BIREP – Representations of finite dimensional algebras at Bielefeld

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 16:00 - 17:00 or by appointment (via email).

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:

- DFG Schwerpunktprogramm 1388 "Darstellungstheorie"
- DFG Sonderforschungsbereich 701 "Spektrale Strukturen und Topologische Methoden in der Mathematik"

I am an editorial board member for these journals:

- Advances in Mathematics
- Algebras and Representation Theory
- Applied Categorical Structures
- Communications in Mathematics and Statistics
- Documenta Mathematica

I am a Fellow of the American Mathematical Society.

- 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]
- WS 2013/14: Algebra II (Vorlesung) [ekvv]
- SS 2014: Spezielle Aspekte der Mathematik: Zahlentheorie (Vorlesung) [ekvv]
- SS 2014: Bachelorseminar zur Algebra (Seminar) [ekvv]
- WS 2014/15: Darstellungstheorie von Algebren I (Vorlesung) [ekvv]
- WS 2015/16: Darstellungstheorie von Algebren III (Vorlesung) [ekvv]
- SS 2016: Ausgewählte Kapitel der Zahlentheorie (Vorlesung) [ekvv]
- WS 2016/17: Lineare Algebra I (Vorlesung) [ekvv]

- 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.
- (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. 64 (2013), 891-901.
- (With S. B. Iyengar) The Bousfield lattice of a triangulated category and stratification, Math. Z. 273 (2013), 1215-1241.
- (With D. J. Benson, S. B. Iyengar, and appendix by G. Stevenson) Module categories for group algebras over commutative rings, J. K-Theory 11 (2013), 297-329.
- Koszul, Ringel, and Serre duality for strict polynomial functors, Compos. Math. 149 (2013), 996-1018.
- Abelian length categories of strongly unbounded type, Int. Math. Res. Not. (2013), doi:10.1093/imrn/rnt184.
- (With Greg Stevenson) A note on thick subcategories of stable derived categories, Nagoya Math. J. 212 (2013), 87-96.
- Morphisms determined by objects in triangulated categories, in: Algebras, Quivers and Representations, The Abel Symposium 2011, 195-207, Abel Symposia 8, Springer, 2013.
- (With G. Bobiński) The Krull-Gabriel dimension of discrete derived categories, Bull. Sci. Math. 139 (2015), 269-282.
- Morphisms determined by objects and flat covers, Forum Math., doi:10.1515/forum-2014-0115.
- Polynomial representations of GL(n) and Schur-Weyl duality, Beitr. Algebra Geom. 56 (2015), 769-773.
- The artinian conjecture (following Djament, Putman, Sam, and Snowden), in: Proceedings of the 47th symposium on ring theory and representation theory (Osaka, 2014), 104-111, Saitama University, Japan, 2015.
- (With D. J. Benson and S. B. Iyengar) A local-global principle for small triangulated categories, Math. Proc. Camb. Phil. Soc. 158 (2015), 451-476.
- Deriving Auslander's formula, Documenta Math. 20 (2015), 669-688.
- Krull-Schmidt categories and projective covers, Expo. Math. 33 (2015), 535-549.
- Cohomological length functions, Nagoya Math. J. 223 (2016), 136-161.
- (With A. Hubery) A categorification of non-crossing partitions, J. Eur. Math. Soc. 18 (2016), 2273-2313.
- Highest weight categories and strict polynomial functors, in: Representation Theory - Current Trends and Perspectives, 331-373, EMS Publishing House, 2017.
- (With D. Benson, S. B. Iyengar, and J. Pevtsova) Stratification and π-cosupport: finite groups, Math. Z. (2017), doi:10.1007/s00209-017-1853-8.
- (With D. Benson, S. B. Iyengar, and J. Pevtsova) Colocalising subcategories of modules over finite group schemes, Ann. K-Theory, to appear.
- (With D. Benson) The variety of subadditive functions for finite group schemes, Fund. Math., to appear.
- Highest weight categories and recollements, Ann. Inst. Fourier (Grenoble), to appear.
- (With K. Großblotekamp) Linear versus set valued Kronecker representations, Comm. Algebra, to appear.

- (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.
- The spectrum of a module category, Mem. Amer. Math. Soc. 149 (2001), no. 707, x+125 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.
- (With D. J. Benson and A. Skowronski) Advances in Representation Theory of Algebras, EMS Publishing House, 2013, 378 pp.

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

- (With D. Benson, S. B. Iyengar, and J. Pevtsova) Stratification for module categories of finite group schemes, arXiv:1510.06773.
- Auslander-Reiten duality for Grothendieck abelian categories, arXiv:1604.02813.
- (With D. Benson, S. B. Iyengar, and J. Pevtsova) Local duality for representations of finite group schemes, arXiv:1611.04197.
- (With P. Balmer and G. Stevenson) The frame of smashing tensor-ideals, arXiv:1701.05937.
- (With D. Vossieck) Length categories of infinite height, arXiv:1702.05415.

- 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)
- Michael Butler - From abelian groups to strings and bands (Sherbrooke, October 2013)
- Relative homological algebra in triangulated categories (Aberdeen, November 2013)
- Morphisms determined by objects and flat covers (Spineto, June 2014)
- Stratifying triangulated categories: support and cosupport of complexes (Nantes, June 2014)
- Stratification of triangulated categories (Notes by Pieter Belmans from a summer school at Nantes, June 2014)
- Stratification of triangulated categories (Aveiro, June 2015)

- 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)
- Workshop "Polynomial functors and Schur algebras" (Bielefeld, November 7 - 9, 2013)
- Workshop "Representation Theory of Quivers and Finite Dimensional Algebras" (Oberwolfach, February 16 - 22, 2014)
- Workshop "Colloquium in honour of the 75th birthday of Helmut Lenzing" (Bielefeld, May 15 - 16, 2014)
- Workshop "Non-crossing partitions in representation theory" (Bielefeld, June 12 - 14, 2014)
- Research program "Interactions between Representation Theory, Algebraic Topology and Commutative Algebra" (CRM Barcelona, Jan 7 - Jun 30, 2015)
- Workshop "Cohomology of Finite Groups: Interactions and Applications" (Oberwolfach, May 3 - 9, 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 on Representations, Support, and Cohomology (in honour of Rolf Farnsteiner for his 60th birthday) (Bielefeld, December 4 - 5, 2015)
- Mini-Workshop "Triangulated Categories and Geometry" (Bielefeld, March 1 - 2, 2016)
- Workshop on Weighted Projective Spaces and Representation Theory (Hefei, March 4 - 9, 2016)
- Workshop "Representation Theory of Quivers and Finite Dimensional Algebras" (Oberwolfach, February 19 - 25, 2017)
- Triangulated Categories and Geometry - a conference in honour of Amnon Neeman (Bielefeld, May 15 - 19, 2017)

- 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.