In the seminal work of Nakajima-Yoshioka in 2003, a blowup formula for the generating function of certain integral on instanton moduli space was established to prove the Nekrasov conjecture. I will survey the recent progress on Nakajima-Yoshioka blowup formulas. I will discuss the generalizations of blowup equations to various supersymmetric gauge theories in 4d, 5d, 6d that are cohomological, K-theoretic, elliptic respectively, and to refined topological string theory on local Calabi-Yau threefolds. I also discuss the relation between blowup equations and (refined) holomorphic anomaly equations which are two universal approaches to solve enumerative invariants of local Calabi-Yau threefolds.

报告人简介：孙凯文，中国科学技术大学数学科学学院特任研究员。2020年博士毕业于意大利国际高等研究院，后在德国波恩马克斯普朗克数学研究所，韩国高等研究院，瑞典乌普萨拉大学做博后，2024年入职中科大。研究方向为数学物理，包括拓扑弦，超对称场论，共形场论等。