Week 09.03.2026 – 15.03.2026

Energy conditions were originally formulated as pointwise bounds on contractions of the stress–energy tensor and have played a central role as assumptions in many foundational results of classical general relativity, most notably the singularity theorems. However, these conditions are generically violated by quantum fields, which admit states with locally negative energy density. Such violations are nevertheless constrained: quantum energy inequalities impose bounds on the magnitude and duration of negative energy.

In this course, I will first introduce the classical energy conditions and review their physical motivation and known violations. Then I will provide a brief introduction to quantum field theory on curved spacetimes and demonstrate how quantum energy inequalities can be derived. Finally, I will discuss in detail the average null energy condition and the limitations it imposes to causality violating spacetimes.

Course plan:
Lecture 1: Classical energy conditions and their violations
Lecture 2: Quantum field theory on curved spacetimes
Lecture 3: A derivation of a quantum energy inequality
Lecture 4: The average null energy condition​

Quantum stochastic calculus is a beautiful theory that flows ineluctably from its classical counterpart. We will start with the basic idea of a normal martingale and demonstrate this natural development, via multiple Wiener-Ito integrals, chaotic representation, probabilistic interpretations of Boson Fock space and the fundamental quantum stochastic integrators.

Quantum stochastic calculus is a beautiful theory that flows ineluctably from its classical counterpart. We will start with the basic idea of a normal martingale and demonstrate this natural development, via multiple Wiener-Ito integrals, chaotic representation, probabilistic interpretations of Boson Fock space and the fundamental quantum stochastic integrators.

******* Please register at: https://forms.gle/9fF2GWkoMWv4D2J19 *******

Asymptotic symmetries, sometimes also known as "large gauge transformations", provide important dynamical information on theories with a gauge freedom formulated on spacetimes having a "boundary at infinity". A review of asymptotic symmetries will be given following the Hamiltonian approach. General features (such as the form of the symmetry generators and the structure of the algebra) will be explained. The discussion will focus on gravity in the asymptotically flat context, where the relevant asymptotic symmetry algebra is the infinite-dimensional BMS algebra.

******* Please register at: https://forms.gle/9fF2GWkoMWv4D2J19 *******

A central challenge in string phenomenology is to understand the scalar potentials that arise from compactifications to lower-dimensional effective field theories. In recent years, the swampland program has called into question many earlier proposals for semi-realistic vacua in the string landscape. In this talk, I will review the relevant swampland conjectures and discuss the current status of proposed counterexamples. I will begin with the construction of four-dimensional N=1 Minkowski vacua with no massless scalar fields. I will then present recently discovered low-energy effective theories with negative cosmological constants - namely AdS vacua - arising in Type II and heterotic string compactifications on G2 spaces.

See: https://www.londonmathfinance.org.uk/seminar

See: https://www.londonmathfinance.org.uk/seminar