Ivan B. Fesenko, Ph. D.
▎Professor of Mathematics
▎Higher Number Theory Group
◢ Website: https://ivanfesenko.org/?page_id=717
◢ Email：ivan.b.fesenko@westlake.edu.cn
Conducting advanced research based on new developments in higher number theory using new algebraic, geometric and analytical tools.
Biography
Ivan Fesenko was the winner of 1979 all-Russian mathematical Olympiad of last year of high school students. He got his PhD in 1987 in Petersburg State University, Russia. In 1992 he was awarded Prize of Petersburg Math Society. He worked as assistant and associate professor in Petersburg State University in 1986-1995. He worked as Chair in Pure Mathematics in the University of Nottingham, UK, in 1995-2022. He was a research visitor at IAS (Princeton), MPIM (Bonn), Poincare Institute (Paris), Newton Institute (Cambridge), RIMS (Kyoto), Higher School of Economics (Moscow), Tsinghua University (Beijing). He coorganised over 40 international conferences, workshops and symposia. He worked with 60 PhD students and postdocs, some are now professors in Kyoto, Tokyo, Beijing, Petersburg, Frankfurt, Paris, Cambridge, Oxford, Durham, Chicago, Los Angeles. One of his former students Birkar became the 2018 Fields Medallist. He joined Westlake University in November 2023.
Research
See https://ivanfesenko.org/?page_id=126 for files of the papers, talks, volumes and books.
Ivan Fesenko contributed to pioneering developments in several areas of modern number theory: explicit reciprocity formulas, explicit class field theory and higher class field theory, higher adelic structures, higher zeta integrals, extensions of the IUT theory and applications, as well as in algebra: algebraic K-theory, infinite group theory, analysis: higher Haar measure and integration and harmonic analysis, and interaction with model theory, quantum theory and quantum computing
In 2008 he proposed a new program of Higher adelic analysis and geometry as a higher version of the Iwasawa and Tate zeta integral theory. His program aims to develop and apply new higher tools to establish meromorphic continuation and functional equation of the zeta function of elliptic surfaces, study its generalised Riemann Hypothesis and the Tate-Birch-Swinnerton-Dyer conjecture. Various stages of the work have been reported at more than 200 talks and 11 distinguished series of lectures worldwide. His work on the program was supported, as PI, by several UK research grants, including 2,300,000 GBP Programme Grant (see https://ivanfesenko.org/wp-content/uploads/scpage.pdf for more details) in 2015-2021.
In 2018 he proposed a program of Unification of generalisations of class field theory, higher class field theory, anabelian geometry and Langlands program, based on the structural study of each of the generalisations and explicit class field theory.
From 2014 he invested large amount of time and efforts in the study of anabelian geometry and the IUT theory of Mochizuki. He produced the first external survey of IUT. His joint paper with Mochizuki, Hoshi, Minamide, Porowski contains the first proof of effective abc inequality, fundamentally changing one of the oldest parts of number theory, Diophantine geometry. As one of first applications the paper contains a new proof of Fermat’s Last Theorem. The paper was published in July 2022; in April 2024 it was awarded the first international IUT Innovator Prize.
In July 2019 he was invited by the UK Prime Minister special advisor to produce a proposal for a substantial increase of funding of UK mathematics; new 300,000,000 GBP funding was announced by the government in January 2020.
In Spring 2020 he helped to assemble an interdisciplinary group that produced a new higher quality epidemic modelling to provide more accurate predictions about covid waves for the decision makers.
Representative Publications
1) On general local reciprocity maps, J. reine angew. Math. 473(1996), 207-222.
2) On just infinite pro-p-groups and arithmetically profinite extensions of local fields, J. reine angew. Math. 517(1999), 61-80.
3) Invitation to Higher Local Fields, I. Fesenko, M. Kurihara (eds.), Geometry and Topology Monographs, Warwick 2000.
4) Noncommutative local reciprocity maps, In Class Field Theory - Its Centenary and Prospects, Advanced Studies in Pure Math., vol. 30, 63-78, Math. Soc. Japan, Tokyo 2001.
5) Sequential topologies and quotients of Milnor K-groups of higher local fields, St. Petersburg Math. J. 13 (2002), 485-501.
6) Local Fields and Their Extensions, 2nd extended edit., Amer. Math. Soc. 2002.
7) Analysis on arithmetic schemes. I, Docum. Math. (2003), 261-284.
8) Measure, integration and elements of harmonic analysis on generalized loop spaces, AMS Transl. Series 2, vol. 219, 149-164, 2006.
9) Adelic approach to the zeta function of arithmetic schemes in dimension two, Moscow Math. J. 8 (2008), 273-317.
10) Analysis on arithmetic schemes. II, J. K-theory 5 (2010), 437-557.
11) I. Fesenko, G. Ricotta, M. Suzuki, Mean-periodicity and zeta functions, Ann. L'Inst. Fourier, 62 (2012), 1819-1887.
12) Geometric adeles and the Riemann–Roch theorem for 1-cycles on surfaces, Moscow Math. J. 15(2015), 435-453.
13) Generalised Kawada-Satake method for Mackey functors in class field theory, Europ. J. Math. 4(2018) 953-987.
14) Class field theory, its three main generalisations, and applications, EMS Surveys 8(2021), 107-133.
15) Sh. Mochizuki, I. Fesenko, Yu. Hoshi, A. Minamide, W. Porowski, Explicit estimates in inter-universal Teichmüller theory, Kodai Math. J. 45(2022), 175-236.
16) On new interactions between quantum theories and arithmetic geometry, and beyond, In Mathematical Foundations for Post-Quantum Cryptography, Mathematics for Industry, Springer-Verlag, 2024.
Contact Information
Email：ivan.b.fesenko@westlake.edu.cn
