkv]
WS 2014/15: Darstellungstheorie von Algebren I (Vorlesung) [ekkv]
SS 2014: Bachelorseminar zur Algebra (Seminar) [ekkv]
SS 2014: Spezielle Aspekte der Mathematik: Zahlentheorie (Vorlesung) [ekkv]
WS 2013/14: Algebra II (Vorlesung) [ekkv]
SS 2013: Algebra I (Vorlesung) [ekkv]
SS 2013: Local cohomology and support (Vorlesung) [ekkv]
WS 2012/13: Elementare Zahlentheorie (Vorlesung) [ekkv]
WS 2012/13: Schur functors and symmetric functions (Seminar) [ekkv]
SS 2012: Lineare Algebra II (Vorlesung) [ekkv]
WS 2011/12: Auslander-Reiten Theorie (Seminar) [ekkv]
WS 2011/12: Gruppen und Symmetrien (Seminar) [ekkv]
WS 2011/12: Lineare Algebra I (Vorlesung) [ekkv]
SS 2011: Darstellungen von endlichen Gruppen (Seminar) [ekkv]
SS 2011: Einführung in die Darstellungstheorie (Vorlesung) [ekkv]
SS 2010: Einführung in die Darstellungstheorie (Vorlesung) [ekkv]

Publications

The following is a selection of publications. The full list of published articles is available on a separate page.

Auslander-Reiten duality for Grothendieck abelian categories, Trans. Amer. Math. Soc. 371 (2019), 2455–2472, doi:10.1090/tran/7379.
(With D. Benson, S. B. Iyengar, and J. Pevtsova) Stratification for module categories of finite group schemes, J. Amer. Math. Soc. 31 (2018), 265–302, doi:10.1090/jams/887.
Highest weight categories and recollements, Ann. Inst. Fourier 67 (2017), 2679–2701, doi:10.5802/aif.3147.
(With D. Benson, S. B. Iyengar and J. Pevtsova) Colocalising subcategories of modules over finite group schemes, Ann. K-Theory 2 (2017), 387–408, doi:10.2140/akt.2017.2.387.
(With A. Hubery) A categorification of non-crossing partitions, J. Eur. Math. Soc. 18 (2016), 2273–2313, doi:10.4171/JEMS/641.
Deriving Auslander's formula, Documenta Math. 20 (2015), 669–688, Link.
Koszul, Ringel, and Serre duality for strict polynomial functors, Compos. Math. 149 (2013), 996–1018, doi:10.1112/S0010437X12000814.
(With D. J. Benson and S. B. Iyengar) Colocalizing subcategories and cosupport, J. Reine Angew. Math. 673 (2012), 161–207, doi:10.1515/CRELLE.2011.180.
Approximations and adjoints in homotopy categories, Math. Annalen 353 (2012), 765–781, doi:10.1007/s00208-011-0703-y.
(With D. J. Benson and S. B. Iyengar) Stratifying modular representations of finite groups, Ann. of Math. 174 (2012), 1643–1684, doi:10.4007/annals.2011.174.3.6.
(With J. Stovicek) The telescope conjecture for hereditary rings via Ext-orthogonal pairs, Adv. Math. 225 (2010), 2341–2364, doi:10.1016/j.aim.2010.04.027.
(With D. Benson and S. B. Iyengar) Local cohomology and support for triangulated categories, Ann. Sci. Ecole Norm. Sup. (4) 41 (2008), 573–619, doi:10.24033/asens.2076.
Derived categories, resolutions, and Brown representability, in: Interactions between homotopy theory and algebra, 101–139, Contemp. Math. 436, Amer. Math. Soc., Providence, RI 2007, doi:10.1090/conm/436/08405.
(With S. B. Iyengar) Acyclicity versus total acyclicity for complexes over noetherian rings, Documenta Math. 11 (2006), 207–240, Link.
The stable derived category of a noetherian scheme, Compos. Math. 141 (2005), 1128–1162, doi:10.1112/S0010437X05001375.
(With D. J. Benson and S. Schwede) Realizibility of modules over Tate cohomology, Trans. Amer. Math. Soc. 356 (2004), 3621–3668, doi:10.1090/S0002-9947-03-03373-7.
(With Ø. Solberg) Applications of cotorsion pairs, J. London Math. Soc. 68 (2003), 631–650, doi:10.1112/S0024610703004757.
A Brown representability theorem via coherent functors, Topology 41 (2002), 853–861, doi:10.1016/S0040-9383(01)00010-6.
(With D. J. Benson) Pure injectives and the spectrum of the cohomology ring of a finite group, J. reine angew. Math. 542 (2002), 23–51, doi:10.1515/crll.2002.008.
The spectrum of a module category, Mem. Amer. Math. Soc. 149 (2001), no. 707, x+125 pp.
On Neeman's well generated triangulated categories, Documenta Math. 6 (2001), 119–125, Link.
Smashing subcategories and the telescope conjecture—an algebraic approach, Invent. Math. 139 (2000), 99–133, doi:10.1007/s002229900022.
Generic modules over artin algebras, Proc. London Math. Soc. 76 (1998), 276–306, doi:10.1112/S0024611598000094.
Stable equivalence preserves representation type, Comment. Math. Helv. 72 (1997), 266–284, doi:10.1007/s000140050016.

