Triangle Seminars
Monday, 23 Mar 2026
Lonti: classical and quantum energy conditions (4/4)
📍 London
Eleni Kontou
Abstract:
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
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
Posted by: Damian Galante
Wednesday, 25 Mar 2026
Aspects of the ODE/IM Correspondence
📍 London
Roberto Tateo
(INFN, Turin)
Abstract:
The ODE/IM correspondence is a striking bridge between spectral theory and exact methods in integrable quantum field theory. In this talk, I will present some aspects of this correspondence from the point of view of integrable models, with particular emphasis on functional relations such as Y-systems and on their role in the thermodynamic Bethe ansatz. I will then discuss several extensions motivated by deformations of simple theories, including richer coupled structures and twisted sectors. The goal is to illustrate both the general framework and some more recent directions that may lead to broader versions of ODE/IM.
The ODE/IM correspondence is a striking bridge between spectral theory and exact methods in integrable quantum field theory. In this talk, I will present some aspects of this correspondence from the point of view of integrable models, with particular emphasis on functional relations such as Y-systems and on their role in the thermodynamic Bethe ansatz. I will then discuss several extensions motivated by deformations of simple theories, including richer coupled structures and twisted sectors. The goal is to illustrate both the general framework and some more recent directions that may lead to broader versions of ODE/IM.
Posted by: Andrew Svesko
Thursday, 26 Mar 2026
Scattering amplitude of massless closed strings at genus one
📍 London
Mehregan Doroudiani
(Southampton)
Abstract:
Perturbative calculations of string amplitudes are twofold: an expansion in the string coupling (the genus expansion of the worldsheet) and a low-energy expansion in the momenta. In this talk, I will focus on the low-energy expansion of closed string amplitudes at genus one, specifically for four- and five-point massless states of type IIB superstrings in flat spacetime. Evaluating these amplitudes involves integrating over the moduli space of punctured tori. I will demonstrate how the formalism of equivariant iterated Eisenstein integrals can be used to systematically calculate these integrals. Additionally, I will discuss the implications of these results for the S-duality of type IIB.
Perturbative calculations of string amplitudes are twofold: an expansion in the string coupling (the genus expansion of the worldsheet) and a low-energy expansion in the momenta. In this talk, I will focus on the low-energy expansion of closed string amplitudes at genus one, specifically for four- and five-point massless states of type IIB superstrings in flat spacetime. Evaluating these amplitudes involves integrating over the moduli space of punctured tori. I will demonstrate how the formalism of equivariant iterated Eisenstein integrals can be used to systematically calculate these integrals. Additionally, I will discuss the implications of these results for the S-duality of type IIB.
Posted by: Nathan Moynihan