Speaker
Description
Sub-Lorentzian geometry is the non-holonomic analogue of Lorentzian geometry and the Lorentzian counterpart of sub-Riemannian geometry. The theory was anticipated in Strichartz’s monograph on sub-Riemannian geometry, but was not systematically studied until the seminal contributions of Grochowski in the early 2000s. Sub-Lorentzian geometry remains largely unexplored, with many fundamental questions still to be addressed. This stands in sharp contrast to the well-developed sub-Riemannian theory, which has become central to metric geometry and the theory of hypoelliptic operators. This talk will give an overview of the current state of sub-Lorentzian geometry, highlighting its relevance to physics as an alternative geometric framework to Kaluza–Klein theory for unifying Einstein’s theory of gravity and electromagnetism, recent achievements such as optimal-transport-based notions of curvature, and its role within the broader program of developing a synthetic theory of Lorentzian length spaces and metric spacetimes.