【数学与统计及交叉学科前沿论坛------高端学术讲座第176场】

报告题目：Uniform resolvent estimates and smoothing effects related to Heisenberg sublaplacians

报 告 人：Luz Roncal (Basque Center for Applied Mathematics)

报告时间：2025年12月10日周三15:30-16:30

报告地点：阜成路校区教三楼西345

报告摘要：Uniform resolvent estimates play a fundamental role in the study of spectral and scattering theory for Schrodinger equations. In particular, they are closely connected to global-in-time dispersive estimates, such as Strichartz estimates. In contrast with the Euclidean setting, a peculiar fact of the Schrodinger evolution equation associated with the sublaplacian on the Heisenberg group is that it fails to be dispersive, as shown by Bahouri, Gerard, and Xu. In fact, Strichartz or $L^p-L^q$ estimates cannot hold in general. In this talk we will discuss uniform resolvent estimates on the Heisenberg group and their application to obtain certain smoothing effects for Schrodinger equations. This is a joint work with Luca Fanelli, Haruya Mizutani, and Nico Michele Schiavone.

报告人简介：Luz Roncal is Ikerbasque Research Associate Professor at the Basque Center for Applied Mathematics in Bilbao, Spain. Her research concerns problems in Harmonic Analysis and Partial Differential Equation Analysis, with relevant contributions within these fields. With a PhD in Mathematics from the Universidad de La Rioja, Luz Roncal has research experience at the Polish Academy of Sciences in Wroclaw (Poland), the Seoul National University (South Korea), the University of Helsinki (Finland), and Indian Institute of Science (IISc) in Bangalore (India), among others. She has also received the Award to Young Scientific Female Talent in 2019, by the Foundation of Royal Academy of Sciences in Spain.