Organizers: Javed Mashreghi (Université Laval, Canada, contact organizer)
Akram Aldroubi (Vanderbilt University, USA)
Rocio Diaz Martin (Vanderbilt University, USA)

Brief Summary: The emergence of wavelet theory in the early 1990s has provided a powerful tool for signal processing, data compression, and image analysis, while compressed sensing has become a common method in various areas of mathematics, engineering, and life sciences. At the core of these developments lies the general theory of sampling in shift-invariant spaces, frame theory, and operator theory. Specifically, the wavelet transform can be seen as a type of sampling and representation in shift-invariant spaces, while frame theory provides a connection to operator theory. Compressed sensing, on the other hand, relies on both sampling theory and operator theoretical methods. Additionally, the scattering transform has emerged as a crucial tool for machine learning, offering a framework for deep learning and neural networks. The interaction between applied harmonic analysis, functional analysis, and operator theory has led to significant advances in these fields, with methods that have practical applications in communication theory, signal processing, learning theory, and biomedicine. For instance, this interaction has helped solve fundamental problems in mathematics, such as the Kadison-Singer/Feichtinger conjecture and the Kato conjecture. Despite the significant progress in these fields, many classical questions in the study of Hilbert spaces of analytic functions, such as the characterization of zero sets, uniqueness sets, boundary behavior, invariant subspaces, and cyclicity, remain largely open, with only partial answers available. To promote further interaction between functional analysis, operator theory, harmonic analysis, and their applications, in this session we will focus on topics such as learning theory, sampling, frames, compressed sensing, high-dimensional data geometry, control theory, and operator classes. The primary goal of the session is to provide a platform for experts in these areas to exchange ideas, identify common problems, and explore new trends.

Organizers: Henry Chimal-Dzul (University of Notre Dame, USA, contact organizer)
Maria Chara (Universidad Nacional del Litoral, Argentina)
Hiram H. Lopez (Virginia Tech, USA)
Luciane Quoos (Universidade Federal Rio de Janeiro, Brazil)

Brief Summary: Coding theory, a field that emerged over 60 years ago to ensure reliable information transmission, has remained a vibrant area of research. Its significance lies in its profound connections to various branches of mathematics, such as algebra, number theory, algebraic geometry, and combinatorics. In recent years, coding theory has undergone significant advancements to meet the demands of increasingly challenging modern applications, including the 6G platform, quantum computations, secure protocols for post-quantum cryptography, and distributed storage systems. Notably, certain classes of codes have garnered considerable attention, including low-density and moderate-density parity-check codes, evaluation codes and their association with Grobner basis, self-orthogonal and self-dual codes, and locally repairable codes. Despite the huge advances in the field, fundamental questions like determining the length, minimum distance, dimension, and error floor of these classes of codes are still challenging and primary for modern applications of coding theory. The main goal of this session is to provide a space for people from the Americas at different stages of their careers, from students to senior researchers that investigate fundamental questions and applications in coding theory and related areas, to exchange ideas and explore new trends in the field.