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
Generalised Hardness of Approximation and the SCI Hierarchy –On Determining the Boundaries of Training Algorithms in AI
– Foundations of Computational Mathematics
(2026)
1
(doi: 10.1007/s10208-026-09764-8)
Artificial intelligence in prostate MRI: Comparative diagnostic performance in a high-prevalence cohort
– Acta Radiologica
(2026)
67,
765
(doi: 10.1177/02841851261470455)
Trustworthiness in AI: on SciCompBot-the scientific computing chatbot.
– Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences
(2026)
384,
20250116
(doi: 10.1098/rsta.2025.0116)
Chapter 11 On generalized hardness of approximation, hallucinations, instability, and trustworthiness in AI for inverse problems
– Handbook of Numerical Analysis
(2026)
27,
507
(doi: 10.1016/bs.hna.2026.05.001)
Instability in deep learning - when algorithms cannot compute uncertainty quantifications for neural networks
– European Journal of Applied Mathematics
(2025)
37,
290
(doi: 10.1017/S095679252510017X)
Do stable neural networks exist for classification problems? – A new view on stability in AI
– European Journal of Applied Mathematics
(2025)
37,
238
(doi: 10.1017/s0956792525100181)
The mathematics of adversarial attacks in AI – why deep learning is unstable despite the existence of stable neural networks
– European Journal of Applied Mathematics
(2025)
37,
259
(doi: 10.1017/s0956792525100193)
The Troublesome Kernel: On Hallucinations, No Free Lunches, and the Accuracy-Stability Tradeoff in Inverse Problems
– SIAM Review
(2025)
(doi: 10.1137/23M1568739)
The Troublesome Kernel: On Hallucinations, No Free Lunches, and the Accuracy-Stability Tradeoff in Inverse Problems
– SIAM Review
(2025)
67,
73
(doi: 10.1137/23M1568739)
The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning
– Lecture Notes in Computer Science
(2023)
14254,
530
(doi: 10.1007/978-3-031-44207-0_44)
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