Emeritus Professor Anthony (Tony) GUTTMANN

Emeritus Professor (Associate) / Professor

School of Mathematics and Statistics

  • Room: G55
  • Building: Peter Hall Building
  • Campus: Parkville

Research Interests

  • Critical Phenomena (phase transitions)
  • Exact solutions of lattice models
  • Statistical Mechanics
  • Enumerative combinatorics
  • Mathematical Physics

Research Groups

Recent Publications

  • N. Beaton, A. Guttmann, I. Jensen. Two-dimensional interacting self-avoiding walks: new estimates for critical temperatures and exponents. Journal of Physics A: Mathematical and Theoretical, 53, 165002 (20pp), 2020. doi: 10.1088/1751-8121/ab7ad1.

  • A. Guttmann, EJ Janse van Rensburg, I. Jensen, S. Whittington. Polygons pulled from an adsorbing surface. Journal of Physics A: Mathematical and Theoretical, 51, 074001 (30pp), 2018. doi: 10.1088/1751-8121/aaa3b9.

  • N. Beaton, A. Guttmann, AR Conway. On consecutive pattern-avoiding permutations of length 4, 5 and beyond. Discrete Mathematics and Theoretical Computer Science, 19, 2018.

  • Andrew R Conway, A. Guttmann, P. Zinn-Justin. 1324-avoiding permutations revisited. Advances in Applied Mathematics, 96, 312-333, 2018. doi: 10.1016/j.aam.2018.01.002.

  • A. Elvey Price, AJ Guttmann, A. Guttmann. Permutations sortable by two stacks in series. Advances in Applied Mathematics, 83, 81-96, 2017. doi: 10.1016/j.aam.2016.09.003.

View all

Extra Information

My research interests are in equilibrium statistical mechanics in general, and more particularly in discrete models of phase transitions. As these are often equivalent to a combinatorial problem, I am equally interested in the relevant combinatorics, and the connection between the two. Additionally, I am regularly looking for new ways to count the underlying graphs efficiently. This leads me into a study of algorithmic complexity. 1978 Awarded Fulbright Senior Fellowship 2000 Fellow of the Australian Mathematical Society 2003 Centenary Medal 2007 Fellow of the Australian Academy of Technological Sciences and Engineering 2009 Fellow of the Society for Industrial and Applied Mathematics 2012 Awarded Australian Mathematical Sciences Institute (AMSI) Medal 2016 Awarded certificate as Most published author by Journal of Physics A. 2020 Member of the Order of Australia (AM).

Past Postgraduate Supervision

Name Thesis title
Nicholas BEATON "Combinatorics of Lattice Paths and Polygons"
Debra BENNETT-WOOD "Numerical studies of Self-avoiding walks"
Yao-ban CHAN "Selected problems in lattice statistical mechanics"
Andrew ELVEY PRICE ""Selected problems in enumerative combinatorics: Permutation classes, random walks and planar maps.""
Will JAMES "The enumeration of heaps and almost-convex polygons"
Andrew RECHNITZER "Some problems in the counting of lattice animals, polyominoes, polygons and walks"
Jason WHYTE "Global a priori identifiability of biomolecular interaction models in flow-cell optical biosensor experiments"
Henry (Ling Heng) WONG "Topics on Lattice Models in Statistical Mechanics"

Past Honours & MSc Students

Name Project title
Mark WASSELL

Recent Grant History

Year(s) Source Type Title
2014 - 2016 ARC Discovery Advanced algorithms for statistical mechanical models (080078)
2012 - 2014 ARC Discovery Critical behaviour of lattice models of spin systems
2010 - 2012 ARC Discovery Green functions, correlation functions and differential equations

Awards

Year Name Organisation
2006 Szekeres Medal Australian Mathematical Society
2005 Lyle Medal Australian Academy of Science
2004 B H Neumann Australian Mathematics Trust
2002 Fellow of The Australian Academy of Science Australian Academy of Science
2000 Centenary Medal Australian Government
1998 Hannan Medal Australian Academy of Science