UBC Math Bio Seminar: Dhananjay Bhaskar

Networks are everywhere in biology - from molecules that interact within a cell to neurons that communicate across the brain. Understanding how signals flow through these networks is key to uncovering how biological systems function - and how they fail in disease.

In this talk, I will describe new mathematical and computational frameworks that use the geometry and dynamics on graphs to learn meaningful representations from biological data. I will begin with learnable geometric scattering, a method based on random walks and diffusion processes that extracts stable, multiscale features of static signals on graphs, such as atoms in molecules or amino acids in proteins. This framework enables the development of powerful generative AI models for molecular design and the analysis of protein conformational landscapes.

Next, I will move from static to observed dynamic signals, showing how combining geometric scattering with tools from topological data analysis reveals the hidden organization of cell-cell communication and brain activity over time. By characterizing how signals propagate, synchronize, and evolve, these methods uncover interpretable spatiotemporal patterns that shed light on processes like wound healing and psychiatric disorders.

Finally, I will introduce DYMAG, a graph neural network that learns dynamics of its own by replacing conventional message passing with solutions to PDEs - such as heat, wave, and chaotic systems - defined on graphs. This physics-inspired approach captures the geometry and topology of graph structure, enabling more expressive representations for learning tasks across biomedical domains.