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Anders C. Hansen

April 13, 2024

For other people named Anders Hansen, see Anders Hansen (disambiguation).

Anders C. Hansen is a Norwegian mathematician, who is currently a Professor of Mathematics at University of Cambridge, where he is the head of the Applied Functional and Harmonic Analysis group, and also Professor II at the University of Oslo.[3] He works in functional analysis, harmonic analysis (applied), foundations of mathematics (computational), data science and numerical analysis .[4]

Education edit

Hansen studied mathematics at the University of Cambridge, University of California, Berkeley and the Norwegian University of Science and Technology, where he was awarded a PhD (2008), a MA (2005) and a BA (2002) respectively.[5]

Career and research edit

He was a von Kármán instructor at California Institute of Technology from 2008 to 2009, held a junior research fellowship at Homerton College, Cambridge from 2009 to 2012, and held a Marie Skłodowska-Curie Actions fellowship at the University of Vienna in 2012. Since 2012, he has held a Royal Society University Research Fellowship (URF)[1] at the University of Cambridge, where he is now a professor at the Faculty of Mathematics, University of Cambridge and a Bye-Fellow of Peterhouse.[6]

Among other results, he has established the Solvability Complexity Index (SCI) and its following classification hierarchy.[7][8][9][10][11] It is linked [8] to Steve Smale's question [12] on the existence of iterative convergent algorithms for polynomial root finding answered by Curt McMullen[13][14] and Peter Doyle,[14] as well as Alan Turing's work and the Arithmetical hierarchy.

Awards and honours edit

In 2017, he was awarded the Leverhulme Prize for having "solved very hard problems and opened new directions in areas of great impact in applied analysis [...] Notably, by introducing the Solvability Complexity Index he has made a major contribution to the advancement of Smale’s programme on the foundation of computational mathematics".[15][16] In 2018, he was awarded the IMA Prize in Mathematics and its Applications[17] for having "made a transformative impact on the mathematical sciences and their applications [...] in particular, for his development of the Solvability Complexity Index and its corresponding classification hierarchy".[18] In 2019, he was awarded the Whitehead Prize of the London Mathematical Society for having "contributed fundamentally to the mathematics of data, sampling theory, computational harmonic analysis and compressed sensing" and "especially his development of the Solvability Complexity Index and its corresponding classification hierarchy ".[19]

Selected publications edit

Research articles
  • Hansen, Anders (12 July 2010). "On the Solvability Complexity Index, the 𝑛-pseudospectrum and approximations of spectra of operators". Journal of the American Mathematical Society. 24 (1). American Mathematical Society (AMS): 81–124. doi:10.1090/s0894-0347-2010-00676-5. ISSN 0894-0347.
  • Antun, Vegard; Renna, Francesco; Poon, Clarice; Adcock, Ben; Hansen, Anders C. (11 May 2020). "On instabilities of deep learning in image reconstruction and the potential costs of AI". Proceedings of the National Academy of Sciences. 117 (48). Proceedings of the National Academy of Sciences: 30088–30095. arXiv:1902.05300. Bibcode:2020PNAS..11730088A. doi:10.1073/pnas.1907377117. ISSN 0027-8424. PMC 7720232. PMID 32393633.
  • Colbrook, Matthew J.; Antun, Vegard; Hansen, Anders C. (16 March 2022). "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. 119 (12): e2107151119. Bibcode:2022PNAS..11907151C. doi:10.1073/pnas.2107151119. ISSN 0027-8424. PMC 8944871. PMID 35294283. S2CID 247499099.
  • ADCOCK, BEN; HANSEN, ANDERS C.; POON, CLARICE; ROMAN, BOGDAN (2017). "Breaking the Coherence Barrier: A New Theory for Compressed Sensing". Forum of Mathematics, Sigma. 5. Cambridge University Press (CUP). arXiv:1302.0561. doi:10.1017/fms.2016.32. ISSN 2050-5094. S2CID 263901.
  • Adcock, Ben; Hansen, Anders C. (20 August 2015). "Generalized Sampling and Infinite-Dimensional Compressed Sensing". Foundations of Computational Mathematics. 16 (5). Springer Science and Business Media LLC: 1263–1323. doi:10.1007/s10208-015-9276-6. ISSN 1615-3375. S2CID 223542.
  • Colbrook, Matthew J.; Roman, Bogdan; Hansen, Anders C. (28 June 2019). "How to Compute Spectra with Error Control". Physical Review Letters. 122 (25). American Physical Society (APS): 250201. Bibcode:2019PhRvL.122y0201C. doi:10.1103/physrevlett.122.250201. ISSN 0031-9007. PMID 31347861. S2CID 198463498.
Research expository highlights
  • A. Bastounis, A. C. Hansen, D. Higham, I. Tyukin and V. Vlacic: "Deep Learning: What Could Go Wrong?", SIAM News (October 2021).
  • V. Antun, N. Gottschling, A. C. Hansen and B. Adcock, "Deep Learning in Scientific Computing: Understanding the Instability Mystery", SIAM News (March 2021).
  • A. Bastounis, B. Adcock and A. C. Hansen, "From Global to Local: Getting More from Compressed Sensing", SIAM News (October 2017).
Books
  • Adcock, Ben; Hansen, Anders C. (2021). Compressive imaging : structure, sampling, learning. Cambridge, United Kingdom. ISBN 978-1-108-37744-7. OCLC 1260468467.{{cite book}}: CS1 maint: location missing publisher (link)

