Anthony Dooley took up the position of Head of the School of Mathematical and Physical Sciences at UTS in January 2016, following a period of 4 years as Professor of Mathematics at the University of Bath, UK, where he was Deputy Head of Department and the inaugural Director of the Bath Institute for Mathematical Innovation. Before that, he was Professor of Mathematics at UNSW, where he was Head of School of Mathematic s and Statistics, Chair of the Academic Board and Associate Dean (Strategy).
His research is in the area of Modern Analysis, including harmonic analysis and dynamical systems. He has published over 90 peer, reviewed articles, held ARC grants continuously for 20 years, and been a Chief Investigator on the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS). He has supervised 18 PhD students to completion, and over 30 honours projects in mathematics.
Dooley has held visiting positions at the University of Yale, Research Institute of Mathematical Sciences(Kyoto), Max Planck Institute for Mathematics, Bonn, Beijing Normal University, Kyushu University, Keio University (Japan), University Paris VII (Jussieu) University of Paris XI (Orsay), University of Aix-Marseilles (Luminy) ,University of Metz, Korean Advanced Institute of Science and Technology, Azhou University (Korea) and the Mittag-Leffler Institute (Sweden).
He has served on the following Boards and Councils: University of Bath Senate, UNSW Council, National Institute of Dramatic Art (NIDA) Board, Australia and New Zealand School of Governance Board, Australian Graduate School of Management Academic Board, Expert Advisory Committee for Australian Research Council MICS panel, Academy of Science National Committee for Mathematics, Australian Mathematical Sciences Institute Board, New Zealand Peer-Based Funding Review Panel in MIST, United Kingdom EPSRC Peer Review College for Mathematics, Royal Academy of Finland Mathematics Research Panel, Unisearch Board .
He holds a PhD from the Australian National University, a Diplome des Etudes Approfondies from Paris 6, and is a Fellow of the Australian Institute of Company Directors.
© 2015 Cambridge University Press. The critical dimension of an ergodic non-singular dynamical system is the asymptotic growth rate of sums of consecutive Radon-Nikodým derivatives. This has been shown to equal the average coordinate entropy for product odometers when the size of individual factors is bounded. We extend this result to G-measures with an asymptotic bound on the size of individual factors. Furthermore, unlike von Neumann-Krieger type, the critical dimension is an invariant property on the class of ergodic G-measures.
© European Mathematical Society. We give criteria for establishing that a measure is L p -improving. Many Riesz product measures and Cantor measures satisfy this criteria, as well as certain Markov measures.
Applebaum, D. & Dooley, A. 2015, 'A generalised Gangolli-Lévy-Khintchine formula for infinitely divisible measures and Lévy processes on semi-simple Lie groups and symmetric spaces', Annales de l'institut Henri Poincare (B) Probability and Statistics, vol. 51, no. 2, pp. 599-619.View/Download from: Publisher's site
© Association des Publications de l'Institut Henri Poincaré, 2015. In 1964 R. Gangolli published a Lévy-Khintchine type formula which characterised K-bi-invariant infinitely divisible probability measures on a symmetric space G/K. His main tool was Harish-Chandra's spherical functions which he used to construct a generalisation of the Fourier transform of a measure. In this paper we use generalised spherical functions (or Eisenstein integrals) and extensions of these which we construct using representation theory to obtain such a characterisation for arbitrary infinitely divisible probability measures on a non-compact symmetric space. We consider the example of hyperbolic space in some detail.
Dooley, A.H., Golodets, V.Y. & Zhang, G. 2014, 'Sub-additive ergodic theorems for countable amenable groups', Journal of Functional Analysis, vol. 267, no. 5, pp. 1291-1320.View/Download from: UTS OPUS or Publisher's site
In this paper we generalize Kingman's sub-additive ergodic theorem to a large class of infinite countable discrete amenable group actions. © 2014 Elsevier Inc.
