Seminario Análisis y Aplicaciones
A noncommutative analogue of Bourgain’s ergodic theorems along arithmetic sets
Ponente: Guixiang Hong (Harbin Institute of Technology)Fecha: jueves 04 de diciembre de 2025 - 12:30Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
Around 40 years ago, Bourgain generalized Birkhoff’s ergodic theorem by considering ergodic averages along arithmetic sets, stimulating further investigation of discrete operators in harmonic analysis, and there have appeared several breakthroughs in recent 20 years. On the other hand, in a rather new setting, Junge and Xu established a noncommutative analogue of Dunford-Schwartz ergodic theorem in 2007, opening up a new research direction called noncommutative ergodic theory; along this research line, we have recently made some progress on the noncommutative analogues of Bourgain’s ergodic theorems. In this talk, I shall present it by focusing on the background, new ingredients, and the difficulties to a full noncommutative verison of Bourgains’ results. Based on joint works with C. Chen and L. Wang.
