{"product_id":"springerbriefs-in-mathematical-physics-9789811678387","title":"SpringerBriefs in Mathematical Physics","description":"\u003cp\u003eThis 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 firstproposed 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.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":53590023405847,"sku":null,"price":6892.45,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9789811678387.jpg?v=1782721323","url":"https:\/\/payment.letskitaboo.com\/products\/springerbriefs-in-mathematical-physics-9789811678387","provider":"Kitaboo One eStore","version":"1.0","type":"link"}