Yukinobu Toda

(Author)

Recent Progress on the Donaldson-Thomas Theory: Wall-Crossing and Refined Invariants (2021)Paperback - 2021, 16 December 2021

Recent Progress on the Donaldson-Thomas Theory: Wall-Crossing and Refined Invariants (2021)
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Part of Series
Springerbriefs in Mathematical Physics
Print Length
104 pages
Language
English
Publisher
Springer
Date Published
16 Dec 2021
ISBN-10
9811678375
ISBN-13
9789811678370

Description

This book is an exposition of recent progress on the Donaldson-Thomas (DT) theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual counting of stable coherent sheaves on Calabi-Yau 3-folds. Later, it turned out that the DT invariants have many interesting properties and appear in several contexts such as the Gromov-Witten/Donaldson-Thomas conjecture on curve-counting theories, wall-crossing in derived categories with respect to Bridgeland stability conditions, BPS state counting in string theory, and others.
Recently, a deeper structure of the moduli spaces of coherent sheaves on Calabi-Yau 3-folds was found through derived algebraic geometry. These moduli spaces admit shifted symplectic structures and the associated d-critical structures, which lead to refined versions of DT invariants such as cohomological DT invariants. The idea of cohomological DT invariants led to a mathematical definition of the Gopakumar-Vafa invariant, which was first proposed by Gopakumar-Vafa in 1998, but its precise mathematical definition has not been available until recently.
This book surveys the recent progress on DT invariants and related topics, with a focus on applications to curve-counting theories.

Product Details

Author:
Yukinobu Toda
Book Edition:
2021
Book Format:
Paperback
Country of Origin:
NL
Date Published:
16 December 2021
Dimensions:
23.39 x 15.6 x 0.61 cm
ISBN-10:
9811678375
ISBN-13:
9789811678370
Language:
English
Location:
Singapore
Pages:
104
Publisher:
Weight:
172.36 gm

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