Meetings: 1.00pm-2.00pm on Mondays in MATH1310.

Schedule (all meetings in MATH 1310 at 1:00pm, unless otherwise noted):

Fall 2024:

September 9: Organizatorial Meeting
September 16: Revati Jadhav, "Characterizing critical density Gabor systems with Zak transform"
September 23: Revati Jadhav, "Characterizing critical density Gabor systems with Zak transform (2)"
September 30: Matthias Wellershoff, "Stability of sorting based embeddings", arXiv 24.10.05446
October 7: Matthias Wellershoff, "Stability of sorting based embeddings (2)", arXiv 24.10.05446
October 14: Matthias Wellershoff, "Stability of sorting based embeddings (3)", arXiv 24.10.05446
October 21: Matthias Wellershoff, "Stability of sorting based embeddings (4)", arXiv 24.10.05446
October 28: no meeting
November 4: Revati Jadhav, "Analyzing rationally oversampled Gabor systems using the Zak transform"
November 11:
November 18:
November 25:
December 2:
December 9: no meeting (winter break)


Spring 2025:

February 3: Organizational Meeting
February 10:
February 17:
February 24:
March 3:
March 10:
March 17: no meeting (spring break)
March 24:
March 31:
April 7:
April 14:
April 21:
April 28:
May 5: no meeting
May 12: no meeting

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: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 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:Generative Networks using Diffusion Models and Lipschitz Extensions
1. McShane
2. Whitney
3. Explicit Kirszbraun formula
4. Nagata dimension and extension
5. Roadmap book:
Volume 1
Volume 2