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. He joined Westlake University in November 2023.
Research
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 and quantum theory.
1. In 2008 he proposed a new program of Higher adelic analysis and geometry which is a higher version of the famous Tate thesis and Iwasawa zeta integral theory. This 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. The work on the program was supported, as PI, by several UK EPSRC grants, including £2.3m Programme Grant in 2015-2021 jointly with Oxford mathematicians.
2. 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. There are already contributions to further developments of this program.
3. In 2015-2021 he invested large amount of time and efforts in the study of anabelian geometry and the famous IUT theory of Mochizuki. He coorganised 4 international conferences on IUT, published the first external survey of IUT and a popular article about IUT in Inference. His joint paper with Mochizuki, Hoshi, Minamide, Porowski about the first proof of effective abc inequality and a new proof of Fermat’s Last Theorem was published in July 2022.
4. Based on his previous research track record, working on research grants and his experience of interacting with young researchers, in July 2019 he was invited to write a proposal for a substantial increase of funding of UK mathematics. £300m funding of the proposal was announced by the government in January 2020.
5. In 2020 Ivan Fesenko helped to assemble and participated in an interdisciplinary group that produced a new higher quality epidemic modelling.
Representative Publications
1) I.B. Fesenko, S.V. Vostokov, Local Fields and Their Extensions, 2nd extended edit., Amer. Math. Soc. 2002, 341pp.
2) Analysis on arithmetic schemes. I, Docum. Math. (2003), 261-284.
3) Measure, integration and elements of harmonic analysis on generalized loop spaces, AMS Transl. Series 2, vol. 219, 149-164, 2006.
4) Adelic approach to the zeta function of arithmetic schemes in dimension two, Moscow Math. J. 8 (2008), 273-317.
5) Analysis on arithmetic schemes. II, J. K-theory 5 (2010), 437-557.
6) I. Fesenko, G. Ricotta, M. Suzuki, Mean-periodicity and zeta functions, Ann. L'Inst. Fourier, 62 (2012), 1819-1887.
7) Geometric adeles and the Riemann–Roch theorem for 1-cycles on surfaces, Moscow Math. J. 15(2015), 435-453.
8) Class field theory, its three main generalisations, and applications, EMS Surveys 8(2021), 107-133.
9) Sh. Mochizuki, I. Fesenko, Yu. Hoshi, A. Minamide, W. Porowski, Explicit estimates in inter-universal Teichmüller theory, Kodai Math. J. 45(2022), 175-236.
10) On new interactions between quantum theories and arithmetic geometry, and beyond, preprint October 2023.
Contact Information
Email：ivan.b.fesenko@westlake.edu.cn
