What we don’t understand and why it matters: from high dimensional geometry to modern AI

In this talk, we journey through several “big” mathematical ideas, from familiar large numbers to simple geometric concepts that behave in surprising ways in high dimensions. These examples set the stage for why mathematics remains essential to understanding modern AI. We focus especially on open questions in deep learning, including why neural networks are able to generalize so effectively, and why this matters for real-world systems. The talk concludes with applications in medicine and criminal justice, highlighting ongoing work with community partners that illustrates the practical impact of mathematical methods.

Deanna Needell earned her PhD from UC Davis before working as a postdoctoral fellow at Stanford University. She is currently a full professor of mathematics at UCLA, the Dunn Family Endowed Chair in Data Theory, and the Executive Director for UCLA's Institute for Digital Research and Education. She has earned many awards including the Alfred P. Sloan fellowship, an NSF CAREER and other awards, the IMA prize in Applied Mathematics, is a 2022 American Mathematical Society (AMS) Fellow and a 2024 Society for industrial and applied mathematics (SIAM) Fellow. She has been a research professor fellow at several top research institutes including the SLMath (formerly MSRI) and Simons Institute in Berkeley. She also serves as associate editor for several journals including Linear Algebra and its Applications and the SIAM Journal on Imaging Sciences, as well as on the organizing committee for SIAM sessions and the Association for Women in Mathematics.

Free and Open to the Public