History of mathematics

An obituary of Professor Helmut Lenzing (1939 - 2022).
An obituary of Professor Herbert Kupisch (1928 - 2022).
An obituary of Professor Bernd Fischer (1936 - 2019).
Crawley-Boevey wird Humboldt-Professor in Bielefeld, Mitt. Deutsch. Math. Verein. 24 (2016), 80–84, doi:10.1515/dmvm-2016-0034.
(With M. Koreuber) Möglichkeiten und Grenzen der Kategorie Geschlecht in der Mathematik – Zur Dialogizität in den mathematischen Texten Emmy Noethers, in: C. von Braunmühl (ed.), Etablierte Wissenschaft und feministische Theorie im Dialog, Berliner Wissenschafts-Verlag (2003), 247–269.
Paul Lazarsfeld – Begründer mathematisch exakter Sozialwissenschaften, Wechselwirkung 38 (1988), 39–43.

Books

Homological Theory of Representations, Cambridge Studies in Advanced Mathematics 195, Cambridge Univers. Press, 2021, 482 pp.
(With P. Littelmann, G. Malle, K.-H. Neeb, C. Schweigert) Representation Theory – Current Trends and Perspectives, EMS Publishing House, 2017, 773 pp.
(With D. J. Benson and A. Skowronski) Advances in Representation Theory of Algebras, EMS Publishing House, 2013, 378 pp.
(With D. J. Benson and S. B. Iyengar) Representations of finite groups: Local cohomology and support, Oberwolfach Seminars 43, Birkhäuser Verlag, 2012, 111 pp.
(With L. Angeleri Hügel and D. Happel) Handbook of Tilting Theory, London Math. Soc. Lecture Note Ser. 332, Cambridge Univ. Press, 2007, 480 pp.
The spectrum of a module category, Mem. Amer. Math. Soc. 149 (2001), no. 707, x+125 pp.
(With C. M. Ringel) Infinite length modules, Proceedings of the Euroconference 'Infinite length modules' 1998 in Bielefeld, Trends in Mathematics, Birkhäuser Verlag, 2000, 440 pp.

Book reviews

Amnon Neeman, Triangulated categories, Jahresber. Dtsch. Math.-Ver. 106 (2004), 6–8.
Paulus Gerdes, Ethnomathematik – dargestellt am Beispiel der Sona Geometrie, Spektrum der Wissenschaft, September (1998), 118–120.

Preprints

(With D. Benson, S. B. Iyengar, and J. Pevtsova) Stratification and duality for unipotent finite supergroup schemes, arxiv.org/2010.10430.
(With S. B. Iyengar) The Nakayama functor and its completion for Gorenstein algebras, arxiv.org/2010.05676.
(With D. Benson, S. B. Iyengar, and J. Pevtsova) Rank varieties and π-points for elementary supergroup schemes, arxiv.org/2008.02727.
(With D. Benson, S. B. Iyengar, and J. Pevtsova) Detecting nilpotence and projectivity over finite unipotent supergroup schemes, arxiv.org1901.08273.

Notes and presentations

Completions of triangulated categories (Aarhus, March 2023)
Zwischen Algebra und Geometrie – Erinnerungen an Helmut Lenzing (Paderborn, January 2023)
Presentation Øyvind 60 (Trondheim, June 2022)
Material about support theory for representations for two CIMPA Schools at Medellín in June 2018 and Isfahan in April 2019
Material about Cauchy sequences and Cauchy completions
The Tamari lattice in representation theory (Isfahan, April 2019)
Stratification of triangulated categories (Aveiro, June 2015)
Stratification of triangulated categories (Notes by Pieter Belmans from a summer school at Nantes, June 2014)
Stratifying triangulated categories: support and cosupport of complexes (Nantes, June 2014)
Morphisms determined by objects and flat covers (Spineto, June 2014)
Relative homological algebra in triangulated categories (Aberdeen, November 2013)
Michael Butler – From abelian groups to strings and bands (Sherbrooke, October 2013)
Notes on local cohomology and support (Summer 2013)
Koszul, Ringel, and Serre duality for strict polynomial functors (Woods Hole, Banff and Guanajuato, April/May 2012)
Functors and morphisms determined by objects revisited (Shanghai, October 2011)
Stratifying triangulated categories: support and cosupport of complexes (Moscow, September 2011)
Classifying representations through local cohomology and support (Tokyo, August 2010)
Cosupport and colocalizing subcategories of modules and complexes (Beijing, May 2010)
Notes on the Gabriel-Roiter measure, arXiv:1107.2631.
(With X.-W. Chen) Introduction to coherent sheaves on weighted projective lines, arXiv:0911.4473.
Representations of quivers via reflection functors, arXiv:0804.1428.

