Professor Andrew Hassell

Future Fellow

Department of Mathematics

Australian National University

Canberra ACT 0200 Australia

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

Fax: (61) (2) 6125 4984

Phone: (61) (2) 6125 4141

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.

During the calendar year 2009, Alan McIntosh, Bryan Wang and I ran a Special Program on Spectral Theory and Operator Theory, including a Workshop on Spectral Theory and Harmonic Analysis during July 13-17.

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.

Research Output

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

To see my MathSciNet listing, click here.

Papers by chronological order

  • J. Gell-Redman, A. Hassell and S. Zelditch, Equidistribution of phase shifts in semiclassical potential scattering. arXiv 1311.2353

  • X. Han, A. Hassell, H. Hezari, S. Zelditch, Completeness of boundary traces of eigenfunctions. arXiv 1311.0935

  • A. Hassell and J. Zhang, Global-in-time Strichartz estimates on non-trapping asymptotically conic manifolds. arXiv 1310.0909

  • H. Christianson, A. Hassell and J. Toth, Exterior mass estimates and L^2 restriction boundary for Neumann data along hypersurfaces. arXiv 1303.4319

  • A. Hassell and M. Tacy, Improvement of eigenfunction estimates on manifolds with nonpositive curvature. Forum Math., to appear. arXiv 1212.2540

  • K. Datchev, J. Gell-Redman, A. Hassell and P. Humphries, Approximation and equidistribution of phase shifts: spherical symmetry. Commun. Math. Phys., to appear. arXiv 1211.4959

  • A. Hassell and P. Lin, The Riesz transform for homogeneous Schroedinger operators on metric cones. Revista Mat. Iberoamericana, to appear. arXiv 1206.2997

  • C. Guillarmou and A. Hassell, Uniform Sobolev estimates for non-trapping metrics. J. Inst. Math. Jussieu, to appear. arXiv 1205.4150

  • A. Barnett and A. Hassell, Fast computation of high frequency Dirichlet eigenmodes via the spectral flow of the interior Neumann-to-Dirichlet map. Comm. Pure Appl. Math., to appear. arXiv 1112.5665

  • J. Gell-Redman and A. Hassell, Potential scattering and the continuity of phase-shifts. Math. Res. Lett. 19 (2012), 719-729. arXiv 1112.3413

  • A. Barnett and A. Hassell, Estimates on Neumann eigenfunctions at the boundary, and the "Method of Particular Solutions" for computing them. AMS Proceedings of symposia in pure mathematics, vol. 84, 195-208. arXiv 1107.2172

  • C. Guillarmou, A. Hassell and A. Sikora, Restriction and spectral multiplier theorems on asymptotically conic manifolds. Analysis and PDE 6 (2013), 893-950. arXiv 1012.3780 Journal article

  • C. Guillarmou, A. Hassell and A. Sikora, Resolvent at low energy III: the spectral measure. Trans. Amer. Math. Soc. 365 (2013), 6103-6148. arXiv 1009.3084 Journal article

  • A. H. Barnett and A. Hassell, Boundary quasi-orthogonality and sharp inclusion bounds for large Dirichlet eigenvalues, SIAM J. Numer. Anal. 49 (2011), 1046-1063. Go to preprint in arXiv Journal article

  • A. Hassell and M. Tacy, Semiclassical L^p estimates of quasimodes on curved hypersurfaces, Jour. Geom. Anal. 22 (2012), 74-89. Go to preprint in arXiv Journal article

  • N. Burq, C. Guillarmou, A. Hassell, Strichartz estimates without loss on manifolds with hyperbolic trapped geodesics, GAFA 20 (2010), 627-656. Go to preprint in arXiv Journal article

  • A. Hassell, Ergodic billiards that are not quantum unique ergodic. With an appendix by A. Hassell and L. Hillairet. Annals of Mathematics 171 (2010), 605 -- 618. Go to preprint in arXiv Journal article

  • A. Hassell, L. Hillairet and J. Marzuola, Eigenfunction concentration for polygonal billiards. Communications in PDE 34 (2009), 475-485. Go to preprint in arXiv Journal article

  • A. Hassell and A.Sikora, Riesz transforms in one dimension. Indiana U. Math. Journal 58 (2009), 823-852. Go to preprint in arXiv Journal article

  • 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 59 (2009), 1553 -- 1610. Go to preprint in arXiv Journal article

  • C. Guillarmou and A. Hassell, Resolvent at low energy and Riesz transform for Schr\"odinger operators on asymptotically conic manifolds. I, Math. Annalen, 341 (2008), no. 4, 859--896. Go to preprint in arXiv Journal article

  • 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 ; Journal article

  • 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 Journal article

  • 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 Journal article

  • A. Hassell, R. B. Melrose and A. Vasy, Microlocal propagation near radial points and scattering for symbolic potentials of order zero, Analysis and PDE 1 (2008), 127-196. Go to preprint in arXiv Journal article

  • 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 Journal article

  • 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 Journal article

  • 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 Journal article

  • A. Hassell and J. Wunsch, On the structure of the Schroedinger propagator, Contemp. Math. 362, 2004. Conference paper. 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 Journal article

  • 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 Journal article

  • 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 Journal article

  • 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

  • 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 Journal article

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

  • 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 Journal article

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

  • 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 Journal article

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

  • 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 Journal article

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

  • 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 Journal article

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

  • 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. Download pdf file (this is a preliminary version, but not very different from the final article. Confusingly, it has a different title!).

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

    Click here to see the same papers listed by topic.

    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.