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Explore the intersection of mathematics and artificial intelligence through this comprehensive program featuring leading researchers presenting cutting-edge work on machine learning applications in mathematical discovery. Delve into data-driven approaches for discovering theorems in knot theory and representation theory, examine new methods for finding singular solutions of Euler equations, and investigate counterexamples in graph theory. Learn about rigorous numerical methods and interactive theorem proving that are revolutionizing mathematical research, while exploring the mathematical structures underlying spectacular progress in AI. Discover how machine learning is being applied to topology, with sessions on learning the smooth 4-genus of knots and topological invariance, and examine applications in fluid dynamics through the study of singularities. Investigate generative modeling with flows and diffusions for scientific computing, explore AI-assisted digitization and intelligentization of mathematics, and understand image generation through score diffusion and renormalization group theory. Examine sparse subgraphs, machine learning approaches to elliptic curves and L-functions, and mathematical discoveries through program search with large language models. Study solvable models of scaling and emergence in deep learning, rigorous results from reinforcement learning, and applications ranging from theorem proving to disproving. Explore data visualization using category theory and geometry, participate in tutorials on the Lean theorem prover, and engage in panel discussions on machine learning in science education. Learn about foundation models for real-time cancer diagnosis, scaling limits of neural networks, and data geometry in deep learning, while examining statistical machine learning for developmental biology and multi-institutional electronic health records. Investigate algorithmic progress in big data and AI, economic opportunity research using big data, high-dimensional stochastic dynamics on networks, and predictive disparity in machine learning applications. Participate in discussions on measuring discrimination in multi-phase systems, automated mathematical discovery, conceptual challenges in modern AI, and the application of transformers to Lyapunov theory.
