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
Which neural networks can be computed by an algorithm? – Generalised hardness of approximation meets Deep Learning
– PAMM
(2023)
22,
e202200174
(doi: 10.1002/pamm.202200174)
The foundations of spectral computations via the Solvability Complexity Index hierarchy
– Journal of the European Mathematical Society
(2022)
25,
4639
(doi: 10.4171/jems/1289)
The foundations of spectral computations via the Solvability Complexity Index hierarchy
(2022)
(doi: 10.48550/arxiv.1908.09592)
Mathematical paradoxes unearth the boundaries of AI
– TheScienceBreaker
(2022)
8,
(doi: 10.25250/thescbr.brk652)
The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem
– CoRR
(2022)
119,
e2107151119
(doi: 10.1073/pnas.2107151119)
The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale's 18th problem.
– Proceedings of the National Academy of Sciences of the United States of America
(2022)
119,
e2107151119
(doi: 10.1073/pnas.2107151119)
Stratified Sampling Based Compressed Sensing for Structured Signals
– IEEE Transactions on Signal Processing
(2022)
70,
3530
(doi: 10.1109/TSP.2022.3184162)
Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling
– Applied and Computational Harmonic Analysis
(2021)
55,
1
(doi: 10.1016/j.acha.2021.04.001)
Deep Learning: What Could Go Wrong?
– SIAM News
(2021)
Deep Learning: What Could Go Wrong?
– SIAM News
(2021)
- <
- 2 of 8