Bernhard Krön

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Address University of Vienna Faculty of Mathematics Nordbergstraße 15 A-1090 Vienna, Austria email: office: +43-1-4277-50647 secretary: +43-1-4277-50601/50602/50603 fax: +43-1-4277-50620 office hours: Tue 14:00-15:00, Wed 15:00-16:00 Achtung: keine Sprechstunde am 23. und 24. Feb.

Contents News and current events Recent teaching Fields of research Publications Curriculum Vitae Some Colleagues Links My Mathematical Genealogy Bernhard's adventures in NY

News and current events

• Students may contact me via email or phone to arrange consultation hours from 28 to 30 December and from 7 January. I am not in Vienna from 2 to 6 January.
  
• Slovenian-Austrian exchange project.
• You will meet me at: Pedagoska fakulta, University of Ljubljana, Mon 6 to Fri 11 Dec (talk on Thursday 10 Dec)
  Graz University of Technolgy, Fri 11 to Mon 14 Dec (talk on Mon 14 Dec)
  "Graph Theory", Sun 21 to Sat 27 February 2010, Mathematisches Forschungsinstitut Oberwolfach.

Recent Teaching

at the University of Vienna:
• planned: 2010/11 lecture - Combinatorics
• 2010 lecture - Graph Theory, Monday 15:15-17:00, C2.09 UZA4
• 2010 UE Analysis 1, Friday 8:15-9:45 HS3 UZA2
• 2009/2010 UE Einführung in die Analysis, Fr 10-12, HS D101
• 2009/2010 UE Diskrete Mathematik, Group 1 Mi 10:15-11:00 D1.01, Group 2 Mi 11:15-12:00 D1.01
• 2008/09 lecture - Graphs And Groups, Infinite Graphs
• 2008 lecture - Combinatorics


• bachelor-, diploma-, master and PhD-theses
  
  at CCNY (personal homepage):
• Math 37500 - Elements of Probability Theory
• Math 39200 - Linear Algebra and Vector Analysis for Engineers

Fields of Research

• geometric group theory, Cayley graphs
• ends of graphs, and groups and other boundaries, quasi-isometries
• group actions on graphs, automorphisms of inifinite graphs, structure tree theory
• ends of topologicale space, non-locally finite graphs, abstract ends
• random walks on graphs and groups

Publications

• B. Krön, E. Teufl. Ends - Group theoretical and topological aspects, pre-print.
• M.J. Dunwoody, B. Krön. Vertex cuts (short version January 2010).
• B. Krön. Infinite faces and ends of almost transitive plane graphs, pre-print.
• B. Krön, R.G. Möller. Quasi-isometries between graphs and trees, J. Combin. Theory Ser. B, 98 994-1013 (2008).
• B. Krön, R.G. Möller. Free groups and ends of graphs, Abh. Math. Sem. Univ. Hamburg, 78 no. 1, 1-15 (2008).
• B. Krön, R.G. Möller. Analogues of Cayley graphs for topological groups, Math. Z., 258 no. 3, 637-675 (2008).
• B. Krön, R.G. Möller. Metric ends, fibers and automorphisms of graphs, Math. Nachr., 281 no. 1, 62-74 (2008).
• D.I. Cartwright, B. Krön. On Stallings' unique factorization groups, Bull. Austral. Math. Soc., 73, 27-36 (2006).
• B. Krön, E. Teufl. Asymptotics of the transition probabilities of the simple random walk on self-similar graphs, Trans. Amer. Math. Soc., 356 393-414 (2004).
• B. Krön. Growth of self-similar graphs, Journal of Graph Theory, 45 no. 3, 224-239 (2004).
• B. Krön. Green functions on self-similar graphs and bounds for the spectrum of the Laplacian, Ann. Inst. Fourier (Grenoble) 52 no. 6, 1875-1900 (2002).
• B. Krön. Quasi-isometries between non-locally-finite graphs and structure trees, Abh. Math. Sem. Univ. Hamburg 71, 161-180 (2001).
• B. Krön. End compactifications in non-locally-finite graphs. Math. Proc. Cambridge Philos. Soc. 131, 427-443 (2001).
• B. Krön. Structural and Spectral Theory of Infinite Graphs, PhD thesis, Graz University of Technology, (2001).
• B. Krön. Topologische Strukturtheorie nicht lokalendlicher Graphen, diploma thesis, University of Salzburg, (1998).