References edit

  1. ^ a b "Royal Society announces prestigious University Research Fellowships for 2012 | The Royal Society".
  2. ^ Anders C. Hansen at the Mathematics Genealogy Project
  3. ^ "Anders Hansen's homepage at the University of Oslo".
  4. ^ "Anders Hansen - Applied Functional and Harmonic Analysis". www.damtp.cam.ac.uk. Retrieved 2024-01-16.
  5. ^ "CV" (PDF).
  6. ^ "Peterhouse Fellows".
  7. ^ Hansen, Anders C. (2011). "On the Solvability Complexity Index, the n-pseudospectrum and approximations of spectra of operators". Journal of the American Mathematical Society. 24: 81–124. doi:10.1090/S0894-0347-2010-00676-5.
  8. ^ a b Ben-Artzi, J.; Hansen, A. C.; Nevanlinna, O.; Seidel, M. (2015). "New barriers in complexity theory: On the solvability complexity index and the towers of algorithms". Comptes Rendus Mathematique. 535 (10): 931–936. doi:10.1016/j.crma.2015.08.002.
  9. ^ Ben-Artzi, J.; Colbrook, M.; Hansen, A. C.; Nevanlinna, O.; Seidel, M. C. (2020). "Computing Spectra -- On the Solvability Complexity Index Hierarchy and Towers of Algorithms". arXiv:1508.03280v5 [cs.CC].
  10. ^ Bastounis, A.; Hansen, A. C.; Vlacic, V. (2021). "The extended Smale's 9th problem -- On computational barriers and paradoxes in estimation, regularisation, computer-assisted proofs and learning". arXiv:2110.15734v1 [math.OC].
  11. ^ Colbrook, Matthew J.; Antun, Vegard; Hansen, Anders C. (2022-03-16). "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 USA. 119 (12): e2107151119. Bibcode:2022PNAS..11907151C. doi:10.1073/pnas.2107151119. ISSN 0027-8424. PMC 8944871. PMID 35294283.
  12. ^ Smale, Steve (1985). "On the Efficiency of Algorithms in Analysis". Bulletin of the American Mathematical Society. 13 (2): 87–121. doi:10.1090/S0273-0979-1985-15391-1.
  13. ^ McMullen, Curt (1987). "Families of rational maps and iterative root-finding algorithms". Annals of Mathematics. 125 (3): 467–493. doi:10.2307/1971408. JSTOR 1971408.
  14. ^ a b Doyle, Peter; McMullen, Curt (1989). "Solving the quintic by iteration". Acta Mathematica. 163: 151–180. doi:10.1007/BF02392735. S2CID 14827783.
  15. ^ "Leverhulme Prize 2017 citations | Leverhulme Trust".
  16. ^ "University of Cambridge Features: Faculty Insight".
  17. ^ "Mathematics People |Hansen Awarded 2018 IMA Prize | Notices of the American Mathematical Society, Volume 66, Number 6" (PDF).
  18. ^ "Anders Hansen Awarded the 2018 IMA Prize in Mathematics and its Applications | Institute for Mathematics and its Applications".
  19. ^ "Whitehead Prize 2019 Citation for Dr Anders Hansen | London Mathematical Society" (PDF).

