Top Global Course Special Lectures by Prof. Ivan Fesenko
Top Global Course Special Lectures by Prof. Ivan Fesenko (University of Nottingham) will take place as follows:
 Course Title
 Top Global Course Special Lectures 3
 Date & Time
 July 25 to August 3, 2018 (5 lectures)

 Wednesday, July 25, 10:0012:00
 Friday, July 27, 10:0012:00
 Monday, July 30, 10:0012:00
 Wednesday, August 1, 10:0012:00
 Friday, August 3, 10:0012:00
 Venue
 127 Conference room, Faculty of Science Bldg. #3, Kyoto University
 Title
 Class field theory standpoint and its so different three fundamental generalisations
 Abstract
 In 1972 A. Weil asserted that “since class field theory pertains to the foundation of mathematics, every mathematician should be as familiar with it as with Galois theory”.
 We are still waiting for this to happen..
 In 1920 T. Takagi became the first mathematician to present the existence theory as part of class field theory of general type. We are still digesting the impact of his work. The breakthrough of Sh. Mochizuki in his IUT theory invites us to conduct a review of class field theory and its generalisations, two of which were initiated and radically influenced by Japanese researchers..
 This series of lectures aims to present class field theory from a revised modern point of view and use this to make new observations about the Langlands program, higher class field theory and anabelian geometry and links between them and their further extensions such as the IUT theory and twodimensional adelic analysis and geometry..

The lectures will include.
 (a) class field theory of special and general type, and how this division has affected and is affecting so much in number theory;
 (b) basic features of higher local fields and their surprising properties;
 (c) the Neukirch class field theory method for onedimensional fields and its generalisations;
 (d) the Vostokov symbol and its use in the study of Milnor Ktheory of higher fields;
 (e) explicit higher class field theory, including the universal KawadaSatake method;
 (f) translation invariant measure and integration on higher fields and adeles;
 (g) two distinct adelic structures on elliptic surfaces and higher zeta integral as a bridge between them;
 (h) links and perspectives.
 Language
 English
 Note
 This series of lectures will be videorecorded and made available online.
Please note that anyone in the front rows of the room can be captured by a video camera.