Federal Grant Award Summary

The National Science Foundation's Division of Mathematical Sciences awarded $295,477 to Stony Brook University (administered through The Research Foundation For The State University Of New York) under the Mathematical and Physical Sciences program (CFDA 47.049) for a three-year project running from July 1, 2026 through June 30, 2029. The award supports fundamental research on renormalization in holomorphic dynamics and Mandelbrot-Julia Set (MLC) theory, with the primary objective of proving the MLC conjecture on local connectivity of the Mandelbrot Set and establishing a unified renormalization framework across five key renormalization schemes. The research outputs will include comprehensive topological and geometric models characterizing the Mandelbrot Set and Julia Sets, as well as topological classification results for neutral quadratic polynomials.

Beyond direct research products, the award supports workforce development and knowledge dissemination critical to the mathematical sciences community. Funding supports training of postdoctoral researchers and graduate students in complex dynamics theory, with emphasis on preparing the next generation of mathematicians for careers in academia and industry. The project also facilitates broader dissemination of research findings and promotes collaboration within the dynamics field through conferences, mini-courses, and maintenance of a dynamics research website. These integrated research and educational deliverables advance fundamental understanding of low-dimensional quadratic dynamical systems with applications across celestial mechanics, fluid dynamics, statistical mechanics, and biological sciences.