Prof. Dr. Henning Krause

Professor

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

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

Office: V5-222

Office hours: Monday 14:00 - 15:00.

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.

I am involved in two major research projects:

I am an editorial board member for these journals:

Teaching

SS 2010: Einführung in die Darstellungstheorie (Vorlesung) [ekvv]
SS 2011: Einführung in die Darstellungstheorie (Vorlesung) [ekvv]
SS 2011: Darstellungen von endlichen Gruppen (Seminar) [ekvv]
WS 2011/12: Lineare Algebra I (Vorlesung) [ekvv]
WS 2011/12: Auslander-Reiten Theorie (Seminar) [ekvv]
WS 2011/12: Gruppen und Symmetrien (Seminar) [ekvv]
SS 2012: Lineare Algebra II (Vorlesung) [ekvv]
WS 2012/13: Elementare Zahlentheorie (Vorlesung) [ekvv]
WS 2012/13: Schur functors and symmetric functions (Seminar) [ekvv]
SS 2013: Algebra I (Vorlesung) [ekvv]
SS 2013: Local cohomology and support (Vorlesung) [ekvv]

Publications since 2000

Smashing subcategories and the telescope conjecture—an algebraic approach, Invent. Math. 139 (2000), 99–133.
(With G. Zwara) Stable equivalence and generic modules, Bull. London Math. Soc. 32 (2000), 615–618.
Finite versus infinite dimensional representations—a new definition of tameness, in: Infinite length modules (Bielefeld, 1998), 393–403, Birkhäuser, Basel, 2000.
(With D. J. Benson) Generic idempotent modules for a finite group, Algebras and Representation Theory 3 (2000), 337–346.
Auslander–Reiten theory via Brown representability, K-theory 20 (2000), 331–344.
(With U. Reichenbach) Endofiniteness in stable homotopy theory, Trans. Amer. Math. Soc. 353 (2001), 157–173.
Brown representability and flat covers, J. Pure Appl. Algebra 157 (2001), 81–86.
On Neeman's well generated triangulated categories, Documenta Math. 6 (2001), 119–125.
The spectrum of a module category, Mem. Amer. Math. Soc. 149 (2001), no. 707, x+125 pp.
(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.
(With A. B. Buan and Ø. Solberg) On the lattice of cotilting modules, AMA Algebra Montp. Announc. 1 (2002), 6 pp.
A Brown representability theorem via coherent functors, Topology 41 (2002), 853–861.
Coherent functors in stable homotopy theory, Fundamenta Math. 173 (2002), 33–56.
A duality between complexes of right and left modules, in: Representations of algebra. Vol. I, 87–97, Beijing Norm. Univ. Press, Beijing, 2002.
(With C. Geiss) On the notion of derived tameness, J. Algebra and Applications 1 (2002), 133–157.
A short proof for Auslander's defect formula, Linear Algebra Appl. 365 (2003), 267–270.
(With Ø. Solberg) Filtering modules with finite projective dimension, Forum Math. 15 (2003), 377–393.
(With A. Beligiannis) Realizing maps between modules over Tate cohomology rings, Beiträge Algebra Geom. 44 (2003), 451–466.
(With A. B. Buan) Cotilting modules over tame hereditary algebras, Pacific J. Math. 211 (2003), 41–59.
Uniqueness of uniform decompositions in abelian categories, J. Pure Appl. Algebra 183 (2003), 125–128.
(With Ø. Solberg) Applications of cotorsion pairs, J. London Math. Soc. 68 (2003), 631–650.
Coherent functors and covariantly finite subcategories, Algebras and Representation Theory 6 (2003), 475–499.
(With A. B. Buan) Tilting and cotilting for quivers of type A_n, J. Pure Appl. Algebra 190 (2004), 1–21.
(With D. J. Benson and S. Schwede) Realizibility of modules over Tate cohomology, Trans. Amer. Math. Soc. 356 (2004), 3621–3668.
Auslander–Reiten triangles and a theorem of Zimmermann, Bull. London Math. Soc. 37 (2005), 361–372.
The stable derived category of a noetherian scheme, Compos. Math. 141 (2005), 1128–1162.
(With D. J. Benson and S. Schwede) Introduction to realizability of modules over Tate cohomology, in: Representations of algebras and related topics, 81–97, Amer. Math. Soc., Providence, RI, 2005.
Epimorphisms of additive categories up to direct factors, J. Pure Appl. Algebra 203 (2005), 113–118.
Cohomological quotients and smashing localizations, Amer. J. Math. 127 (2005), 1191–1246.
(With S. B. Iyengar) Acyclicity versus total acyclicity for complexes over noetherian rings, Documenta Math. 11 (2006), 207–240.
(With D. Kussin) Rouquier's theorem on representation dimension, in: Trends in representation theory of algebras and related topics, 95–103, Contemp. Math. 406, Amer. Math. Soc., Providence, RI, 2006.
(With J. Le) The Auslander–Reiten formula for complexes of modules, Adv. Math. 207 (2006), 133–148.
Derived categories, resolutions, and Brown representability, in: Interactions between homotopy theory and algebra, 101–139, Contemp. Math. 436, Amer. Math. Soc., Providence, RI, 2007.
(With A. B. Buan and Ø. Solberg) Support varieties: an ideal approach, Homology, Homotopy Appl. 9 (2007), 45–74.
An axiomatic characterization of the Gabriel–Roiter measure, Bull. London Math. Soc. 39 (2007), 550–558.
(With D. J. Benson) Complexes of injective kG-modules, Algebra Number Theory 2 (2008), 1–30.
(With an appendix by S. B. Iyengar) Thick subcategories of modules over commutative rings, Math. Annalen 340 (2008), 733–747.
(With D. Benson and S. B. Iyengar) Local cohomology and support for triangulated categories, Ann. Sci. Ecole Norm. Sup. (4) 41 (2008), 573–619.
(With A. Beligiannis) Thick subcategories and virtually Gorenstein algebras, Illinois J. Math. 52 (2009), 551–562.
(With P. A. Bergh, S. B. Iyengar and S. Oppermann) Dimensions of triangulated categories via Koszul objects, Math. Z. 265 (2010), 849–864.
Localization theory for triangulated categories, in: Triangulated categories, 161–235, London Math. Soc. Lecture Note Ser. 375, Cambridge Univ. Press, Cambridge, 2010.
(With J. Stovicek) The telescope conjecture for hereditary rings via Ext-orthogonal pairs, Adv. Math. 225 (2010), 2341–2364.
(With Y. Ye) On the centre of a triangulated category, Proc. Edinburgh Math. Soc. 54 (2011), 443–466.
(With X.-W. Chen) Expansions of abelian categories, J. Pure Appl. Algebra 215 (2011), 2873–2883.
(With D. J. Benson and S. B. Iyengar) Stratifying triangulated categories, J. Topology 4 (2011), 641–666.
(With D. J. Benson and S. B. Iyengar) Module categories for finite group algebras, in: Representations of Algebras and Related Topics, 55-83, European Math. Soc., 2011.
(With D. J. Benson and S. B. Iyengar) Localising subcategories for cochains on the classifying space of a finite group, C. R. Math. Acad. Sci. Paris 349 (2011), 953-956.
(With D. J. Benson and S. B. Iyengar) Stratifying modular representations of finite groups, Ann. of Math. 174 (2011), 1643-1684.
Approximations and adjoints in homotopy categories, Math. Annalen 353 (2012), 765-781.
Report on locally finite triangulated categories, J. K-Theory 9 (2012), 421-458.
(With D. J. Benson and S. B. Iyengar) Colocalizing subcategories and cosupport, J. Reine Angew. Math. 673 (2012), 161-207.
(With Mike Prest) The Gabriel-Roiter filtration of the Ziegler spectrum, Quart. J. Math., doi:10.1093/qmath/has020.
(With S. B. Iyengar) The Bousfield lattice of a triangulated category and stratification, Math. Z., doi:10.1007/s00209-012-1051-7.
(With D. J. Benson, S. B. Iyengar, and appendix by G. Stevenson) Module categories for group algebras over commutative rings, J. K-Theory, doi:10.1017/is013001031jkt214.
Koszul, Ringel, and Serre duality for strict polynomial functors, Compos. Math., doi:10.1112/S0010437X12000814.

