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.

Speaker Biography: Kaiwen Sun

Dr. Kaiwen Sun is a Specially Appointed Researcher at the School of Mathematical Sciences, University of Science and Technology of China (USTC). He obtained his Ph.D. in 2020 from SISSA (International School for Advanced Studies), Italy. Following his doctorate, he held postdoctoral positions at the Max Planck Institute for Mathematics in Bonn, Germany; the Korea Institute for Advanced Study (KIAS), South Korea; and Uppsala University, Sweden. He joined USTC in 2024.

His research focuses on mathematical physics, including topological strings, supersymmetric field theories, and conformal field theory.