Course 1: Patrick Flandrin - "Time-frequency perspectives"
Considering a number of issues related to different types of nonstationarities, time-frequency analysis will be introduced as a natural paradigm, and the main classical methods that have been developed since half a century for their analysis will be recalled. It will be discussed how time-frequency frameworks permit to address specific problems such as testing for nonstationarity, localizing chirps in the time-frequency plane, or disentangling multicomponent nonstationary signals. Some focus will be given to recent advances in spectrogram geometry, paving the way to filtering and denoising methods based on extremal points. Two typical examples that are naturally amenable to time-frequency approaches, namely gravitational waves and bat sonar, will be discussed in some detail, and a historical and epistemological perspective of the field will be provided.
Keywords: Fourier, chirps, Wigner, Cohen, wavelet, reassignment, synchrosqueezing, Empirical Mode Decomposition.

Course 2: Yang Wang - "Mathematics of Deep Neural Networks: A First Introduction"
This will be an introductive course to the mathematical foundation of Deep Neural Networks. One lecture will be devoted to the mathematical foundation of blockchain.

Course 3: Hau-Tieng Wu - "Modern time series analysis via time-frequency analysis and complex analysis"
Explosive advances in sensor technologies lead to explosive datasets being available in many fields, particularly the bio-medical field. Multimodal heterogeneous types of signals pile on an extra layer of difficulties on the data analysis mission. We focus on the high frequency time series in this lecture, and study its underlying intricate nature. We will introduce various signal processing techniques based on time-frequency (TF) analysis and complex analysis for the sake of extracting relevant information for practical usage. Theoretical and statistical analysis of the introduced techniques will be discussed based on real examples. Topics to cover include but not exclusively 1. synchrosqueezing transform; 2. de-shape short time Fourier transform; 3. Blaschke decomposition; 4. phase extraction; 5. statistical inference; 6. clinical applications. If time permits, how to combine these tools with differential geometry will be introduced. I will assume basic knowledge of Fourier analysis, complex analysis and probability.