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

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

February 5: Organizatorial Meeting
February 12: Fushuai (Black) Jiang, "Square-summable rank-one decomposition of nuclear operators" notes
February 19: Presidents' day (no meeting)
February 26: Fushuai (Black) Jiang, "Square-summable rank-one decomposition of nuclear operators (2)" notes
March 4: Fushuai (Black) Jiang, "Square-summable rank-one decomposition of nuclear operators (3) notes
March 11:(no meeting)
March 18: (no meeting)
March 25: Kathryn Linehan: "CUR Matrix Approximation Using Convex Optimization" abstract
April 1: (no meeting)
April 8: (no meeting) solar eclipse
April 15: Fushuai (Black) Jiang, "A short survey on Lipschitz extension problems" abstract
April 22: (no meeting)
April 29:
May 6:

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:Linear Independence of TF shifts (HRT Conjecture):

Point Configurations:
1. THE HRT CONJECTURE FOR TWO CLASSES OF SPECIAL CONFIGURATIONS, K. Okoudjou, V. Oussa (2021)
2. ZERO SET OF ZAK TRANSFORM AND THE HRT CONJECTURE, V. Oussa (2023)
3. LINEAR INDEPENDENCE OF TIME FREQUENCY TRANSLATES FOR SPECIAL CONFIGURATIONS, C. Demeter (2016)
4. PROOF OF THE HRT CONJECTURE FOR (2,2) CONFIGURATIONS, C. Demeter, A. Zaharescu (2010)
Behavior At Infinity:
5. Linear Independence of Time-Frequency Shifts Up To Extreme Dilations, M. Kreisel (2019). See also: A Note on the HRT Conjecture and a New Uncertainty Principle for the Short-Time Fourier Transform, N. Fabio, I. Trapasso (2020)
6. LINEAR INDEPENDENCE OF TIME-FREQUENCY TRANSLATES OF FUNCTIONS WITH FASTER THAN EXPONENTIAL DECAY, M. Bownick, D. Speegle (2012)
7. Linear Independence of Finite Gabor Systems Determined by Behavior at Infinity, J. Benedetto , A. Bourouihiya (2012)
8. Remarks on the HRT Conjecture, D. Strooks (2015)
Lattice Case:
8. VON NEUMANN ALGEBRAS AND LINEAR INDEPENDENCE OF TRANSLATES, P.A. Linnell (1999)
9. LINEAR INDEPENDENCE OF COHERENT SYSTEMS ASSOCIATED TO LATTICES, U. Enstad, J.T. Van Velthoven (2023)

Theme 2:Embeddings and Representations:

1. G-invariant Representations using Coorbits: Bi-Lipschitz Properties arXiv:2308.11784 (2023)
2. G-invariant Representations using coorbits: Injectivity Properties arXiv: 2310:16365 (2023)

Theme 3:Lipschitz Extensions
1. McShane
2. Whitney
3. Explicit Kirszbraun formula
4. Nagata dimension and extension
5. Roadmap book:
Volume 1
Volume 2