Books

(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.
(With L. Angeleri Hügel and D. Happel) Handbook Tilting Theory, London Math. Soc. Lecture Note Ser. 332, Cambridge Univ. Press, Cambridge, 2007, 480 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.

Preprints

Morphisms determined by objects in triangulated categories, to appear in “Algebras, quivers and representations”, The Abel Symposium 2011, arXiv:1110.5625.
(With Greg Stevenson) A note on thick subcategories of stable derived categories, to appear in Nagoya Math. J., arXiv:1111.2220.
Cohomological length functions, arXiv:1209.0540.
Abelian length categories of strongly unbounded type, arXiv:1301.6665.

Some notes and presentations

Krull-Remak-Schmidt categories and projective covers (June 2008, revised May 2012)
Representations of quivers via reflection functors, arXiv:0804.1428.
(With X.-W. Chen) Introduction to coherent sheaves on weighted projective lines, arXiv:0911.4473.
Notes on the Gabriel-Roiter measure, arXiv:1107.2631.
Cosupport and colocalizing subcategories of modules and complexes (Beijing, May 2010)
Classifying representations through local cohomology and support (Tokyo, August 2010)
Stratifying triangulated categories: support and cosupport of complexes (Moscow, September 2011)
Functors and morphisms determined by objects revisited (Shanghai, October 2011)
Koszul, Ringel, and Serre duality for strict polynomial functors (Woods Hole, Banff and Guanajuato, April/May 2012)
Notes on local cohomology and support (Summer 2013)

Recent and forthcoming meetings

Workshop "Representation Theory of Quivers and Finite Dimensional Algebras" (Oberwolfach, February 20 - 26, 2011)
Darstellungstheorie Schwerpunkttagung 2011 (Münster, March 1 - 4, 2011)
Workshop "Matrix Factorizations" (Bielefeld, May 6 - 8, 2011)
Workshop "Representation Theory: Cohomology and Support" (Morningside Center of Mathematics, Beijing, September 26 - 30, 2011)
Groups 2012 – A conference in honour of the 75th birthday of Bernd Fischer (Bielefeld, March 12 - 16, 2012)
Summer School and Workshop "Cohomology and Support in Representation Theory" (Seattle, July 27 - August 5, 2012)
Workshop and International Conference "Representations of Algebras (ICRA 2012)" (Bielefeld, August 8 - 17, 2012)
Conference in memoriam of Dieter Happel (Chemnitz, May 4 - 6, 2013)
Workshop "Matrix Factorizations in Algebra, Geometry, and Physics " (Oberwolfach, September 1 - 7, 2013)

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.