Time-Frequency Analysis (Lecture Notes)

Lecture notes on the co-representation theory of the compact quantum group $SU_{q}(2).$

This is an exposition of S.L Woronowicz co-representation theory of the compact quantum group $SU_{q}(2)$ written for a seminar series.

Lecture Notes on Noncommutative Lp-Spaces

These lecture notes were written during a mini-course on noncommutative Lp-spaces at the Basque Center of Applied Mathematics. It starts presenting the theory of weights and traces in von Neumann algebra, followed by the theory of noncommutative measure. After that, it presents a construction of these spaces in all detail and give some important results e.g. the noncommutative Radon-Nikodym theorem.

讲义：Galerkin方法

Lecture Notes: The Galerkin Method

本文通过讲义形式介绍Galerkin方法，用于逼近偏微分方程和积分方程的解，包括分析背景、计算示例以及用该方法证明非线性边值问题解的存在性。

Lecture notes on differential calculus on RCD spaces

These are extended notes of the course given by the author at RIMS, Kyoto, in October 2016. The aim is to give a self-contained overview on the recently developed approach to differential calculus on metric measure spaces. The effort is directed into giving as many ideas as possible, without losing too much time in technical details and utmost generality: for this reason many statements are given under some simplifying assumptions and proofs are sometimes only sketched.

高维数据讲义

Lecture notes on high-dimensional data

本讲义介绍高维数据的数学基础，涵盖高维测度集中、高维高斯随机向量、随机投影及高斯数据分离等核心理论与方法，为数据科学提供严谨的数学导论。