[Colloquium] From Laplacians to Learning: Bridging Networks, Dynamics, and Chaos

Speaker: Sanjukta Krishnagopal, UCSB

Title:  From Laplacians to Learning: Bridging Networks, Dynamics, and Chaos

Abstract: Many interesting physical systems—from turbulent fluids to neural and social networks—share a common principle: structure determines dynamics. In this talk, I will trace a path from Laplacians and topology, which describe how information propagates through networks, to the emerging role of artificial intelligence as a new paradigm for understanding and predicting complex physical behavior. 

I will begin by discussing higher-order networks and simplicial complexes, which capture multi-body interactions, and reveal how signals diffuse and evolve on topological structures. I will then turn to machine learning viewed through a physical lens - showing (1) how the neural tangent kernel provides a theoretical framework for how neural networks learn, (2) how topological representations can make AI more interpretable, and (3) how physics-informed neural networks can capture and explain chaotic dynamics.

Together, these threads illustrate a unifying theme: that the same geometric and dynamical principles underlying physical systems can be harnessed to advance how intelligent systems learn from them.

Bio: Sanjukta is an assistant professor in the Department of Computer Science at UCSB. Her research interests are multidisciplinary, with the goal of developing computational and mathematical tools to answer questions about real world physical, social, and biological systems. She received undergraduate degrees in Physics and Mechanical Engineering from BITS in India, followed by Master's research at TU Berlin in theoretical physics. Following this, she received her PhD in Physics at the University of Maryland. She then held research positions at the Gatsby Unit in London working with Google DeepMind, and as a UC Presidential Postdoctoral Fellow with a joint appointment at UC Berkeley CS and UCLA Math. She enjoys traveling and has lived on four continents. In her free time she enjoys dancing, hiking, art, and attempting to climb mountains.