Conference: Geometric Spectral Theory and Applications

This award provides funding to support the participation of early-career researchers, including graduate students, postdoctoral fellows, and recently appointed tenure-track assistant professors from U.S. institutions, in the six-month program on Geometric Spectral Theory and Applications, hosted and funded by the Isaac Newton Institute for Mathematical Sciences (INI), Cambridge, UK, from January to June 2026. The NSF funds will be used exclusively to support U.S.-based researchers attending one of the week-long workshops within the program. A significant portion of the funds is designated for early-career researchers (ECRs) participating in the Emerging Horizons in Geometric Spectral Theory: An ECRs Workshop, to be held February 2-6, 2026. Applications to attend other workshops, Geometry of Eigenvalues (March 23-27, 2026), Interactions of Geometric Spectral Theory with Numerical Methods and Applications (April 13-17, 2026), and Random and Arithmetic Models in Spectral Theory (May 11-15, 2026) will also be considered. Distributing funding across all workshops maximizes collaborative opportunities and offers greater flexibility, thereby enhancing participation by U.S. researchers. Participation in these activities is open to all who meet the scientific criteria. Applications will be submitted through the INI program website, where U.S.-based applicants will be offered the option to apply for NSF funding. The Principal Investigators of this grant will oversee the evaluation of NSF funding requests applying rigorous academic merit criteria.

Geometric spectral theory is a vibrant and rapidly evolving area of mathematics with deep historical roots, from Ernst Chladni’s pioneering experiments on vibrating plates to Lord Rayleigh’s foundational work on acoustics and Mark Kac’s famous question, “Can one hear the shape of a drum?” The field maintains strong connections with differential geometry, mathematical physics, partial differential equations, number theory, dynamical systems, and numerical analysis. Applications range widely, from acoustics and scattering theory to computer imaging and scientific computing. The highly competitive INI program will focus on four interconnected themes: eigenvalues and geometry; geometry of eigenfunctions and spectral asymptotics; probabilistic and number-theoretic methods in geometric spectral theory; and numerical aspects and applications. These themes form the core of the workshops for which the funds of NSF award are used. The goal is to foster productive exchanges among these communities, leading to advances at their intersections, resolution of open problems, and the generation of new questions and applications. Participation in these workshops, embedded within a broader and vibrant six-month program, offers early-career U.S. mathematicians professional and academic benefits far beyond those of a single event. Given the concentration and breadth of expertise at INI, the workshops provide a unique opportunity for young researchers to present their work, engage with leading experts, and build lasting international collaborations that are critical to their future careers.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

Award Number: 2519641
Principal Investigator: Fioralba Cakoni
Funds Obligated: $44,000
State: NJ