# Andrew Hassell

Professor and Associate Director Research

I am currently a Professor and Associate Director of Research in the Mathematical Sciences Institute at ANU.

My PhD was done at MIT in the period 1990-94. After that, I did a 2 year postdoc at Stanford University, and then I moved to ANU, initially as an ARC Postdoctoral Fellow. I became an ARC Research Fellow during 1999-2004, and a Future Fellow during 2010-2014. I was elected to the Australian Academy of Science in 2013.

### Research interests

My research interests are in spectral and scattering theory, partial differential equations, microlocal analysis and semiclassical analysis. Specific recent topics include wave equations with rough coefficients, analysis of resolvents and heat kernel on complete Riemannian manifolds, Fredholm theory for non-elliptic operators and nonlinear dispersive equations.

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 PhD scholarships. The ANU CRICOS number (relevant for international students) is 00120C.

### Projects

To see my papers on the math arXiv.

To see my MathSciNet listing.

## Papers by chronological order

• J. Gell-Redman, A. Hassell, J. Shapiro, Regularity of the Scattering Matrix for Nonlinear Helmholtz Eigenfunctions,  arXiv:2012.12505
• A. Hassell, J. Rozendaal, Lp and HpFIO regularity for wave equations with rough coefficients, Part I. arXiv:2010.13761
• A. Hassell, D. Nix, A. Sikora, Riesz transforms on a class of non-doubling manifolds II. arXiv:1912.06405
• S. Gomes, A. Hassell, Semiclassical scarring on tori in KAM Hamiltonian systems. arXiv:1811.11346
• J. Gell-Redman, A. Hassell, J. Shapiro, J. Zhang, Existence and asymptotics of nonlinear Helmholtz eigenfunctions. SIAM J. Math. Anal., 52 (2020), no. 6, 6180–6221. Journal article  arXiv:1908.04890
• C. Guillarmou, A. Hassell, K. Krupchyk, Eigenvalue bounds for non-self-adjoint Schrödinger operators with nontrapping metrics. Anal. PDE 13 (2020), no. 6, 1633–1670. Journal article  arXiv:1709.09759
• J. Gell-Redman, A. Hassell, The distribution of phase shifts for semiclassical potentials with polynomial decay, Int. Math. Res. Not. 2020 (2020), no. 19, 6294--6346. Journal article arXiv:1509.03468
• X. Chen, A. Hassell, The heat kernel on asymptotically hyperbolic manifolds, Comm. PDE 45 (2020), no. 9, 1031--1071. Journal article  arXiv:1612:06044
• A. Hassell, P. Portal, J. Rozendaal, Off-singularity bounds and Hardy spaces for Fourier integral operators. Trans. Amer. Math. Soc. 373 (2020), no.8, 5773–5832. Journal article arXiv:1811.11376
• A. Hassell, A. Sikora, Riesz transforms on a class of non-doubling manifolds. Comm. PDE 44 (2019), no. 11, 1072–1099. Journal article arXiv:1805.00132
• A. Barnett, A. Hassell, M. Tacy, Comparable upper and lower bounds for boundary values of Neumann eigenfunctions and tight inclusion of eigenvalues. Duke Math. J. 167 (2018), no.16, 3059–3114. Journal article arXiv:1512.04165
• X. Chen, A. Hassell, Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds II: Spectral measure, restriction theorem, spectral multipliers. Ann. Inst. Fourier 68 (2018), no.3,   1011–1075. Journal article arXiv:1412.4427
• G. A. Ford, A. Hassell, L. Hillairet,  Wave propagation on Euclidean surfaces with conical singularities I: Geometric diffraction. J. Spectral Theory 8 (2018), no.2,  605–667. Journal article  arXiv 1505:01043
• A. Hassell, V. Ivrii, Spectral asymptotics for the semiclassical Dirichlet-to-Neumann operator. J. Spectral Theory 7 (2017), no.3,  881–905. Journal article  arXiv:1505:04894
• X. Chen and A. Hassell, Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds I: Resolvent construction at high energy. Comm. PDE 41 (2016), no.3, 515–578. Journal article arXiv 1410.6881
• A. Hassell and J. Zhang, Global-in-time Strichartz estimates on non-trapping asymptotically conic manifolds. Anal. PDE 9 (2016), no.1, 151–192. Journal article  arXiv 1310.0909
• J. Gell-Redman, A. Hassell and S. Zelditch, Equidistribution of phase shifts in semiclassical potential scattering. J. Lond. Math. Soc. 91 (2015), no.1, 159–179. Journal article  arXiv 1311.2353
• X. Han, A. Hassell, H. Hezari, S. Zelditch, Completeness of boundary traces of eigenfunctions. Proc. Lond. Math. Soc. 111 (2015), no.3, 749–773. Journal article   arXiv 1311.0935
• H. Christianson, A. Hassell and J. Toth, Exterior mass estimates and L^2 restriction boundary for Neumann data along hypersurfaces. Int. Math. Res. Not. 2015, no. 6, 1638–1665. Journal article arXiv 1303.4319
• A. Hassell and M. Tacy, Improvement of eigenfunction estimates on manifolds with nonpositive curvature. Forum Math. 27 (2015), no.3, 1435–1451. Journal article  arXiv 1212.2540
• K. Datchev, J. Gell-Redman, A. Hassell and P. Humphries, Approximation and equidistribution of phase shifts: spherical symmetry. Commun. Math. Phys. 326 (2014), no.1,  209–236. Journal article   arXiv 1211.4959
• A. Hassell and P. Lin, The Riesz transform for homogeneous Schroedinger operators on metric cones. Revista Mat. Iberoamericana,  Rev. Mat. Iberoam. 30 (2014), no.2, 477–522. Journal article  arXiv 1206.2997
• C. Guillarmou and A. Hassell, Uniform Sobolev estimates for non-trapping metrics.  J. Inst. Math. Jussieu 13 (2014), no. 3, 599-632. Journal article   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. 67 (2014), no. 3, 351-407.  Journal article  arXiv 1112.5665
• 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
• J. Gell-Redman and A. Hassell, Potential scattering and the continuity of phase-shifts. Math. Res. Lett. 19 (2012), 719-729. arXiv:1112.3413  Journal article
• 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, 2012. arXiv 1107.2172
• 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
• 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
• 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 arXivJournal 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
• 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
• 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
• 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
• 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 arXivJournal 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
• 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