Part II

I will discuss the full GW theory of Hilb(C^2,n) and the lifting of the older genus 0 equivalences to all genera (recent joint work with H.-H. Tseng). The lifted local curve theories are new and require definitions. The main steps in the proof involve understanding the freedom of the Givental-Teleman classification and an explicit analytic continuation of the fundamental solution of the QDE of Hilb(C^2,n) obtained in a previous paper with Okounkov. An outcome is a proof of the full crepant resolution conjecture for Hilb(C^2,n) -> Sym^n(C^2). I will discuss some geometric examples to show the consequences of the results.

Professor Rahul Pandharipande is a leading expert in algebraic geometry and related fields. He got his Bachelor's degree from Princeton University in 1990 and earned his Ph.D. in 1994 under Joe Harris from Harvard University. After spending four years at the University of Chicago, he moved to Caltech where he stayed till 2001. He became professor at Princeton University in 2002. He then moved to Europe in 2010, visiting IST Lisbon for a year and joining ETH Zurich in 2011.

He has received many academic honors and awards including Fellowships from the Sloan Foundation (1999) and the Packard Foundation (2000), the Compositio Prize (2009), the Clay Research Award (2013), and the Infosys Prize (2013). He was an invited speaker at the ICM 2002 in Beijing, and will be a plenary speaker at the ICM 2018 in Rio de Janeiro.