Anders C. Hansen Explained

Anders C. Hansen
Nationality:Norwegian
Fields:Mathematics
Workplaces:University of Cambridge
University of Oslo
California Institute of Technology
Alma Mater:University of Cambridge
University of California, Berkeley
Norwegian University of Science and Technology
Doctoral Advisor:Arieh Iserles
Known For:Mathematical analysis
Foundations of mathematics (computational)
Data science
Awards:Whitehead Prize (2019)
IMA Prize in Mathematics and its Applications (2018)
Leverhulme Prize (2017)
Royal Society University Research Fellowship (2012) [1]

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.[2] He works in functional analysis, harmonic analysis (applied), foundations of mathematics (computational), data science and numerical analysis .[3]

Education

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.[4]

Career and research

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.[5]

Among other results, he has established the Solvability Complexity Index (SCI) and its following classification hierarchy.[6] [7] [8] [9] [10] It is linked [7] to Steve Smale's question [11] on the existence of iterative convergent algorithms for polynomial root finding answered by Curt McMullen[12] [13] and Peter Doyle, as well as Alan Turing's work and the Arithmetical hierarchy.

Awards and honours

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".[14] [15] In 2018, he was awarded the IMA Prize in Mathematics and its Applications[16] 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".[17] 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 ".[18]

Selected publications

Research articles
Research expository highlights
Books

Notes and References

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

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