In this talk, we suggest a simple definition of Laplacian on a compact quantum group (CQG) associated with a first-order differential calculus (FODC) on it. Applied to the classical differential calculus on a compact Lie group, this definition yields classical Laplacians, as it should. Moreover, on the CQG $ K_q $ arising from the $ q $-deformation of a compact semisimple Lie group $ K $, we can find many interesting linear operators that satisfy this definition, which converge to a classical Laplacian on $ K $ as $ q $ tends to 1, and share many desirable properties. In light of this, we call them $ q $-Laplacians on $ K_q $. We explore some problems related to the heat equations on $ K_q $ defined by them. This work is based on the preprint arXiv:2410.00720.

报告人简介: Dr. Heon Lee is currently a postdoctoral researcher at the Institute for Advanced Study in Mathematics at Harbin Institute of Technology. He received his PhD in Mathematics from Seoul National University. His research interests lie in the interplay between symmetry, geometry, and analysis, spanning abstract harmonic analysis on Lie groups, the noncommutative geometry of quantum groups, and aspects of mathematical physics, with a particular focus on q-deformed compact semisimple Lie groups.