On the KZ--BPZ Correspondence for Painleve II

by Babak Haghighat (Tsinghua University)

Thursday 29 Oct 2026, 15:10 → 16:10 Asia/Shanghai

B105 (CHEP)

We construct an irregular KZ--BPZ correspondence for quantum Painlev\'e II from a rank-three Wakimoto--Whittaker module. The irregular KZ equation and the quantum isomonodromy equation form a joint affine system whose Drinfeld--Sokolov reduction yields scalar BPZ equations. We obtain matrix-integral solutions of this system for one fundamental insertion. An exact quantum Langlands duality exchanges the fundamental insertion with the zero of the dual Whittaker differential and allows affine solutions to be reconstructed from the BPZ equations. This duality interchanges the classical and Nekrasov--Shatashvili limits, which yield the Painlev\'e-II Lax connection and an irregular Gaudin oper, respectively.

Bio:
Babak Haghighat is an Associate Professor at the Yau Mathematical Science Center, Tsinghua University, where he has been a faculty member of the String Theory Group since 2016. He studied at the University of Bonn, completing his Ph.D. there in 2010 under the supervision of Albrecht Klemm, before holding postdoctoral positions at ITF Utrecht and at Harvard University (in both the Physics and Mathematics Departments). His research spans diverse aspects of superconformal field theories in various dimensions and their connections to string and topological string theory, sitting at the interface of physics and mathematics and touching on moduli spaces, algebraic and enumerative geometry, and modular and automorphic forms, while on the physics side addressing perturbative and non-perturbative aspects of supersymmetric quantum field theories and their observables. More recently, his work has focused on topological quantum field theories in low dimensions, their connections to 2d CFT and topological phases of matter, and—mathematically—to representation theory, fusion categories, and knot invariants.