University of Cambridge DAMTP, Cambridge, UK a.hansen@damtp.cam.ac.uk Education University of Cambridge, King s College, UK. Ph.D, Mathematics, June 2008. University of California, Berkeley, USA. M.A., Mathematics, June 2005 (GPA: 4.0). Norwegian University of Science and Technology, NTNU, Norway. Siv. Ing. in Applied Mathematics, August 2002. Thesis title: On the Order of Deferred Correction. (Grade: A) Academic Positions Research interests Publications Lecturer University of Cambridge, UK 2013-present. Royal Society University Research Fellow University of Cambridge, UK 2012-present. Marie Curie Fellow University of Vienna, Austria 2012. Junior Research Fellow University of Cambridge, Homerton College, UK 2009-2012. von Karman Instructor California Institute of Technology, USA 2008-2009. Functional Analysis (applied), Operator/Spectral Theory, Compressed Sensing, Mathematical Signal Processing, Sampling Theory, Computational Harmonic Analysis, Inverse Problems, Medical Imaging, Geometric Integration, Numerical Analysis, C - algebras 1. On asymptotic structure in compressed sensinga (with B. Roman and B. Adcock) 2. Analyzing the Structure of Multidimensional Compressed Sensing Problems through Coherence (with B. Adcock and A. Jones) 3. Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples (with B. Adcock and M. Gataric) 4. Can everything be computed? - On the Solvability Complexity Index and Towers of Algorithms (with J. Ben-Artzi, O. Nevanlinna and M. Seidel) 5. Breaking the coherence barrier: A new theory for compressed sensing (with B. Adcock, C. Poon and B. Roman) 6. Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements (with B. Adcock, G. Kutyniok and J. Ma)
7. On asymptotic incoherence and its implications for compressed sensing for inverse problems (with A. Jones and B. Adcock) 8. The Infinite Dimensional QR-Algorithm 9. On the Computation of Spectra and Pseudospectra of Self-Adjoint and Non-Self-Adjoint Schrödinger Operators (with C. Wong) 10. Generalized Sampling and Infinite-Dimensional Compressed Sensing (with B. Adcock) Found. of Comp. Math. 11. On stable reconstructions from univariate nonuniform Fourier measurements (with B. Adcock and M. Gataric) SIAM Jour. on Imag. (to appear) 12. Mathematics of information (with B. Adcock) Encyclopedia of Applied and Computational Mathematics, Springer (to appear) 13. The quest for optimal sampling: computationally efficient, structure-exploiting measurements for compressed sensing (with B. Adcock and B. Roman) Compressed Sensing and its Applications, Springer (to appear) 14. Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum (with B. Adcock, B. Roman and G. Teschke) Adv. in Imag. and Electr. Phys. 182, 187-279 (2014) 15. Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing (with B. Adcock, C. Poon and B. Roman) Proc. of the 10th Int. Conf. on Samp. Theory and Appl. (2013) 16. Optimal wavelet reconstructions from Fourier samples via generalized sampling (with B. Adcock and C. Poon) Proc. of the 10th Int. Conf. on Samp. Theory and Appl. (2013) 17. Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem (with B. Adcock and C. Poon) SIAM J. Math. Anal. 45, no. 5, 3132-3167 (2013) 18. A stability barrier for reconstructions from Fourier samples. (with B. Adcock and A. Shadrin) SIAM J. Num. Anal. 52, no. 1, 125-139 (2014) 19. Generalized Sampling and the Stable and Accurate Reconstruction of Piecewise Analytic Functions From Their Fourier Coefficients (with B. Adcock) Math. Comp. (to appear) 20. On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate. (with B. Adcock and C. Poon) Appl. Comput. Harmon. Anal. 36, no. 3, 387-415 (2014) 21. Generalized Sampling: Extensions to Frames and Ill-Posed Problems (with B. Adcock, E. Herrholz and G. Teschke) Inverse Prob. 29, no. 1, 015008 (2013) 22. Complexity Issues in Computing Spectra, Pseudospectra and Resolvents (with O. Nevanlinna) Banach Center Publ. (to appear) (2014) 23. Stable Reconstructions in Hilbert Spaces and the Resolution of the Gibbs Phenomenon (with B. Adcock) Appl. Comput. Harmon. Anal. 32, no. 3, 357-388 (2012) 24. A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases (with B. Adcock) J. Fourier Anal. Appl. 18, no. 4, 685-716 (2012)
