Dr. Andrew Hassell

Reader

Department of Mathematics

Australian National University

Canberra ACT 0200 Australia

Email: andrew.hassell {AT} maths.anu.edu.au

Fax: (61) (2) 6125 4984

Phone: (61) (2) 6125 4141

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Teaching/ Undergraduate Students

I am the Mathematics Coordinator of the Bachelor of Philosophy degree and will be advising Ph.B. students on enrolments, particularly in relation to mathematics courses.

Research Interests

My research interests are in spectral and scattering theory, partial differential equations and microlocal analysis. My papers are sorted below into the following categories: Schroedinger equation, asymptotics of eigenfunctions, scattering theory, quantum N body problem, spectral invariants, and miscellaneous.

I am a member of the Analysis and Geometry research program at ANU. There is also a closely related Nonlinear Analysis research program.

Enquiries from prospective PhD students are welcome. Scholarships are available for Australian and international students. Click here for information about Ph.D. scholarships. The ANU CRICOS number (relevant for international students) is 00120C.

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Research Output

To see my papers on the math arXiv, click here.

To see my MathSciNet listing, click here.

Low energy asymptotics of the resolvent and Riesz transform

A. Hassell and A.Sikora, Riesz transforms in one dimension. Go to preprint in arXiv

C. Guillarmou and A. Hassell, Resolvent at low energy and Riesz transform for Schr\"odinger operators on asymptotically conic manifolds. II. Annales de l'Institut Fourier, to appear. Go to preprint in arXiv

C. Guillarmou and A. Hassell, Resolvent at low energy and Riesz transform for Schr\"odinger operators on asymptotically conic manifolds. I. Math. Annalen, to appear. Go to preprint in arXiv

Schroedinger equation

A. Hassell and J. Wunsch, The semiclassical resolvent and the propagator for nontrapping scattering metrics, Advances in Mathematics 217 (2008), 586-682. Go to preprint in arXiv ; Go to journal

A. Hassell, T. Tao and J. Wunsch, Sharp Strichartz estimates on non-trapping asymptotically conic manifolds, American Journal of Mathematics, 128 (2006), 963-1024. Go to preprint in arXiv

A. Hassell, T. Tao and J. Wunsch, A Strichartz inequality for the Schroedinger equation on non-trapping asymptotically conic manifolds, Communications in PDE 30(2005), 157-205. Go to preprint in arXiv

A. Hassell and J. Wunsch, The Schroedinger propagator for scattering metrics, Annals of Mathematics, 162 (2005), 487-523. Go to preprint in arXiv

A. Hassell and J. Wunsch, On the structure of the Schroedinger propagator, Contemp. Math. 362, 2004. Conference paper. Go to preprint in arXiv

Asymptotics of eigenfunctions and eigenvalues

A. Hassell, Stadium domains that are not QUE. Go to preprint in arXiv

A. Hassell and J. Marzuola, Eigenfunction concentration for pseudointegrable billiards. Go to preprint in arXiv

A. Hassell and S. Marshall, Eigenvalues of Schroedinger operators with potential asymptotically homogeneous of degree -2, Trans. Amer. Math. Soc 360 (2008), no. 8, 4145--4167. Go to preprint in arXiv

N. Burq, A. Hassell and J. Wunsch, Spreading of quasimodes in the Bunimovich stadium, Proc. Amer. Math. Soc 135 (2007), 1029-1037. Go to preprint in arXiv

A. Hassell and S. Zelditch, Quantum ergodicity of boundary values of eigenfunctions, Communications in Mathematical Physics, 248, 119-168, 2004. Go to preprint in arXiv

A. Hassell and T. Tao, Upper and lower bounds for normal derivatives of Dirichlet eigenfunctions. Math. Res. Lett. 9 (2002), 289-307. Go to preprint in arXiv

A. Hassell and T. Tao, L^ 2 bounds for normal derivatives of Dirichlet eigenfunctions, Proc. Centre Math. Appl. Austral. Nat. Univ., 41, 57 -- 67, 2003. Conference paper. Download pdf file