April 13, 2024
anders, hansen, other, people, named, anders, hansen, anders, hansen, disambiguation, norwegian, mathematician, currently, professor, mathematics, university, cambridge, where, head, applied, functional, harmonic, analysis, group, also, professor, university, . For other people named Anders Hansen see Anders Hansen disambiguation Anders C Hansen is a Norwegian mathematician who is currently a Professor of Mathematics at University of Cambridge where he is the head of the Applied Functional and Harmonic Analysis group and also Professor II at the University of Oslo 3 He works in functional analysis harmonic analysis applied foundations of mathematics computational data science and numerical analysis 4 Anders C HansenNationalityNorwegianAlma materUniversity of Cambridge University of California Berkeley Norwegian University of Science and TechnologyKnown forMathematical analysis Foundations of mathematics computational Data scienceAwardsWhitehead Prize 2019 IMA Prize in Mathematics and its Applications 2018 Leverhulme Prize 2017 Royal Society University Research Fellowship 2012 1 Scientific careerFieldsMathematicsInstitutionsUniversity of Cambridge University of Oslo California Institute of TechnologyDoctoral advisorArieh Iserles 2 Websitewww wbr damtp wbr cam wbr ac wbr uk wbr research wbr afha wbr anders wbr Contents 1 Education 2 Career and research 2 1 Awards and honours 3 Selected publications 4 ReferencesEducation editHansen studied mathematics at the University of Cambridge University of California Berkeley and the Norwegian University of Science and Technology where he was awarded a PhD 2008 a MA 2005 and a BA 2002 respectively 5 Career and research editHe was a von Karman instructor at California Institute of Technology from 2008 to 2009 held a junior research fellowship at Homerton College Cambridge from 2009 to 2012 and held a Marie Sklodowska Curie Actions fellowship at the University of Vienna in 2012 Since 2012 he has held a Royal Society University Research Fellowship URF 1 at the University of Cambridge where he is now a professor at the Faculty of Mathematics University of Cambridge and a Bye Fellow of Peterhouse 6 Among other results he has established the Solvability Complexity Index SCI and its following classification hierarchy 7 8 9 10 11 It is linked 8 to Steve Smale s question 12 on the existence of iterative convergent algorithms for polynomial root finding answered by Curt McMullen 13 14 and Peter Doyle 14 as well as Alan Turing s work and the Arithmetical hierarchy Awards and honours edit In 2017 he was awarded the Leverhulme Prize for having solved very hard problems and opened new directions in areas of great impact in applied analysis Notably by introducing the Solvability Complexity Index he has made a major contribution to the advancement of Smale s programme on the foundation of computational mathematics 15 16 In 2018 he was awarded the IMA Prize in Mathematics and its Applications 17 for having made a transformative impact on the mathematical sciences and their applications in particular for his development of the Solvability Complexity Index and its corresponding classification hierarchy 18 In 2019 he was awarded the Whitehead Prize of the London Mathematical Society for having contributed fundamentally to the mathematics of data sampling theory computational harmonic analysis and compressed sensing and especially his development of the Solvability Complexity Index and its corresponding classification hierarchy 19 Selected publications editResearch articlesHansen Anders 12 July 2010 On the Solvability Complexity Index the 𝑛 pseudospectrum and approximations of spectra of operators Journal of the American Mathematical Society 24 1 American Mathematical Society AMS 81 124 doi 10 1090 s0894 0347 2010 00676 5 ISSN 0894 0347 Antun Vegard Renna Francesco Poon Clarice Adcock Ben Hansen Anders C 11 May 2020 On instabilities of deep learning in image reconstruction and the potential costs of AI Proceedings of the National Academy of Sciences 117 48 Proceedings of the National Academy of Sciences 30088 30095 arXiv 1902 05300 Bibcode 2020PNAS 11730088A doi 10 1073 pnas 1907377117 