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.
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.
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 | |
| Will JAMES | "The enumeration of heaps and almost-convex polygons" |
| Robin LANGER | "Symmetric functions and Macdonald polynomials" |
| 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 |