Dooley, A.H. & Golodets, V.Y. 2012, 'On the entropy of actions of nilpotent Lie groups and their lattice subgroups', ERGODIC THEORY AND DYNAMICAL SYSTEMS, vol. 32, pp. 535-573.View/Download from: UTS OPUS or Publisher's site
Dooley, A.H. & Hagihara, R. 2012, 'Computing the critical dimensions of Bratteli-Vershik systems with multiple edges', ERGODIC THEORY AND DYNAMICAL SYSTEMS, vol. 32, pp. 103-117.View/Download from: UTS OPUS or Publisher's site
Dooley, A.H., Hawkins, J. & Ralston, D. 2011, 'Families of type III0 ergodic transformations in distinct orbit equivalent classes', MONATSHEFTE FUR MATHEMATIK, vol. 164, no. 4, pp. 369-381.View/Download from: UTS OPUS or Publisher's site
Pollett, P.K., Dooley, A.H. & Ross, J.V. 2010, 'Modelling population processes with random initial conditions', MATHEMATICAL BIOSCIENCES, vol. 223, no. 2, pp. 142-150.View/Download from: Publisher's site
Craddock, M.J. & Dooley, A.H. 2010, 'On The Equivalence Of Lie Symmetries And Group Representations', Journal of Differential Equations, vol. 249, no. 3, pp. 621-653.View/Download from: UTS OPUS or Publisher's site
We consider families of linear, parabolic PDEs in n dimensions which possess Lie symmetry groups of dimension at least four. We identify the Lie symmetry groups of these equations with the (2n+1)-dimensional Heisenberg group and SL(2, R). We then show th
Dooley, A.H. & Golodets, V.Y. 2009, 'The geometric dimension of an equivalence relation and finite extensions of countable groups', ERGODIC THEORY AND DYNAMICAL SYSTEMS, vol. 29, pp. 1789-1814.View/Download from: Publisher's site
Dooley, A.H., Golodets, V.Y., Rudolph, D.J. & Sinel'shchikov, S.D. 2008, 'Non-Bernoulli systems with completely positive entropy', ERGODIC THEORY AND DYNAMICAL SYSTEMS, vol. 28, pp. 87-124.View/Download from: Publisher's site
Dooley, A.H. & Raffoul, R.W. 2007, 'Matrix coefficients and coadjoint orbits of compact Lie groups', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 135, no. 8, pp. 2567-2571.View/Download from: Publisher's site
Bezuglyi, S., Dooley, A.H. & Kwiatiowski, J. 2006, 'Topologies on the group of homeomorphisms of a Cantor set', TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, vol. 27, no. 2, pp. 299-331.
Bezuglyi, S., Dooley, A.H. & Kwiatkowski, J. 2006, 'Topologies on the group of Borel automorphisms of a standard Borel space', TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, vol. 27, no. 2, pp. 333-385.
Dooley, A.H. & Stenflo, O. 2006, 'A criterion for uniqueness in G-measures and perfect sampling', Mathematical Proceedings of the Cambridge Philosophical Society, vol. 140, no. 3, pp. 545-551.View/Download from: Publisher's site
Using coupling techniques, we prove uniqueness in G-measures under a weak regularity condition and give estimates of the associated rates of convergence. We also show how to generate a random variable distributed according to the unique G-measure on cylinder sets for any fixed level of precision. © 2006 Cambridge Philosophical Society.
Dooley, A.H. & Stenflo, O. 2006, 'A criterion for uniqueness in G-measures and perfect sampling', MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, vol. 140, pp. 545-551.View/Download from: Publisher's site
Dooley, A.H. & Wildberger, N.J. 2006, 'Orbital convolution theory for semi-direct products', JOURNAL OF LIE THEORY, vol. 16, no. 4, pp. 743-776.
We show that the Morse system is approximately transitive (AT) and that a system of positive entropy cannot be AT. We give examples of zero-entropy systems that are not AT, one of which is a two-point extension of a system that is AT. © 2004 Cambridge University Press.