25. Reduced Consistency Sampling in Hilbert Spaces (with B. Adcock) Proc. of the 9th Int. Conf. on Samp. Theory and Appl. (2011) 26. A Theoretical Framework for Backward Error Analysis on Manifolds J. Geom. Mech. 3, no. 1, 81-111 (2011) 27. On the Order of Deferred Correction (with J. Strain) Appl. Num. Math. 61, no. 8, 961-973 (2011) 28. On the Complexity Index, the n-pseudospectrum and Approximations of Spectra of Operators J. Amer. Math. Soc. 24, no. 1, 81-124 (2011) 29. Infinite Dimensional Numerical Linear Algebra; Theory and Applications Proc. Roy. Soc. A. 466, no. 2124, 3539-3559 (2010) 30. On the Approximation of Spectra of Linear Operators on Hilbert Spaces J. Funct. Anal. 254(8), 2092-2126 (2008) 31. Convergence Theory for Spectral Deferred Correction Correction, (with J. Strain) Preprint, UC Berkeley. (2007) Papers are available at http://www.damtp.cam.ac.uk/user/na/people/anders/ Professional Activities Referee - Found. Comp. Math., - Proc. Royal. Soc. Ser. A, - J. Comp. Phys., - Constr. Approx., IEEE Trans. Inf. Theory., - IEEE Trans. Medical Imag., - IEEE Trans. Sign. Proc., Jour. Four. Anal. Appl. - Math. Comp., - J. Oper. Theory, - J. Approx. Theory, - IMA J. Num. Anal., - Sign. Proc., - Appl. Num. Math., - BIT Num. Math., Conferences (Plenary/ invited speaker or organizer) Breaking the coherence barrier - A new theory for compressed sensing (Pleanary Speaker) The UCL-Duke Workshop on Sensing and Analysis of High- Dimensional Data, London, Sept. 2014 Can everything be computed? - On the Solvability Complexity Index and Towers of Algorithms (Invited Speaker) Foundations of Computational Mathematics, Montevideo, Dec. 2014 Computations in Infinite Dimensions - Challenges in a Continuous World (Organizer) Kavli Royal Society International Centre, Chicheley Hall, July 2014 Compressed Sensing in the Real World - The Need for a New Theory (Plenary Speaker) international Traveling Workshop on Interactions between Sparse models and Technology (itwist 14), Belgium, August 2014 (Invited Speaker) 5th International Conference on Computational Harmonic Analysis, Vanderbilt University, Tennessee, May 2014 (Plenary Speaker) French-German Conference on Mathematical Image Analysis, Institut Henri Poincare, Paris, Jan 2014 (Invited Speaker) Compressed sensing and its Applications, Berlin, Dec 2013 Sampling and compressed sensing over the continuum (Invited mini symposium organizer) 8th international Conference: Curves and Surfaces, Paris, June 2014 Breaking the Coherence Barrier: Asymptotic Incoherence and Asymptotic Sparsity in Compressed Sensing
(Invited Speaker) Sparse Representation of Functions: Analytic and Computational Aspects, Berlin, Dec 2012 (Plenary Speaker) Workshop on Sparsity, Localization and Dictionary Learning (the European UNLocX and SMALL projects). London, June 2012 Generalized Sampling and Infinite Dimensional Compressed Sensing, (Invited speaker) Analytic and Geometric Methods in Medical Imaging, I. Newton Institute, Aug 2011 (Invited speaker) London Mathematical Society Lectures on Compressed Senisng, I. Newton Institute, March 2011 (Plenary speaker) Workshop on Compressed Sensing, Sparsity and Inverse Problems, TU Braunschweig, Sep 2010 Computational Complexity and Compressed Sensing, (Plenary speaker) Summer School on Applied Analysis 2010, TU Chemnitz, Oct 2010 Computations with the Infinite Matrix, (Plenary speaker) Operator Theory and Applications: Perspectives and Challenges, Jurata, March 2010 (Plenary speaker) Wales Workshop on Analytical Computational Mathematics, Cardiff Feb 2010. Seminar Talks