Work in progress

• B. Krön, J. Lehnert, M.J. Stein, Linear boundary and HNN-extensions.
• B. Krön, J. Lehnert, N. Seifter, E. Teufl, The linear boundary of nilpotent groups.

Other publicationss.

• Talk on "Tree Decompositions" (printable version) (version used in the presentation) in Ljubljana (10.12.2009) and Graz (14.12.2009)
  
• The slides of my talk on "Vertex cuts" at "Boundaries", June 29 - July 4 2009 in Graz, Austria.
• R.G. Möller, Groups acting on locally finite graphs - a survey of the infinitely ended case, C. M. Campbell (ed.) et al., Groups '93 Galway/St. Andrews'. Proceedings of the international conference, Galway, Ireland, August 1-14, 1993. Volume 2. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 212, (1995) 426-456. A good introduction, unfortunately this version is without the pictures.
• This is an old handout to a series of talks on ends of graphs. I am planning to rewrite this notes according to my present lecture on Ends of Graphs and Groups.

Curriculum Vitae

• Visiting Professor at the City College of New York (CCNY) of the City University of New York (CUNY), (Jan. 2009 - May 2009).
• Universitätsassistent, University of Vienna Faculty of Mathematics (similar to Ass.Prof. or Assoc.Prof.)
• Christian Doppler Preis 2006, the Salzburg State (Land Salzburg) science award
• Marie Curie Fellowship (IEF) of the Commission of the European Union for a stay at the Universität Hamburg in cooperation with Reinhard Diestel (Feb. 2006 to Oct. 2007).
• Erwin Schrödinger overseas fellowship of the Austrian Science Fund (FWF) for a stay at the School of Mathematics and Statistics at the University of Sydney, in cooperation with Donald I. Cartwright (March 2004 - Jan. 2006).
• Postdoctoral research fellow of Klaus Schmidt (March 2003 - Feb. 2004 and Oct. 2001 - Sept. 2002) and Christian Krattenthaler (Jan. - Feb. 2003) at the Faculty of Mathematics, University of Vienna.
• Postdoctoral research fellow of Herbert Fleischner at the Austrian Academy of Science (Oct. - Dec. 2002).
• Universitätsassistent, Vetretungsstelle (similar to Ass.Prof., substitute), at the Department of Mathematics (C), Wolfgang Woess, Graz University of Technology (Oct. 1999 - Jan. 2001), Tutor (March - July 2001).
• PhD-Study at Graz University of Technology, supervised by Peter Grabner (1999 - 2001), degree Dr.techn.
  
• Civil service, probation office (Neustart) Salzburg, at the "Saftladen" (1998-1999).
  
• Writing the Master's Thesis at the Department of Mathematics of the Università degli Studi di Milano, supervised by Wolfgang Woess (1996 - 1997).
  
• Study of Mathematics at the Department of Mathematics at the University of Salzburg (1990 - 1998), degree Mag.rer.nat.
  
• Born 1972 in Salzburg (Austria).
  

You can download a detailed curriculum vitae (6 pages).

Some Colleagues

• people at our department
• Henning Bruhn
• Donald I. Cartwright
• Reinhard Diestel
  
• Martin J. Dunwoody
• Agelos Georgakopoulos
• Peter J. Grabner
• Robert Gray
• Jörg Lehnert
• Rögnvaldur G. Möller
• Norbert Seifter
• Maya J. Stein
• Elmar Teufl
• Wolfgang Woess

Links

• Vienna is famouse for its coffeehouses. But the nicest coffeehouse in the world is here.
• Hader live im SF.
• August 25 - 27 2008: workshop Groups and Infinite Graphs at the Erwin Schrödinger International Institute, Vienna.

Last modified on 18 October 2009