{"product_id":"recent-progress-on-the-donaldson-thomas-yukinobu-toda-9789811678370","title":"Recent Progress on the Donaldson-Thomas Theory: Wall-Crossing and Refined Invariants","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. \u003cbr\u003eRecently, 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.\u003cbr\u003eThis book surveys the recent progress on DT invariants and related topics, with a focus on applications to curve-counting theories.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Yukinobu Toda\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 9811678375\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9789811678370\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 12\/16\/2021\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 104\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.38lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.24d","brand":"Yukinobu Toda","offers":[{"title":"Paperback","offer_id":43992734400767,"sku":"9789811678370","price":69.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_488d9976-a813-4f80-8437-4e577fbdb821.jpg?v=1683320489","url":"https:\/\/www.whiterainbookhouse.com\/products\/recent-progress-on-the-donaldson-thomas-yukinobu-toda-9789811678370","provider":"WR Book House","version":"1.0","type":"link"}