Recent Progress on the Donaldson–Thomas Theory

Released on by Yukinobu Toda
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  • Recent Progress on the Donaldson–Thomas Theory Book Detail

  • Author : Yukinobu Toda
  • Release Date : 2021-12-15
  • Publisher : Springer Nature
  • Genre : Science
  • Pages : 110
  • ISBN 13 : 9811678383
  • File Size : 25,25 MB
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Recent Progress on the Donaldson–Thomas Theory by Yukinobu Toda PDF Summary

Book 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.

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Recent Progress in Mathematics

Recent Progress in Mathematics

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This book consists of five chapters presenting problems of current research in mathematics, with its history and development, current state, and possible future