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Department of Applied Mathematics and Theoretical Physics

Career

  • 2013-date: University Lecturer, DAMTP, University of Cambridge, UK
  • 2012-date: Royal Society University Research Fellow, University of Cambridge, UK 
  • 2012: Marie Curie Fellow, University of Vienna Austria
  • 2009 -2012: Junior Research Fellow, University of Cambridge, Homerton College UK
  • 2008 -2009: Von Karman Instructor, California Institute of Technology, USA

Research

Anders is a member of the Department of Applied Mathematics and Theoretical Physics and head of the Applied Functional and Harmonic Analysis research group. His current research interests include but are not limited to Functional Analysis (applied), operator/ Spectral Theory, Compressed Sensing, Mathematical Signal Processing, Sampling Theory, Compressed Sensing, Mathematical Signal Processing, Sampling Theory, Computational Harmonic Analysis, Inverse problems, Medical Imaging, Geometric Intergration, Numerical Analysis, C*- algebras.

Selected Publications

  • A. C. Hansen, On the Solvability Complexity Index, the n-Pseudospectrum and Approximations of Spectra of Operators, J. Amer. Math. Soc. 24, no. 1, 81-124
  • A. C. Hansen, On the approximation of Spectra of linear operators on Hilbert spaces, J. Funct. Anal. 254 no.8, 2092--2126
  • A. C. Hansen, Infinite dimensional numerical linear algebra; theory and applications, Proc. R. Soc. Lond. Ser. A. 466, no.2124, 3539-3559
  • B. Adcock, A. C. Hansen, Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon, Appl. Comput. Harmon. Anal. 32, no.3, 357-388

Publications

Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling
B Adcock, V Antun, AC Hansen
– Applied and Computational Harmonic Analysis
(2021)
55,
1
Non-uniform Recovery Guarantees for Binary Measurements and Infinite-Dimensional Compressed Sensing
L Thesing, AC Hansen
– Journal of Fourier Analysis and Applications
(2021)
27,
14
Can stable and accurate neural networks be computed? - On the barriers of deep learning and Smale's 18th problem.
MJ Colbrook, V Antun, AC Hansen
– CoRR
(2021)
abs/2101.08286,
On structure and optimisation in computational harmonic analysis - The key aspects in sparse regularisation
AC Hansen, B Roman
(2021)
168,
125
On instabilities of deep learning in image reconstruction and the potential costs of AI
V Antun, F Renna, C Poon, B Adcock, AC Hansen
– Proceedings of the National Academy of Sciences
(2020)
117,
30088
Compressed sensing MRI with variable density averaging (CS-VDA) outperforms full sampling at low SNR
J Schoormans, GJ Strijkers, AC Hansen, AJ Nederveen, BF Coolen
– Physics in medicine and biology
(2020)
65,
045004
On Reconstructing Functions from Binary Measurements
A Hansen, R Calderbank, B Roman, L Thesing
(2019)
How to Compute Spectra with Error Control.
MJ Colbrook, B Roman, AC Hansen
– Phys Rev Lett
(2019)
122,
250201
On the infinite-dimensional QR algorithm.
M Colbrook, A Hansen
– Numerische Mathematik
(2019)
143,
17
On Reconstructing Functions from Binary Measurements
R Calderbank, A Hansen, B Roman, L Thesing
(2019)
97
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Research Groups

Applied Functional and Harmonic Analysis
Cantab Capital Institute for the Mathematics of Information
Centre for Mathematical Imaging in Healthcare