Bezuglyi, S., Dajani, K., Dooley, A.H. & Hamachi, T. 2004, 'Isornorphic actions of group extensions on a measure space', INDAGATIONES MATHEMATICAE-NEW SERIES, vol. 15, no. 2, pp. 167-188.View/Download from: Publisher's site
Dooley, A.H. & Golodets, V.Y. 2002, 'The spectrum of completely positive entropy actions of countable amenable groups', JOURNAL OF FUNCTIONAL ANALYSIS, vol. 196, no. 1, pp. 1-18.View/Download from: Publisher's site
Dooley, A.H. & Gupta, S.K. 2002, 'Transferring Fourier multipliers from S2p-1 to Hp-1', ILLINOIS JOURNAL OF MATHEMATICS, vol. 46, no. 3, pp. 657-677.
Dooley, A.H. & Wildberger, N.J. 1999, 'Global character formulae for compact Lie groups', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 351, no. 2, pp. 477-495.View/Download from: Publisher's site
Dooley, A.H. & Zhang, G. 1999, 'Spherical functions on harmonic extensions of H-type groups', Journal of Geometric Analysis, vol. 9, no. 2, pp. 254-255.
We consider the harmonic extension AN of an H-type group N with Lie algebra n = v + 3, and [v, v] = 3. We characterize the positive definite spherical functions on AN. © 1999 The Journal of Geometric Analysis.
Cowling, M., Dooley, A., Korányi, A. & Ricci, F. 1998, 'An approach to symmetric spaces of rank one via groups of Heisenberg type', Journal of Geometric Analysis, vol. 8, no. 2, pp. 235-237.
We give an elementary unified approach to rank one symmetric spaces of the noncompact type, including proofs of their basic properties and of their classification, with the development of a formalism to facilitate future computations. Our approach is based on the theory of Lie groups of H-type. An algebraic condition of H-type algebras, called J 2 , is crucial in the description of the symmetric spaces. The classification of H-type algebras satisfying J 2 leads to a very simple description of the rank one symmetric spaces of the noncompact type. We also prove Kostant's double transitive theorem; we describe explicitly the Riemannian metric of the space and the standard decompositions of its isometry group. Examples of the use of our theory include the description of the Poisson kernel and the admissible domains for convergence of Poisson integrals to the boundary. © 1998 The Journal of Geometric Analysis.
Dooley, A.H. & Zhang, G.K. 1998, 'Algebras of invariant functions on the Shilov boundaries of Siegel domains', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 126, no. 12, pp. 3693-3699.View/Download from: Publisher's site
Dooley, A.H., Klemes, I. & Quas, A.N. 1998, 'Product and Markov measures of type III', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, vol. 65, pp. 84-110.
Cotton, P. & Dooley, A.H. 1997, 'Contraction of an adapted functional calculus', Journal of Lie Theory, vol. 7, no. 2, pp. 147-164.
We aim to show, using the example of a Riemannian symmetric pair (G, K) = (SL 2 (), SO(2)), how contraction ideas may be applied to functional calculi constructed on coadjoint orbits of Lie groups. We construct such calculi on principal series orbits and generic orbits of the Cartan motion group V K , and show how the two are related. Since the calculi are adapted to the representations traditionally attached to the orbits, we recover at the Lie algebra level the contraction results of Dooley and Rice . © 1997 Heldermann Verlag.
Dooley, A.H. & Zhang, G.K. 1997, 'Generalized principal series representations of SL(1+n, C)', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 125, no. 9, pp. 2779-2787.View/Download from: Publisher's site
Dajani, K. & Dooley, A. 1996, 'The mean ratio set for ax + b valued cocycles', Publications of the Research Institute for Mathematical Sciences, vol. 32, no. 4, pp. 671-688.View/Download from: Publisher's site
Let X = i=1 Z l(i) be acted upon by the group = i=1 Z l(i) of changes in finitely many coordinates and a G-measure on X which is nonsingular for the -action on X. We consider cocycles on (X, , ) taking values in the ax + b group. We give a structure theorem for such cocycles, we define the mean ratio set which is a closed subgroup of the ax + b group and we exhibit for each closed subgroup a cocycle whose mean ratio set is the given subgroup.