Recent and forthcoming meetings

Workshop "Cohomology of Finite Groups: Interactions and Applications" (Oberwolfach, August 9 - 15, 2020)
Workshop and 19th International Conference on Representations of Algebras (ICRA 2020) (Trieste, July 21 - 31, 2020)
Workshop "Representation Theory of Quivers and Finite Dimensional Algebras" (Oberwolfach, January 19 - 25, 2020)
Workshop "Algebraic Representation Theory and Related Topics" (Sanya, October 7 - 11, 2019)
Conference "50 Years of Mathematics at Bielefeld – the Unity of Mathematics" (Bielefeld, September 26 - 27, 2019)
Workshop "Representation Theory in Bielefeld – Past and Future" (Bielefeld, September 24 - 26, 2019)
Workshop "Tilting Theory, Singularity Categories, and Noncommutative Resolutions" (Oaxaca, Mexico, September 1 - 6, 2019)
Workshop "Computational Applications of Quiver Representations: TDA and QPA" (Bielefeld, May 2 - 4, 2019)
CIMPA School "Advanced School on Representations of Algebras" (Isfahan, Iran, April 7 - 19, 2019)
Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) (Prague, August 8 - 17, 2018)
CIMPA School "Geometric and Homological Methods in the Representation Theory of Associative Algebras and their Applications" (Medellín, June 18 - 27, 2018)
Workshop "Discrete Categories in Representation Theory" (Bielefeld, April 20 - 21, 2018)
Mini-Workshop "Chromatic Phenomena and Duality in Homotopy Theory and Representation Theory" (Oberwolfach, March 4 - 10, 2018)
Algebraic Topology and Representation Theory (Lille, June 26 - 30, 2017)
Triangulated Categories and Geometry – a conference in honour of Amnon Neeman (Bielefeld, May 15 - 19, 2017)
Masterclass: Stratifications and duality in modular representation theory (Copenhagen, March 27 - 31, 2017)
Workshop "Representation Theory of Quivers and Finite Dimensional Algebras" (Oberwolfach, February 19 - 25, 2017)
Workshop on Weighted Projective Spaces and Representation Theory (Hefei, March 4 - 9, 2016)
Mini-Workshop "Triangulated Categories and Geometry" (Bielefeld, March 1 - 2, 2016)
Workshop on Representations, Support, and Cohomology (in honour of Rolf Farnsteiner for his 60th birthday) (Bielefeld, December 4 - 5, 2015)
Groups, Representations and Cohomology: Summer School and Conference in honour of Dave Benson's 60th birthday (Isle of Skye, June 19 - 26, 2015)
Workshop "Cohomology of Finite Groups: Interactions and Applications" (Oberwolfach, May 3 - 9, 2015)
Research program "Interactions between Representation Theory, Algebraic Topology and Commutative Algebra" (CRM Barcelona, Jan 7 - Jun 30, 2015)
Workshop "Non-crossing partitions in representation theory" (Bielefeld, June 12 - 14, 2014)
Workshop "Colloquium in honour of the 75th birthday of Helmut Lenzing" (Bielefeld, May 15 - 16, 2014)
Workshop "Representation Theory of Quivers and Finite Dimensional Algebras" (Oberwolfach, February 16 - 22, 2014)
Workshop "Polynomial functors and Schur algebras" (Bielefeld, November 7 - 9, 2013)
Workshop "Matrix Factorizations in Algebra, Geometry, and Physics " (Oberwolfach, September 1 - 7, 2013)
Conference in memoriam of Dieter Happel (Chemnitz, May 4 - 6, 2013)
Workshop and International Conference "Representations of Algebras (ICRA 2012)" (Bielefeld, August 8 - 17, 2012)
Summer School and Workshop "Cohomology and Support in Representation Theory" (Seattle, July 27 - August 5, 2012)
Groups 2012 – A conference in honour of the 75th birthday of Bernd Fischer (Bielefeld, March 12 - 16, 2012)
Workshop "Representation Theory: Cohomology and Support" (Morningside Center of Mathematics, Beijing, September 26 - 30, 2011)
Workshop "Matrix Factorizations" (Bielefeld, May 6 - 8, 2011)
Darstellungstheorie Schwerpunkttagung 2011 (Münster, March 1 - 4, 2011)
Workshop "Representation Theory of Quivers and Finite Dimensional Algebras" (Oberwolfach, February 20 - 26, 2011)

About my family

Next generation: A picture of my two children Judith and Simon taking off (from the ruins of St. Petri at Kloster Dalheim).
Previous generations: The lecture of my great-grandfather on the occasion of his 60th Doktorjubiläum. Incidentally, his father was teaching the same subject at the same school, while his grandfather was coming from a different direction; see a biographical entry from "Allgemeine Deutsche Biographie", Zwanzigster Band, Königl. Akademie der Wissenschaften, Leipzig, 1884.

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