Bernhard Krön

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Address University of Vienna Faculty of Mathematics Nordbergstraße 15 A-1090 Vienna, Austria Sprechstunde nach Vereinbarung email: office: +43-1-4277-50647 mobil: +43-680-1285929 fax: +43-1-4277-50620

Contents news and current events teaching fields of research publications curriculum vitae some colleagues links

News and current events

• Es gibt nun eine eigene Seite mit Infos zu meiner Übungsgruppe 1 - mit den Ergebnissen des ersten Tests.

Teaching

• 2013 VO+UE Einführung in die Analysis
• 2012/13 SE Analysis für LAK (Do 16:00-17:30, 2A310 UZA2) und SE Stochastik für LAK (geblockt an Samstagen)
• 2012 UE Lineare Algebra und Geometrie 1, Gruppe 2 Freitag 11:00-13:00 im HS3, UZA 2
• 2012 UE Stochastik für das Lehramt, Gruppe 3 Donnerstag 13:15-14:45 im C 2.09, UZA 4
• 2011/12 UE Diskrete Mathematik, Gruppe 2 Do 13.15-14.00 HS 3, UZA 2; Gruppe 3 Di 17.00-17.45 D1.03, UZA 4
• 2011/12 SE Graph Theory, Mi 11.15-12.45, D1.03 UZA 4
• 2011 UE Einführung in Lineare Algebra und Geometrie, Gruppe 4
• 2011 UE Lineare Algebra und Geometrie 1, Gruppe 2
• 2010/11 lecture - Combinatorics
• 2010 lecture - Graph Theory
• 2010 UE Analysis 1
• 2009/10 UE Einführung in die Analysis
• 2009/10 UE Diskrete Mathematik
• 2008/09 lecture - Graphs And Groups, Infinite Graphs
• 2008 lecture - Combinatorics


• Here you find the teaching evaluations of my courses at the University of Vienna.
  


• bachelor-, diploma-, master and PhD-theses
  
  

Fields of research

• graphs, automorphisms of inifinite graphs, structure tree theory
• combinatorial and geometric group theory, Cayley graphs, ends of graphs and groups and other boundaries, group splittings, Bass-Serre Theory, quasi-isometry invariants

Publications

• B. Krön, J. Lehnert, M.J. Stein. Linear boundary and HNN-extensions (submitted).
• B. Krön, J. Lehnert, N. Seifter, E. Teufl. The linear boundary of nilpotent groups (submitted).
• B. Krön. Form und Stil mathematischer Texte, Int. Math. Nachr., 218, 29-42 (2011)
• B. Krön. Cutting up graphs revisited - a short proof of Stallings' structure theorem. Groups Complex. Cryptol., 2 no. 2, 213-221 (2010).
• M.J. Dunwoody, B. Krön. Vertex cuts.
• 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 no. 1, 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. Wessely. Consitent cycles in infinite graphs.
• B. Krön, E. Teufl. A theorem of Halin for path connected Hausdorff space.

Other publicationss.

• Talk on "Vertex cuts and group splitting" at XXI Escola de Álgebra, Brasilia (26.07.2010).
  
• 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 hope I find time to rewrite it completely and extend it one day.

Curriculum Vitae

• Teacher at Wienerwaldgymnasium (part time, since Sept. 2012).
• Habilitation at University of Vienna, (March 2011).
• Visiting Professor at the City College of New York of the City University of New York, (Jan. 2009 - May 2009).
• Universitätsassistent, University of Vienna Faculty of Mathematics (similar to Ass.Prof. or Lecturer)
• 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, and of Herbert Fleischner at the Austrian Academy of Science (Oct. - Dec. 2002).
• Universitätsassistent, 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).
  
• Civil service, probation office (Neustart) Salzburg, at the "Saftladen" (1998-1999).
  
• Study of Mathematics at the Department of Mathematics at the University of Salzburg (1990 - 1998).
  

You can download a detailed curriculum vitae.

Some colleagues

• people at our department
• Donald I. Cartwright
• Reinhard Diestel
  
• Martin J. Dunwoody
• Agelos Georgakopoulos
• Peter J. Grabner
• Jörg Lehnert
• Aleksander Malnič
• Christoph Marx
• Rögnvaldur G. Möller
• James Parkinson
• Primož Potočnik
• Norbert Seifter
• Primo Šparl
• Maya J. Stein
• Elmar Teufl
• Wolfgang Woess

Links

• Wienerwaldgymnasium
• Get your quality tipi handmade my Irmi Krön.
• Fotos meiner Hochzeit.
• Slovenian-Austrian exchange project.
• Vienna is famouse for its coffeehouses. But the nicest coffeehouse in the world is here.
• August 25 - 27 2008: workshop Groups and Infinite Graphs at the Erwin Schrödinger International Institute, Vienna.
• My Mathematical Genealogy
• Bernhard's adventures in NY