Jack studied Mathematics at the University of Cambridge as an undergraduate before completing his PhD at Harvard University in 2012. He returned to Cambridge in 2014 and is now Kuwait Professor of Number Theory and Algebra in the Department of Pure Mathematics and Mathematical Statistics. He is a Fellow of the Royal Society and of the Academy for the Mathematical Sciences.

Topic: How big are rational points?

Abstract: Rational points are solutions to Diophantine equations (such as xn + yn = zn). Mathematicians seek to understand when such solutions exist and, when they do, how large they can be. Jack will explore what it means to measure the size of a rational point.

David studied Mathematical Physics at the University of Nottingham before completing an MSc at King’s College London and a PhD in Theoretical Physics at Swansea University. He went on to hold research positions at the Tata Institute of Fundamental Research in Mumbai, King’s College London, and Columbia University, and later served as a Pappalardo Fellow at MIT. Since joining Cambridge in 2004, he has been Professor of Theoretical Physics in the Department of Applied Mathematics and Theoretical Physics and a Fellow of Trinity College. His research focuses on quantum field theory and its applications to a wide range of physical phenomena, from condensed matter systems to particle physics and cosmology.

Topic: Why can't we simulate the laws of physics on a computer?

Abstract: Computers cannot fully simulate the laws of physics. In this talk, David will explain the reasons behind this fundamental limitation.

Maria studied theoretical physics in Milan as an undergraduate and obtained a joint doctoral degree from the University of Edinburgh and the University of Louvain in 2010. Since 2013, she has been at Cambridge, where she is now Professor of Particle Physics Theory and Phenomenology in the Department of Applied Mathematics and Theoretical Physics. Maria is a Fellow of Newnham College and Sheila Edmonds Lecturer in Mathematics. 

Topic: Effective theories in particle physics: a mathematical bridge to the unknown

Abstract: Our current understanding of the elementary building blocks of Nature, encapsulated by the Standard Model (SM) of particle physics, is one of the most successful theoretical constructions of the past century, yet it is necessarily incomplete. Several experimental observations, such as the presence of Dark Matter and the matter–antimatter asymmetry of the Universe, remain unexplained by the SM. Maria will discuss how effective theories provide us with a mathematical bridge to the uncharted territory beyond the SM, and how Machine Learning can help in the fascinating quest for the unknown.

Julia obtained her PhD from the University of Cambridge in 2008. After postdoctoral positions at Princeton, Berkeley, and Rutgers, she held roles at École Polytechnique in Paris and the University of Bristol before returning to Cambridge in 2018. She is now Professor in the Department of Pure Mathematics and Mathematical Statistics and a Fellow of Trinity College. Her research at the interface of combinatorics and logic is currently supported by an EPSRC Open Fellowship.

Topic: Beyond VC-Dimension

Abstract: VC‑dimension measures the combinatorial complexity of mathematical structures and plays a key role across combinatorics, model theory, statistics, and machine learning. Julia will describe recent progress on higher‑dimensional generalisations that promise new tools for understanding more complex relational structures in a variety of settings.