Open mathematical problems in applied AI

Speaker: Isaac Donnelly
Affiliation: Optus

Abstract

This presentation explores open mathematical questions arising from recent advances in generative AI. It covers how models like ChatGPT and diffusion-based image generators work, with a focus on the mathematical principles behind them. It also examines multi-agent systems, where interactions between AI agents lead to complex and sometimes unpredictable dynamics, drawing on ideas from statistical physics and game theory. Open challenges in applying generative AI—such as mode collapse, controllability, alignment, and emergent behaviour—are discussed throughout. These problems invite new contributions from areas including analysis, probability, topology, and dynamical systems. No prior knowledge of AI is assumed.

Biography

Isaac is the Senior Director of AI for Optus Enterprise. Prior to Optus Isaac was General Manager for Software at a wholesale insurer, founded his own AI start up, and led AI projects at McKinsey. He holds a PhD in Applied Mathematics from UNSW and was a Fulbright Scholar at Northeastern University in Boston.