Project Grant 2617222

The National Science Foundation Division of Mathematical Sciences awarded the University of Southern California $250,000 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop machine learning methods for geometry and topology.

The project establishes a systematic framework for applying modern machine learning to open problems in symplectic geometry and low-dimensional topology. Work will organize around three complementary approaches: training problem-specific neural networks and reinforcement-learning agents to search for geometric constructions; refining and sampling near-optimal constructions using diffusion-based generative models; and distilling machine-discovered strategies into short, interpretable algorithms that mathematicians can verify, generalize, and extend. The symplectic ball-packing problem—determining how efficiently balls can be embedded into a given region while preserving signed areas of surfaces—serves as a central testbed, alongside questions about Lagrangian submanifolds, four-dimensional topology, and related structures. The project will support graduate students and postdoctoral researchers and release openly available software and datasets to lower the threshold for other researchers to apply machine learning in mathematics.

Performance occurs at the University of Southern California in Los Angeles, California. The period of performance runs from September 1, 2026, through August 31, 2029.