People in the Analysis and Geometry Program

View full list of people in the MSI.

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Academic Staff
Name	Extn	Room	Local email
Carey, Alan	x52957	JD 1173	Alan.Careyatmaths.anu.edu.au
Guillarmou, Colin	x53995	JD 2158	colin.guillarmouatmaths.anu.edu.au
Hassell, Andrew	x54141	JD 2145	Andrew.Hasselatmaths.anu.edu.au
Hutchinson, John	x54042	JD 2135A	John.Hutchinsonatmaths.anu.edu.au
Isaev, Alexander	x54575	JD 1183	Alexander.Isaevatmaths.anu.edu.au
Loy, Rick	x52919	JD 1188	Rick.Loyatmaths.anu.edu.au
McIntosh, Alan	x53625	JD 2141	Alan.McIntoshatmaths.anu.edu.au
Mendelson, Shahar	x58357	JD 2150	Shahar.Mendelsonatmaths.anu.edu.au
Portal, Pierre	x53384	JD 2156	Pierre.Portalatmaths.anu.edu.au
Sikora, Adam	x52963	JD 2152	Adam.Sikoraatmaths.anu.edu.au
Wang, Bryan	x52905	JD 2142	Bai-Ling.Wangatmaths.anu.edu.au
Retired Visiting Fellows
Name	Extn	Room	Local email
Robinson, Derek	x52914	JD 2148	Derek.Robinsonatmaths.anu.edu.au
Visitors
Name	Extn	Room	Home email
Klimek, Slawomir	x53620	JD 1184	sklimekatmath.iupui.edu
Kozdoba, Mark	x52960	JD 2144	marikkattechunix.technion.ac.il
Milman, Vitali	x54233	JD 2146	milmanatpost.tau.ac.il
Tomczak-Jaegermann, Nicole	x58398	JD 2154	nicole.tomczakatulberta.ca

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Students
Name	Extn	Room	Local email	Supervisor
Bharucha, Pourus	x51007	JD LG103	Pourus.Bharuchaatmaths.anu.edu.au	Rick Loy
Brooker, Phil	x54992	JD LG09	Phil.Brookeratmaths.anu.edu.au	Rick Loy
Dolman, Ben	x54992	JD LG09	ben.dolmanatmaths.anu.edu.au	Alan Carey
Price, Brendon	x54695	JD G17	brendon.priceatmaths.anu.edu.au	Andrew Hassell
Ratnam, Rishni	x54992	JD LG09	Rishni.Ratnamatmaths.anu.edu.au	Alan Carey
Scealy, Bob	x53994	PM 1000	Bob.Scealyatmaths.anu.edu.au	John Hutchinson
Tong, Kester	x54678	JD LG14	Kester.Tongatmaths.anu.edu.au	Alan Carey
Ware, Griff	x51007	JD LG103	Griff.Wareatmaths.anu.edu.au	Rick Loy

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Research Interests

Prof. Alan Carey

Geometric Analysis and Noncommutative Geometry:

Invariants of manifolds constructed using von Neumann algebras and applications of these methods to quantum field theory.

Dr Colin Guillarmou

Scattering and Spectral Theory in Geometric Settings:

Resonances, hyperbolic geometry, links with conformal geometry.

Dr Mark Harmer

Spectral and Scattering Theory:

Scattering theory on graphs, spectral theory of non compact discrete manifolds, spectral theory and algebraic geometry.

Dr Andrew Hassell

Spectral and Scattering Theory:

Analysis of partial differential operators on noncompact or singular spaces, including resolvent kernels and associated operators, asymptotic properties of eigenfunctions and generalized eigenfunctions, and solutions of time-dependent Schroedinger equations and wave equations on such spaces.

Microlocal analysis:

Pseudodifferential and Fourier integral operators, Lagrangian and Legendrian distributions, analysis on manifolds with corners.

Prof. John Hutchinson

Fractal geometry:

My original research interests were set theory and model theory. Subsequently I have worked on fractals, geometric measure theory and in particular generalised notions of curvature, elliptic systems and nonlinear elasticity type problems, and other geometric variational problems. I am particularly interested in applying techniques from analysis, differential equations and geometric measure theory to physical and geometric problems. In recent years this has included finite element approximations to surfaces of prescribed mean curvature, random fractals and phase transition problems. My current primary area of research is in the general area of fractals and fractal geometry.

Dr Alexander Isaev

Several Complex Variables:

Equivalence problems for domains in complex space and complex manifolds, characterization of domains and manifolds by their groups of holomorphic automorphisms, actions of Lie groups on complex manifolds, complex Monge-Ampère equation and the Kähler-Einstein metric, Reinhardt domains, hyperbolic complex manifolds.

Analysis on Cauchy-Riemann Manifolds:

Systems of differential invariants and differential operators on CR-manifolds, equations of prescribed CR-curvature, mappings of CR-manifolds, algebraic structures arising in CR-geometry, e.g. graded Lie algebras of Levi-Tanaka type.

Dr Rick Loy

Banach Algebras, Cohomology Theory:

The interrelation between algebraic and topological properties, automatic continuity for homomorphisms and derivations, analytic space methods; Banach algebra amenability and its variants, implications of cohomological properties of algebras of operators on Banach spaces, and of algebras over locally compact groups, on the structure of the underlying spaces or groups; structure of radical Banach algebras.

Prof. Alan McIntosh

Harmonic Analysis, Operator Theory and Partial Differential Equations:

Singular integrals and square function estimates on Lipschitz surfaces, with applications to boundary value problems for partial differential equations; scattering theory for Maxwell's equations on irregular domains; spectral theory and functional calculi of operators in Banach spaces; Clifford analysis; heat kernel bounds and functional calculi of elliptic partial differential operators.

Dr Shahar Mendelson

Geometry of Banach spaces, Statistical Learning Theory:

High dimensional phenomena and, in particular, connections between the geometry of Banach spaces and Statistical Learning Theory.

Dr Pierre Portal

Functional and Harmonic Analysis:

Power-bounded operators and applications to difference equations in Banach spaces; harmonic analysis of Banach space valued functions and applications to partial differential equations.

Emeritus Professor Derek W. Robinson

Functional Analysis and Partial Differential Equations:

Strongly elliptic, subelliptic and degenerate operators on Euclidean space and more general manifolds: separation and isolation phenomena, capacity and non-ergodicity.

Dr Adam Sikora

Linear Partial Differential Equations and Harmonic Analysis, Analysis, Lie groups:

singular integrals, spectral and Fourier multiplier theorems, Bochner-Riesz summability, functional calculi and spectral analysis of elliptic and sub-elliptic differential operators, spectral analysis of operators with periodic or almost periodic coefficients, Riesz transforms, semi-groups of operators and heat kernels, wave equation.

Dr Bai-Ling Wang

Geometric Analysis, Topology and Mathematical Physics:

Twisted K-theory, Twisted K-homology and D-branes; Geometry and Topology: Invariants from A-B-C fields; Representation theory and Modular tensor categories; Mathematical physics: Gauge theory and Conformal field theory.