A theory of counting surfaces in projective varieties

主講人：蔣云峰 美國堪薩斯大學(xué)教授

時間：2024年6月14日10：30

地點(diǎn)：三號樓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)?，幾何表示論，枚舉組合，S-對偶猜想和鏡面對稱間的聯(lián)系?？蒲谐晒S碩，在Adv. Math., JDG, JAG, IMRN, Math. Ann. 等著名數(shù)學(xué)雜志發(fā)表論文多篇，是國際著名的代數(shù)幾何專家。

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.