Scattering Theory and Operator Kernels

A. Hassell, R. B. Melrose and A. Vasy, Scattering for symbolic potentials of order zero and microlocal propagation near radial points. Go to preprint in arXiv

G. Carron, T. Coulhon and A. Hassell, Riesz transform and L^p cohomology for manifolds with Euclidean ends. Duke Math. J., 133 (2006), 59-93. Go to preprint in arXiv

A. Hassell, R. B. Melrose and A. Vasy, Spectral and scattering theory for symbolic potentials of order zero, Advances in Mathematics 181(2004), 1-87. Go to preprint in arXiv

A. Hassell, R. B. Melrose and A. Vasy, Spectral and scattering theory for symbolic potentials of order zero. Seminaire: Equations aux Derivees Partielles, 2000--2001, Exp. No. XIII, 21 pp., Semin. Equ. Deriv. Partielles, Ecole Polytech., Palaiseau, 2001. Download ps file. Conference paper.

A. Hassell and A. Vasy, The resolvent for Laplace-type operators on asymptotically conic spaces. Ann. l'Inst. Fourier 51 (2001), 1299-1346. Download ps file Go to preprint in arXiv

A. Hassell and A. Vasy, The spectral projections and resolvent for scattering metrics, Journal d'Analyse Mathematique 79 (1999), 241-298. With Andras Vasy. Reprints available. Download ps file Go to preprint in arXiv

A. Hassell and M. Zworski, Resonant rigidity of S^2, J. Funct. Anal. 169, 604-609 (1999). Reprints available. Download ps file

Quantum N body problem

A. Hassell, Distorted plane waves for the 3 body Schroedinger operator, Geometric and Functional Analysis 10, 1-50 (2000). Download ps file

A. Hassell and A. Vasy, Symbolic functional calculus and N body resolvent estimates, Journal of Functional Analysis 173, 257-283, 2000. Reprints available. Download ps file

A. Hassell, Scattering matrices for the quantum N body problem, Transactions of the AMS 352 (2000), 3799-3820. Reprints available. Download ps file

Spectral invariants

A. Hassell and S. Zelditch, Determinants of Laplacians in exterior domains, IMRN, 1999, number 18, 971-1004. Reprints available. Download ps file Go to preprint in arXiv

A. Hassell, Analytic surgery and analytic torsion, Commun. in Anal. and Geom. 6, 255-289 (1998). Reprints available. Download ps file

A. Hassell, R. Mazzeo and R. B. Melrose, A signature theorem for manifolds with corners of codimension two, Topology 36, 1055-1075, 1997. Reprints available.

A. Hassell, R. Mazzeo and R. B. Melrose, Analytic surgery and the accumulation of eigenvalues, Commun. in Anal. and Geom. 3, 115-222, 1995. Reprints available.

Miscellaneous papers in spectral theory and PDE

A. Hassell and A. Vasy, Intersecting Legendrians and blowups. Mathematical Research Letters 8 (2001), 413-428. Download ps file Go to preprint in arXiv

A. Hassell, The Yang-Mills-Higgs Heat Flow on R^3, J. Funct. Anal. 111, 431-448, 1993. Reprints available.

Talks:

The Schroedinger propagator for scattering metrics. Talk given at MSRI, May 6, 2003. Download pdf file

Eigenvalues and eigenfunctions of the Laplacian. Colloquium talk. Download pdf file

The b-calculus and index theory. Talk, workshop on Dirac operators, ANU, March 11 2004. Download pdf file. Analytic surgery and gluing formulae for determinants. Talk following the previous talk, March 12, 2004. Download pdf file

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Links with other web sites:

Mathematical Sciences Institute, A.N.U.

Andras Vasy's home page.

Terry Tao's home page.

Maciej Zworski's home page.

Jared Wunsch's home page.

Richard Melrose's home page.

Steve Zelditch's home page.

Rafe Mazzeo's home page.

Thierry Coulhon's home page.

Gilles Carron's home page.

Nicolas Burq's home page.

Colin Guillarmou's home page.