Lecturer of Applied Mathematics

- Office Location: Alan Turing 2.228
- Telephone: 0161 275 5835
- email: sean.holman[at]manchester.ac.uk

In the autumn of 2016 I am on sabbatical and not teaching, but in the past I have been known to teach MATH34032 and MATH36041. Here is the website for MATH36041.

Slides from various expository talks I have given. For talks on current research, see the research tab.

I am generally interested in inverse problems, PDES, and differential geometry. Inverse problems is the area of mathematics which studies the recovery of parameters in a differential equation from some observations of solutions to that equation. One of the main themes of my past and ongoing research has been the application of methods from microlocal analysis to questions of stable invertibility for a variety of inverse problems in tomography and seismic imaging. A general heuristic for inverse problems is that stable inversion is possible if the singularities of the quantity to be reconstructed appear in the data, and I am interested in investigating applications of this general principle

Together with Marta Betcke from University College London, and Natalia Bochkina from the University of Edinburgh I am an organiser for the research group Inverse Problems: Theory and Applications. This is funded by an LMS scheme 3 grant, and we are organising a series of workshops throughout the UK. Links to the workshops can be found here.

Where links to pdf documents or arXiv are given below the linked versions are generally prior to peer review, and may not match the published articles.

- Recovering a tensor on the boundary from polarization and phase measurements, Inverse Problems, 2009, 25(3).
- The weighted Doppler transform, with P. Stefanov. Inverse Problems and Imaging, February 2010, 4(1).
- Generic local uniqueness and stability in polarization tomography, Journal of Geometric Analysis, January 2013, 23(1).
- On the microlocal analysis of the geodesic X-ray transform with conjugate points, with G. Uhlmann, accepted by the Journal of Differential Geometry.
- Generic Uniqueness in Polarization Tomography. (Thesis)

- Recovering the isometry type of a Riemannian manifold from local boundary diffraction travel times, with M. de Hoop, E. Iversen, M. Lassas, and B. Ursin. To appear, preprint: www.arxiv.org 1211.6127.
- Reconstruction of a conformally Euclidean metric from local boundary diffraction travel times, with M. de Hoop, E. Iversen, M. Lassas, and B. Ursin. To appear, preprint: www.arxiv.org 1211.6132.

Starting with my work on seismic imaging I have also become interested in models of wave propagation in complicated, possibly random, media. This can be combined with inverse problems by asking whether statistical properties of a random medium may be recovered based on observations of waves propagating through that medium.

- Regularity and multi-scale discretization of the solution construction of hyperbolic evolution equations with limited smoothness, with M. de Hoop, H. Smith, and G. Uhlmann. Applied and Computational Harmonic Analysis, November 2012, 33(3).
- Retrieval of a Greens function with reflections from partly coherent waves generated by wave packets using cross correlations, with M. de Hoop, J. Garnier, and K. Sølna, SIAM Journal on Applied Mathematics, 2013, 73(1).
- Scattering enabled retrieval of Green's functions from remotely incident wave packets using cross correlations, with M. de Hoop, J. Garnier, and K. Sølna Comptes Rendus Geoscience, September 2011, 343(8-9).

- Recovering a tensor on the boundary from polarization and phase measurements, Inverse Problems, 2009, 25(3).
- The weighted Doppler transform, with P. Stefanov. Inverse Problems and Imaging, February 2010, 4(1).
- Generic local uniqueness and stability in polarization tomography, Journal of Geometric Analysis, January 2013, 23(1).
- Regularity and multi-scale discretization of the solution construction of hyperbolic evolution equations with limited smoothness, with M. de Hoop, H. Smith, and G. Uhlmann. Applied and Computational Harmonic Analysis, November 2012, 33(3).
- Retrieval of a Greens function with reflections from partly coherent waves generated by wave packets using cross correlations, with M. de Hoop, J. Garnier, and K. Sølna, SIAM Journal on Applied Mathematics, 2013, 73(1).
- Scattering enabled retrieval of Green's functions from remotely incident wave packets using cross correlations, with M. de Hoop, J. Garnier, and K. Sølna Comptes Rendus Geoscience, September 2011, 343(8-9).
- Recovering the isometry type of a Riemannian manifold from local boundary diffraction travel times, with M. de Hoop, E. Iversen, M. Lassas, and B. Ursin. Journal de Mathématics Pures et Appliquées, 2014.
- Reconstruction of a conformally Euclidean metric from local boundary diffraction travel times, with M. de Hoop, E. Iversen, M. Lassas, and B. Ursin. SIAM Journal on Mathematical Analysis, 2014 46(6), pp. 3705-3726.
- On the microlocal analysis of the geodesic X-ray transform with conjugate points, with G. Uhlmann, accepted by the Journal of Differential Geometry.

Welcome to my homepage!
## LMS Joint Research Group

Together with Marta Betcke from University College London, and Natalia Bochkina from the University of Edinburgh I am an organiser for the research group Inverse Problems: Theory and Applications which is funded by an LMS scheme 3 grant. We are organising a series of workshops on inverse problems throughout the UK. Links to the workshops can be found on the group's page here, or click the red button LMS Group above.