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

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

September 11: Organizatorial Meeting;
September 18: Efstratios Tsoukanis, "Coorbit Invariant Embeddings (1)" paper
September 25: Efstratios Tsoukanis, "Coorbit Invariant Embeddings (2)" paper
October 2: Efstratios Tsoukanis, "Coorbit Invariant Embeddings (3)" paper
October 9: Matthias Wellershoff, "The HRT conjecture from the point of view of the Fock space (1)" paper; presentation is here.
October 16: Matthias Wellershoff, "The HRT conjecture from the point of view of the Fock space (2)" paper; presentation is here.
October 23: Matthias Wellershoff, "The HRT conjecture from the point of view of the Fock space (3)" paper; presentation is here.
October 30: Revati Jadhav, "Linear independence of time frequency translates of functions with greater than exponential decay" paper
November 6: Revati Jadhav, "Linear independence of time frequency translates of functions with greater than exponential decay (2)" paper
November 13: "Linear independence of time frequency translates of functions with greater than exponential decay (3)" paper
November 20: No meeting (Thanksgiving break)
November 27: Shashank Sule, "Bilevel optimization for hyperparameter tuning"
December 4: Revati Jadhav, "Turan-Nazarov inequality" slides
December 11: Shashank Sule, "Bilevel optimization for hyperparameter tuning (2)"

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.