ISSN 0027 8424 PMC 7720232 PMID 32393633 Colbrook Matthew J Antun Vegard Hansen Anders C 16 March 2022 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 119 12 e2107151119 Bibcode 2022PNAS 11907151C doi 10 1073 pnas 2107151119 ISSN 0027 8424 PMC 8944871 PMID 35294283 S2CID 247499099 ADCOCK BEN HANSEN ANDERS C POON CLARICE ROMAN BOGDAN 2017 Breaking the Coherence Barrier A New Theory for Compressed Sensing Forum of Mathematics Sigma 5 Cambridge University Press CUP arXiv 1302 0561 doi 10 1017 fms 2016 32 ISSN 2050 5094 S2CID 263901 Adcock Ben Hansen Anders C 20 August 2015 Generalized Sampling and Infinite Dimensional Compressed Sensing Foundations of Computational Mathematics 16 5 Springer Science and Business Media LLC 1263 1323 doi 10 1007 s10208 015 9276 6 ISSN 1615 3375 S2CID 223542 Colbrook Matthew J Roman Bogdan Hansen Anders C 28 June 2019 How to Compute Spectra with Error Control Physical Review Letters 122 25 American Physical Society APS 250201 Bibcode 2019PhRvL 122y0201C doi 10 1103 physrevlett 122 250201 ISSN 0031 9007 PMID 31347861 S2CID 198463498 Research expository highlightsA Bastounis A C Hansen D Higham I Tyukin and V Vlacic Deep Learning What Could Go Wrong SIAM News October 2021 V Antun N Gottschling A C Hansen and B Adcock Deep Learning in Scientific Computing Understanding the Instability Mystery SIAM News March 2021 A Bastounis B Adcock and A C Hansen From Global to Local Getting More from Compressed Sensing SIAM News October 2017 BooksAdcock Ben Hansen Anders C 2021 Compressive imaging structure sampling learning Cambridge United Kingdom ISBN 978 1 108 37744 7 OCLC 1260468467 a href Template Cite book html title Template Cite book cite book a CS1 maint location missing publisher link References edit a b Royal Society announces prestigious University Research Fellowships for 2012 The Royal Society Anders C Hansen at the Mathematics Genealogy Project Anders Hansen s homepage at the University of Oslo Anders Hansen Applied Functional and Harmonic Analysis www damtp cam ac uk Retrieved 2024 01 16 CV PDF Peterhouse Fellows Hansen Anders C 2011 On the Solvability Complexity Index the n pseudospectrum and approximations of spectra of operators Journal of the American Mathematical Society 24 81 124 doi 10 1090 S0894 0347 2010 00676 5 a b Ben Artzi J Hansen A C Nevanlinna O Seidel M 2015 New barriers in complexity theory On the solvability complexity index and the towers of algorithms Comptes Rendus Mathematique 535 10 931 936 doi 10 1016 j crma 2015 08 002 Ben Artzi J Colbrook M Hansen A C Nevanlinna O Seidel M C 2020 Computing Spectra On the Solvability Complexity Index Hierarchy and Towers of Algorithms arXiv 1508 03280v5 cs CC Bastounis A Hansen A C Vlacic V 2021 The extended Smale s 9th problem On computational barriers and paradoxes in estimation regularisation computer assisted proofs and learning arXiv 2110 15734v1 math OC Colbrook Matthew J Antun Vegard Hansen Anders C 2022 03 16 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 USA 119 12 e2107151119 Bibcode 2022PNAS 11907151C doi 10 1073 pnas 2107151119 ISSN 0027 8424 PMC 8944871 PMID 35294283 Smale Steve 1985 On the Efficiency of Algorithms in Analysis Bulletin of the American Mathematical Society 13 2 87 121 doi 10 1090 S0273 0979 1985 15391 1 McMullen Curt 1987 Families of rational maps and iterative root finding algorithms Annals of Mathematics 125 3 467 493 doi 10 2307 1971408 JSTOR 1971408 a b Doyle Peter McMullen Curt 1989 Solving the quintic by iteration Acta Mathematica 163 151 180 doi 10 1007 BF02392735 S2CID 14827783 Leverhulme Prize 2017 citations Leverhulme Trust University of Cambridge Features Faculty Insight Mathematics People Hansen Awarded 2018 IMA Prize Notices of the American Mathematical Society Volume 66 Number 6 PDF Anders Hansen Awarded the 2018 IMA Prize in Mathematics and its Applications Institute for Mathematics and its Applications Whitehead Prize 2019 Citation for Dr Anders Hansen London Mathematical Society PDF Retrieved from https en wikipedia org w index php title Anders C Hansen amp oldid 1214527131, wikipedia, wiki, book, books, library,

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