Breaking the Coherence Barrier: Asymptotic Incoherence and Asymptotic Sparsity in Compressed Sensing Computer Lab. Sem., Univ. of Cambridge, May 2013 Appl. Math. Colloq., TU Berlin, May 2013 Electr. Eng. Colloq., EPFL, April 2013 Harm. Anal., Sem., INRIA, Rennes, April 2013 Appl. Math. Colloq., Univ. of Bergen, Dec 2012 Can Everything be Computed? On the Solvability Complexity Index and Towers of Algorithms, Math. Colloq., Univ. of Oslo, March 2013 Centre for Advanced Studies, Oslo, March 2013 Harm. Anal., Sem., Univ. of Vienna, April 2012 Generalized Sampling and Semi-Random Sampling in Infinite-Dimensional Compressed Sensing, Appl. Math. Colloq., Univ. of Maryland., March 2012. Appl. Math. Colloq., Purdue Univ., Dec 2011. Appl. Math. Colloq., Univ. of Warwick, Nov 2011. Harm. Anal., Sem., Univ. of Vienna, Oct. 2011 Harm. Anal., Sem., Aalborg University (Denmark), Sept. 2011 The Solvability Complexity Index and Approximations of Spectra of Operators, Geom. and Anal. Sem., Univ. of London, Queen Mary, Sept. 2011 London Anal. Sem., King s College London, May 2011 Compressed Sensing and Generalized Sampling in Magnetic Resonance Imaging, Medical Imag. Sem., Imperial College (Hammersmith Hospital), June 2011
Generalized Sampling and Infinite-Dimensional Compressed Sensing, Electr. Eng. Colloq., EPFL June 2011 London Math. Soc. Lect., Cambride, Mar 2011 Appl. Math. Sem., Helmholtz Zentrum Munchen, Feb 2011 Math. Colloq., Helsinki Univ. of Tech., Nov 2010. Compressed Sensing in Infinite Dimensions, Stats. Colloq., Univ. Coll. London, May 2010. Appl. Math. Colloq., Caltech, April 2010. Appl. Math. Colloq., Stanford, April 2010. Num. Anal. Sem., UC Berkeley, April 2010. Stats Colloq., Univ. of Cambridge, Feb 2010. ECOS Seminar, Univ. of Edinburgh, Feb 2010. Computations with the Infinite Matrix, Appl. Math. Colloq., Durham University, March 2010. Compressed Sensing in Hilbert Space, C -Alg. Sem., Univ. of Oslo, Dec 2009. Compressed Sensing - Introduction and Further Aspects, Math. Colloq., Univ. of Oslo, Dec 2009, Stats. Seminar, Univ. of Cambridge, Nov 2009. Computations in Infinite Dimensions, Appl. Math. Colloq., UCLA, Jan 2009. On the Complexity Index and Approximations of Spectra and Pseudospectra, Appl. Math. Colloq., Caltech, Nov 2008. Math. Colloq., Univ. of Reading, April 2008. Appl. Math. Sem., Heriot-Watt University, Nov 2007. Math. Colloq., Univ. of Cardiff, October 2007. How to Compute Spectra of Infinite Matrices, Num. Anal. Sem., Univ. of Oxford, October 2007. Infinite Dimensional Numerical Linear Algebra: Theory and Applications, Appl. Math. Sem., ETH (Zurich), Nov 2007. Matrix Computations Sem., UC Berkeley, April 2007. On the Approximation of Spectra and Pseudospectra of Linear Operators on Hilbert Spaces, I. Newton Inst., Cambridge, May 2007. Operator Alg. Sem., UC Berkeley, April 2007. C -Alg. Sem., Univ. of Oslo, March 2007. On the Approximation of Spectra of Schrödinger Operators, Math. Phys. Sem., Caltech, April 2006. Operator Theory in Infinite Dimensional Numerical Linear Algebra, Operator Alg. Sem., UC Berkeley, April 2006. C -algebras and Perturbation theory in Computational Quantum Mechanics, Centre of Mathematics for Applications, Oslo, August 2004.
Grants PhDstudents supervised Royal Society University Research Fellowship (2012-2017), (2017-2020) EPSRC grant EP/L003457/1 (2013-2016) Approximate value of the total grants: 1 million GBP = 1.7 million USD Alexander Bastounis (Cambridge). Graduating: 2016 Milana Gataric (Cambridge). Graduating: 2015 Ben Jennings (Cambridge). Graduating: 2017 Alexander Jones (Cambridge). Graduating: 2015 Clarice Poon (Cambridge). Graduating: 2015 Post-Docs Jonathan Ben-Artzi (PhD: Brown University) 2011-2014 mentored Bogdan Roman (PhD: University of Cambridge) 2013-2016 Masterstudents supervised Benoit Huet (Ecole Normale Superieure). Graduated: 2013 Jackie MA (TU Berlin). Graduated: 2013