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Recent Progress on the Donaldson-Thomas Theory (eBook)

Wall-Crossing and Refined Invariants
Artikelnummer: 978-981-1678-38-7
Einband: PDF
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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.

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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VerlagSpringer Nature Singapore
EinbandPDF
Erscheinungsjahr2021
Seitenangabe104 S.
AusgabekennzeichenEnglisch
AbbildungenVIII, 104 p. 3 illus.
Masse1'960 KB
PlattformPDF
ReiheSpringerBriefs in Mathematical Physics; Mathematics and Statistics; Mathematics and Statistics
AutorToda, Yukinobu

Alle Bände der Reihe "SpringerBriefs in Mathematical Physics; Mathematics and Statistics; Mathematics and Statistics (R0)"

Über den Autor Yukinobu Toda

Prof. Yukinobu Toda received his PhD from the University of Tokyo in 2006, and held a JSPS postdoctoral position at the University of Tokyo from 2006 to 2007. Subsequently, he started at the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU) in 2008, initially as a project assistant professor, and since 2017, he has held the position of full professor at Kavli IPMU. He was an ICM invited speaker in 2014 in Seoul.

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