Undergraduate students, graduate students, postdocs, professors, not necessarily working in number theory.
Basic number theory and commutative algebra, such as congruences, quadratic reciprocity law, groups, commutative rings.
Researchers in one area are often unable to understand research work in another area, even inside number theory. Still, there are few common underlying fundamental theories that unite many areas. This first series of lectures will present some fundamental unifying theories in number theory. They will include class field theory and its three generalisations: higher class field theory, Langlands program, anabelian geometry.
This recent paper in the EMS Surveys
About Ivan Fesenko
--Contributor to class field theory, higher class field theory, higher adelic theory, higher harmonic analysis, zeta functions and zeta integrals of arithmetic schemes, and interaction of modern number theory with various areas.
--Principal investigator of the Engineering and Physical Sciences Research Council program grant “Symmetries and Correspondences”.
--Contributor to the recent paper on effective abc inequalities and a new proof of FLT.
--Supervisor and host of 60 PhD students and postdoctoral researchers.
--Co-organizer of over 40 workshops, conferences and symposia.
--His research visits include stays at Poincaré Institute, Newton Institute, Hebrew University, RIMS, Max Planck Institute for Mathematics, Caltech, Columbia University, University of Chicago, University of Toronto, Bogomolov’s laboratory at the Higher School of Economics (Russia), the Institute for Advanced Study, Kyoto University. His previous positions include chair in pure mathematics at the University of Nottingham.
--Mentor Professor of 2018 Fields Medalist Caucher Birkar