A theory of counting surfaces in projective varieties

發(fā)布者:文明辦發(fā)布時(shí)間:2024-06-07瀏覽次數(shù):157

主講人:蔣云峰 美國(guó)堪薩斯大學(xué)教授


時(shí)間:2024年6月14日10:30


地點(diǎn):三號(hào)樓332室


舉辦單位:數(shù)理學(xué)院


主講人介紹:蔣云峰,堪薩斯大學(xué)教授,研究方向?yàn)榇鷶?shù)幾何和數(shù)學(xué)物理,特別是Gromov-Witten理論和Donaldson-Thomas理論,以及與雙有理幾何,辛拓?fù)洌瑤缀伪硎菊?,枚舉組合,S-對(duì)偶猜想和鏡面對(duì)稱(chēng)間的聯(lián)系??蒲谐晒S碩,在A(yíng)dv. Math., JDG, JAG, IMRN, Math. Ann. 等著名數(shù)學(xué)雜志發(fā)表論文多篇,是國(guó)際著名的代數(shù)幾何專(zhuān)家。


內(nèi)容介紹:The theory of enumerative invariants of counting curves (Riemann surfaces) in projective varieties has been an important theory in the last decades. The enumerative invariants were motivated by theretical physics---string theory and gauge theory, and include Gromov-Witten theory, Donaldson-Thomas theory and more recently Vafa-Witten theory. It is hoped that there may exist a theory of counting algebraic surfaces in projective varieties. A theory of counting surface in a Calabi-Yau 4-fold has been constructed using Donaldson-Thomas theory of 4-folds. In this talk I will try to give evidences of a counting surface theory using stable maps, and explain why it is difficult to construct the counting surface invaraints.