Dr. Alexander Borisovich Zheglov, Ph.D., Dr. Sci. (hab.)
Born August 23, 1974 in Ivanovo, Russia
Education:
a) graduated the Kolmogorov Physical-Mathematical School by Moscow State University in 1991;
b) graduated Moscow State University in 1996 (Department of Higher Algebra, Faculty of Mechanics and Mathematics of MSU), under the supervision of A.N.Parshin, diploma with distinction, 1996
c) postgraduate student of Higher Algebra Department of Mechanics and Mathematics Faculty of Moscow State University since 1996 till December 1999, under the supervision of A.N.Parshin.
d) postgraduate student of the Graduiertenkolleg ”Geometry und Nichtlinear Analisys” of Humboldt University in Berlin since January 2000 till July 2002, under the supervision of A.N.Parshin and E.-W. Zink.
e) Ph.D. in mathematics, Moscow State University, Humboldt University in Berlin (July 2002); candidate dissertation (Ph.D. Thesis) ”Multidimensional local skew-fields”,
electronic publication of Humboldt University in http://edoc.hu-berlin.de/browsing/dissertationen/
f) Dr. Sci. (habilitation) in mathematics, Steklov Mathematical Institute of Russian Academy of Science (Oktober 2016); habilitation Thesis ”Torsion free sheaves on varieties and integrable systems” (in russian), http://www.mi.ras.ru/dis/ref16/zheglov/dis.pdf
Appointments:
August 2002 – April 2006: postdoctoral fellow of DFG (Deutsche Forschungsgemeinschaft)-Schwerpunkt ”Globale Methoden in der komplexen Geometrie”, project ”Higher-dimensional Krichever correspondence” hosted by Prof. H. Kurke at the Department of pure and applied mathematics, Humboldt University of Berlin, Germany.
November 2002 – May 2006: Research fellow, Institute of Pure and Applied Mathematics, Fareastern part of Russian Academy of Science; Chabarovsk, Russia.
May 2006 – August 2020: Associate Professor at the Chair of Differential Geometry and applications, Department of Mechanics and Mathematics, Moscow State University
Since September 2020 - Professor of the Department of Differential Geometry and Applications, Department of Mechanics and Mathematics, Moscow State University Short-term research appointments (several weeks) at: University of Salamanca, Mat. Institute of Oberwolfach, Max Plank Inst. in Bonn, ICTP (Trieste), ESI (Wien), Cologne University
Reseach interests:
Algebraic geometry, algebraic number theory, integrable systems, higher local fields, valuation theory My major research field at present time is the algebraic theory of integrable systems. Since 2002, together with colleagues from the Mathematical Institute of the Russian Academy of Sciences, as well as with colleagues from Germany (Humboldt University of Berlin, Cologne University), I developed the theory of higher-dimensional Krichever correspondence, which is a generalization of the well-known algebraic theory of the KP equation, and which connects many modern areas of mathematics. The results obtained on this topic from 2002 to 2016 formed the basis of my doctoral dissertation "Torsion free sheaves on varieties and integrable systems". In particular, we developed an approach to a solution of the well-known classification problem of commuting rings of partial differential or differential-difference operators, as well as an approach to the study of their isospectral deformations, based on the study of spectral sheaves on projective algebraic varieties. In the framework of this approach, using fundamentally new algebraic-geometric and number-theoretic ideas and constructions developed by the school of A.N. Parshin, we investigated the geometric spectral data of a wide class of well-known examples of algebraically integrable systems; commutative subalgebras of operators in two variables were classified in terms of geometric spectral data; multidimensional analogues of the KP hierarchy were proposed, explicit isospectral deformations of well-known examples of algebraically integrable Calogero-Moser system with rational potential were found.
Mailing address:
A.B.Zheglov, Department of Differential Geometry and applications, Moscow State University, Leninskie gory, 1, Moscow, 117966, Russia
E-mail:
azheglov@math.msu.su
azheglov@mathematik.hu-berlin.de
abzv24@mail.ru
Webpage
http://dfgm.math.msu.su/people/zheglov/English/AlexanderZheglov.html
Conference presentations:
the list of talks given since 2011 see on the webpage https://istina.msu.ru/profile/azheglov/
Textbook based on two-semester lecture courses given at MSU and at the Peking University, available at http://dfgm.math.msu.su/people/zheglov/English/AlexanderZheglov.html
