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Periodic Monopoles and Difference Modules by Takuro Mochizuki
Periodic Monopoles and Difference Modules by Takuro Mochizuki
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Periodic Monopoles and Difference Modules

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Description

This book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis–Kapustin (GCK) type. It presents a classification of the latter in terms of difference modules with parabolic structure, revealing a kind of Kobayashi–Hitchin correspondence between differential geometric objects and algebraic objects. It also clarifies the asymptotic behaviour of these monopoles around infinity. The theory of periodic monopoles of GCK type has applications to Yang–Mills theory in differential geometry and to the study of difference modules in dynamical algebraic geometry. A complete account of the theory is given, including major generalizations of results due to Charbonneau, Cherkis, Hurtubise, Kapustin, and others, and a new and original generalization of the nonabelian Hodge correspondence first studied by Corlette, Donaldson, Hitchin and Simpson. This work will be of interest to graduatestudents and researchers in differential and algebraic geometry, as well as in mathematical physics.

Author Biography:

Takuro Mochizuki has been awarded the 2022 Breakthrough Prize in Mathematics for advancing the understanding of holonomic D-modules through his research on harmonic bundles and twister D-modules, which he has studied at the "interface of algebraic geometry and differential geometry".
Release date Australia
February 24th, 2022
Audience
  • Professional & Vocational
Edition
1st ed. 2022
Illustrations
XVIII, 324 p.
Pages
324
ISBN-13
9783030944995
Product ID
35691860

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