A conjecture about the L 4 -norms of trigonometric polynomials on SU(2) is discussed and some partial results are proved.
Dooley, A.H. & Eigen, S.J. 1996, 'A family of generalized Riesz products', CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, vol. 48, no. 2, pp. 302-315.View/Download from: Publisher's site
Dooley, A.H. & Gupta, S.K. 1996, 'Continuous singular measures with absolutely continuous convolution squares', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 124, no. 10, pp. 3115-3122.View/Download from: Publisher's site
Dooley, A.H., Orsted, B. & Zhang, G. 1996, 'Relative discrete series of line bundles over bounded symmetric domains', ANNALES DE L INSTITUT FOURIER, vol. 46, no. 4, pp. 1011-&.
We show how to calculate the ratio sets of g-measures as limit points of infinite products of the associated g-functions. In particular, we show that every g-measure is of type III 1 . © 1995 Tohoku University, Mathematical Institute.
DOOLEY, A.H. & RICFCI, F. 1995, 'CHARACTERIZATION OF G-INVARIANT FOURIER ALGEBRAS', BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, vol. 9A, no. 1, pp. 37-45.
BENSON, C., DOOLEY, A.H. & RATCLIFF, G. 1993, 'FUNDAMENTAL-SOLUTIONS FOR POWERS OF THE HEISENBERG SUB-LAPLACIAN', ILLINOIS JOURNAL OF MATHEMATICS, vol. 37, no. 3, pp. 455-476.
DOOLEY, A.H. & WILDBERGER, N.J. 1993, 'HARMONIC-ANALYSIS AND THE GLOBAL EXPONENTIAL MAP FOR COMPACT LIE-GROUPS', FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, vol. 27, no. 1, pp. 21-27.View/Download from: Publisher's site
We investigate a natural generalization of the problem of the description of the eigenvalues of the sum of two Hermitian matrices both of whose eigenvalues are known. We describe more generally the convolution of the invariant probability measures supported on any two adjoint orbits of a compact Lie group. Our techniques utilize the convexity results of Guillemin and Sternberg and Kirwan on the one hand, and the character formulae of Weyl and Kirillov on the other. Applications to representation theory are discussed. © 1993, Taylor & Francis Group, LLC. All rights reserved.
BROWN, G. & DOOLEY, A.H. 1991, 'ODOMETER ACTIONS ON G-MEASURES', ERGODIC THEORY AND DYNAMICAL SYSTEMS, vol. 11, pp. 279-307.
DOOLEY, A.H. 1988, 'CENTRAL LACUNARY SETS FOR LIE-GROUPS', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, vol. 45, pp. 30-45.
DOOLEY, A.H. 1986, 'TRANSFERRING LP MULTIPLIERS', ANNALES DE L INSTITUT FOURIER, vol. 36, no. 4, pp. 107-136.
BROWN, G. & DOOLEY, A.H. 1985, 'ERGODIC MEASURES ARE OF WEAK PRODUCT TYPE', MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, vol. 98, no. JUL, pp. 129-145.View/Download from: Publisher's site
A limiting formula is given for the representation theory of the Cartan motion group associated to a Riemannian symmetric pair (G, K) in terms of the representation theory of G. © 1985 American Mathematical Society.
DOOLEY, A.H. & GAUDRY, G.I. 1984, 'AN EXTENSION OF DELEEUW THEOREM TO THE N-DIMENSIONAL ROTATION GROUP', ANNALES DE L INSTITUT FOURIER, vol. 34, no. 2, pp. 111-135.
