This workshop, sponsored by AIM and the NSF, In 1960, the quantum mechanist Eugene P. Wigner famously wrote about "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." He was referring to the profound ability of abstract concepts to predict real-world phenomena. While this ability has found what seems to be an endless number of successful use cases in science, engineering, and medicine, it remains mathematically unproven. At about the same time, and enabled by quantum technologies such as the transistor, the first high-performance computers (HPCs) were being built. The internet's precursor, ARPANet, was also enabled by such quantum technologies as the transistor and housed four of these early HPCs. HPCs automated the execution of fundamental computations, including the singular value decomposition (SVD) and the pseudo-inverse. Ultimately, the quantum mechanics-enabled computing automation and internet communication brought about advances in data science, from chaos theory to deep learning, which were previously limited to mostly unsolvable equations. Today, these mathematical methods are contributing solutions, not just to science, engineering, and medicine, but to all human and societal urgent challenges. This year, as the world is celebrating the 100th anniversary of quantum mechanics, the AIM Quantum Research Community will start work to define, develop, and deploy novel advances in mathematics and its applications that are inspired and enabled by, as well as inspiring and enabling of, new quantum science and technology. This interplay is expected to advance such active mathematical fields as linear and multi-linear algebra, topology, probability and statistics, calculus of variations, spectral theory, and information theory, and disparate application fields as personalized medicine, drug and biomarker development, materials science, climate modeling, quantitative finance, and cybersecurity. We will kickstart the AIM Quantum Research Community work with a symposium in Fall 2026. Please visit the AIM-Q webpage [link to https://alterlab.org/aim-q/ [alterlab.org]] for more information and updates. If you have questions about the program, please contact us at aim-q@sci.utah.edu.
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
For more information email workshops@aimath.org