Speaker: Jean-Emile Bourgine (SIMIS, Fudan)
Time: 2025-12-17 16:00-18:00
Location: 1710, SIMIS
Zoom Meeting ID: 848 2160 6173 Passcode: 715381
摘要：
The study of classical integrable hierarchies of PDE is an important subject in Mathematical Physics. It has a long history, and shows many connections to various problems in physics (e.g. solitons, hydrodynamics, condensed matter, non-linear optics,…) and pure mathematics (enumerative geometry, combinatorics, Painleve equations,…). In [2308.16583], motivated by a correspondence with topological strings amplitudes, Sasha Garbali and I proposed to introduce a refinement of these integrable hierarchies. In this talk, I will review the algebraic approach to integrable hierarchies of Date-Jimbo-Kashiwara-Miwa, and use this setting to introduce the quantum group deformation. I will present the derivation of PDEs, and a certain class of solutions. Finally, I will discuss recent progress toward understanding polynomial solutions.
About Speaker
Jean-Emile Bourgine is an Assistant Professor at SIMIS and Fudan University. He did his PhD at Institut de Physique Théorique (IPhT) CEA-Saclay and graduated from Université Paris Sud XI (now Paris-Saclay) in 2010. Prior to joining SIMIS, he previously held research positions in South Korea (Sogang University, APCTP, KIAS), Italy (INFN) and Australia (University of Melbourne). He has published a number of articles on a variety of topics in mathematical physics, including random matrix models, 2D quantum gravity, lattice statistical models, integrable hierarchies, supersymmetric gauge theories, quantum algebras and string theory. He is currently working mainly on the representation theory of quantum toroidal algebras, on which he has obtained several important new results that find application in the description of brane systems in string theory.
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