DOOLEY, A.H. & RICE, J.W. 1983, 'CONTRACTIONS OF ROTATION GROUPS AND THEIR REPRESENTATIONS', MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, vol. 94, no. NOV, pp. 509-517.View/Download from: Publisher's site
DOOLEY, A.H. 1980, 'RANDOM FOURIER-SERIES FOR CENTRAL FUNCTIONS ON COMPACT LIE-GROUPS', ILLINOIS JOURNAL OF MATHEMATICS, vol. 24, no. 4, pp. 545-553.
Results concerning a class of lacunary sets are generalized from compact abelian to compact nonabelian groups. This class was introduced for compact abelian groups by Bozejko and Pytlik; it includes the p-Sidon sets of Edwards, and Ross. A notion of test family is introduced and is used to give necessary' conditions for a set to be lacunary. Using this, it is shown that [formula omitted](2) has no infinite p-Sidon sets for [formula omitted] . © 1985, Cambridge University Press. All rights reserved.
Dooley, A.H. 1978, 'Some techniques of harmonic analysis on compact Lie groups with applications to lacunarity', Bulletin of the Australian Mathematical Society, vol. 18, no. 02, pp. 299-299.View/Download from: Publisher's site
DOOLEY, A.H. & SOARDI, P.M. 1978, 'LOCAL P-SIDON SETS FOR LIE GROUPS', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 72, no. 1, pp. 125-126.
DOOLEY, A.H. 1976, 'SPECTRAL THEORY OF POSETS AND ITS APPLICATIONS TO C-STAR-ALGEBRAS', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 224, no. 1, pp. 143-155.View/Download from: Publisher's site
Dooley, A.H. 1976, 'The spectral theory of posets and its applications to c*-algebras', Transactions of the American Mathematical Society, vol. 224, no. 1, pp. 143-155.View/Download from: Publisher's site
This paper uses methods from the spectral theory of partially ordered sets to clarify and extend some recent results concerning approximately finite-dimensional C*-algebras. An extremely explicit description is obtained of the Jacobson topology on the primitive ideal space, and it is shown that this topology has a basis of quasi-compact open sets. In addition, the main results of  are proved using only elementary means. © 1976 American Mathematical Society.
Dooley, A.H. 2009, 'Intertwining operators, the Cayley transform, and the contraction of K to NM', New Developments in Lie Theory and Their Applications, 7th Workshop in Lie Theory and Its Applications, AMER MATHEMATICAL SOC, Cordoba, Argentina, pp. 101-108.
Bezuglyi, S., Dooley, A.H. & Medynets, K. 2005, 'The Rokhlin lemma for homeomorphisms of a cantor set', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 2957-2964.View/Download from: Publisher's site
Dooley, A.H. 2005, 'The critical dimension: an approach to non-singular entropy', Algebraic and Topological Dynamics, pp. 65-76.
Dooley, A.H. 1992, 'On Kakutani's criterion and Shiryaev's theorem', Proceedings of the Centre for Mathematics and its Applications, Miniconference on Probability and Analysis, Australian National University, Canberra, pp. 58-62.
Dooley, A.H. 1989, 'Solvability of differential operators on semiradial products', Proceedings of the Centre for Mathematical Analysis, Miniconference on Operators in Analysis, Macquarie University, Sydney, pp. 79-82.
Brown, G. & Dooley, A.H. 1988, 'A class of ergodic measures', Proceedings of the Centre for Mathematical Analysis, pp. 8-14.
Battesti, F.D. & Dooley, A.H. 1987, 'Invariant differential operators on some Lie groups', Proceedings of the Centre for Mathematical Analysis, Miniconference on Harmonic Analysis, pp. 6-20.
Dooley, A.H. 1985, 'Transferring Fourier multipliers', Proceedings of the Centre for Mathematical Analysis, Miniconfrence on Linear Analysis and Function Spaces, Australian National University, pp. 194-199.