Explore a comprehensive collection of lectures from the Hausdorff Research Institute for Mathematics' trimester program on the mathematics of signal processing. Delve into cutting-edge topics including compressive sensing fundamentals with Simon Foucart's four-part series, large-scale machine learning and convex optimization through Francis Bach's lectures, and geometric optimization aspects presented by Suvrit Sra. Examine Gabor analysis mysteries across Karlheinz Gröchenig's four-lecture series, discover phase retrieval methods from convex to nonconvex approaches, and investigate low-rank matrix recovery techniques. Learn about Fourier analysis via the Banach Gelfand Triple, explore the toric code's connection to topological order, and understand polynomial approximation of random PDEs. Study quantized random projections, noncommutative geometry applications of the finite Heisenberg group, and Weyl-Heisenberg signal design in wireless communications. Gain insights into support vector machines' non-asymptotic analysis, exact support recovery for sparse spikes deconvolution, and the solvability complexity index. Access advanced mathematical concepts in data assimilation, projections and sparsity for efficient data processing, and number-theoretic features of symmetric informationally complete measurements, all presented by leading experts in mathematical signal processing during this intensive academic program.

Syllabus

Simon Foucart: Essentials of Compressive Sensing (Lecture 1)
Francis Bach: Large scale Machine Learning and Convex Optimization (Lecture 1)
Suvrit Sra: Lecture series on Aspects of Convex, Nonconvex, and Geometric Optimization (Lecture 1)
Felix Krahmer: The Restricted Isometry Property for Random Gabor Synthesis Matrices
Karlheinz Gröchenig: Gabor Analysis and its Mysteries (Lecture 1)
Xiadong Li: Phase Retrieval from Convex to Nonconvex Methods
Hans Feichtinger: Fourier Analysis via the Banach Gelfand Triple
David Gross: The Toric Code Finite WH meets Topological Order
Simon Foucart: Essentials of Compressive Sensing (Lecture 2)
Francis Bach: Large scale Machine Learning and Convex Optimization (Lecture 2)
Ke Wei: Low rank matrix recovery From iterative hard thresholding to Riemannian optimization
Simon Foucart: Essentials of Compressive Sensing (Lecture 4)
Suvrit Sra: Lecture series on Aspects of Convex, Nonconvex, and Geometric Optimization (Lecture 2)
Suvrit Sra: Lecture series on Aspects of Convex, Nonconvex, and Geometric Optimization (Lecture 3)
Romanos Malikiosis: Full spark Gabor frames in finite dimensions
Simon Foucart: Essentials of Compressive Sensing (Lecture 3)
Gabriel Peyré: Exact Support Recovery for Sparse Spikes Deconvolution
David Gross: Diamond norm as improved regularizer for low rank matrix recovery
Albert Cohen: Data assimilation in reduced modeling
Karlheinz Gröchenig: Gabor Analysis and its Mysteries (Lecture 2)
Rémi Gribonval: Projections, Learning, and Sparsity for Efficient Data Processing
Fabio Nobile: Polynomial Approximation of Random PDEs by discrete least squares with observations in
Anders Hansen: What is the Solvability Complexity Index SCI....
Francis Bach: Large scale Machine Learning and Convex Optimization (Lecture 3)
Francis Bach: Large scale Machine Learning and Convex Optimization (Lecture 4)
Laurent Jacques/Valerio Cambareri: Small width, low distortions: quantized random projections of...
Franz Luef: The finite Heisenberg group in noncommutative geometry
Peter Jung: Some Aspects of Weyl Heisenberg Signal Design in Wireless Communication
Marcus Appleby: Number theoretic features of a SIC
Karlheinz Gröchenig: Gabor Analysis and its Mysteries (Lecture 4)
Karlheinz Gröchenig: Gabor Analysis and its Mysteries (Lecture 3)
Jan Vybiral: Non asymptotic analysis of l1 support vector machines
Martin Lotz: A blind spot in the probabilistic complexity analysis of algorithms