{"product_id":"recent-progress-on-the-donaldson-thomas","title":"Recent Progress On The Donaldson-thomas","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. \u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\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 first proposed by Gopakumar-Vafa in 1998, but its precise mathematical definition has not been available until recently.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eThis book surveys the recent progress on DT invariants and related topics, with a focus on applications to curve-counting theories.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e","brand":"MediaPlace","offers":[{"title":"Default Title","offer_id":57311789941118,"sku":"NW9789811678370","price":43.65,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1379\/1261\/files\/9789811678370.jpg?v=1778584625","url":"https:\/\/mediaplace.com\/products\/recent-progress-on-the-donaldson-thomas","provider":"MediaPlace","version":"1.0","type":"link"}