Meetings: 11.00am-12.00noon on Mondays in MATH1310.

Schedule (all meetings in MATH 1310 at 11:00am, unless otherwise noted):

Fall 2025:

September 15: Organizational Meeting
September 22: Radu Balan, "l1-Sparse Matrix Factorizations and a Blind Source Separation Problem " arXiv2409.20372
September 29: Radu Balan, "l1-Sparse Matrix Factorizations and a Blind Source Separation Problem (2)" arXiv2409.20372
October 6: Radu Balan, "l1-Sparse Matrix Factorizations and a Blind Source Separation Problem (3)" arXiv2409.20372, ACHA 2024
October 13: No RIT: Fall break
October 20: Sanghoon Na, "Frame Quantization of Neural Networks", JFAA 2025
October 27: Sanghoon Na, "Curse of Dimensionality in Neural Network Optimization", arXiv
November 3:
November 10:
November 17:
November 24: likely no meeting (Thanksgiving week)
December 1:
December 8:


Spring 2026:

February 2: Organizational Meeting
February 9:
February 16:
February 23:
March 2:
March 9:
March 16: no meeting (spring break)
March 23:
March 30:
April 6:
April 13:
April 20:
April 27:
May 4:
May 11:

Topics:
We plan to discuss topics in harmonic analysis and related fields (functional analysis, operator and representation theory) with applications to various fields such as signal processing, machine learning, graph representations, quantum information theory.

References:

Theme 1:Matrix Factorizations

1. Factorization of positive-semidefinite operators with absolutely summable entries, arXiv:2409.20372
2. ACHA vol. 73 (2024), A. Bandeira, D.Mixon, S. Steinerberger

Theme 2:Embeddings and Representations:

1. Stability of sorting based embeddings, arXiv:2410.05446
2. G-invariant Representations using Coorbits: Bi-Lipschitz Properties arXiv:2308.11784 (2023)
3. G-invariant Representations using coorbits: Injectivity Properties arXiv: 2310:16365 (2023)

Theme 3:TF Analysis:

1. K. Groechenig, Foundations of Time-Frequency Analysis, Birkhauser, 2000
2. Zibulski and Zeevi, Analysis of Multiwindow Gabor-Type Schemes by Frame Methods, ACHA 1997.
3. Bolcskei and Janssen, Gabor frames, unimodularity, and window decay, JFAA 2000
4. Janssen, On rationally oversampled Weyl-Heisenberg frames, Signal Processing 1995.

Theme 4: Lipschitz Analysis and Uncertainty Quantification in Deep Learning:

1. W. Czaja, S. Na, Frame Quantization of Neural Networks, JFAA 2025 local
2. S. Na, H. Yang, Curse of Dimensionality in Neural Network Optimization, arXiv 2025