In this talk I will discuss how thermodynamic equations of state are encoded in quantum field theory. Through a simple concrete example, I will show how these can be derived in a Feynman diagrammatic approach, and discuss how the calculation of the thermal loops that emerge out of this expansion ...
I will explain the mathematical formulation of this tantalising question, will give a bit of an overview of what is known about it, and will tell you what Aurel Page and I recently contributed to the area. In the spirit of the seminar, I will explain how I, as a ...
Higher-derivative scalar field theories extend the familiar two-derivative kinetic term by introducing additional derivatives. In this talk, we will look at a 4-derivative scalar field and explore how some of its well-known pathologies arise. We’ll start with the equations of motion which give not only the usual plane-wave solutions ...
Natural ecosystems display an extraordinary diversity of species, a phenomenon that has recently attracted the interest not only of ecologists but also of theoretical physicists.
In this talk, I will introduce a Generalised Lotka–Volterra model of ecological communities that accounts for random interactions among species and finite noise. Remarkably ...
In 1995, James Dolan and I formulated a series of “hypotheses” about topology and higher categories, before the theory of higher categories was sufficiently developed to make these into precisely stated conjectures. In 2009 Jacob Lurie reformulated one of these using infinity-categories, called it the “cobordism hypothesis”, and gave a ...
This purpose of this informal workshop is to discuss connections between music theory and topics in mathematics including groupoids and self-similar quasicrystals.
Recent years have seen two major approaches to flat space holography: the codimension-2 Celestial Holography and the codimension-1 Carrollian Holography. In this talk, I will show how Carrollian Holography naturally emerges by taking the flat space limit of AdS/CFT, carefully tracking the null boundary direction. I will discuss how ...
The Magnus expansion provides an alternative series solution to the Schrödinger equation in terms of N, the log of the S-matrix. Unlike the usual time ordered exponential, the Magnus Expansion is in terms of nested commutators of Hamiltonians with a fixed temporal ordering. While it is known that matrix elements ...
How does classical physics emerge from the quantum world? In this talk, I’ll introduce the KMOC (Kosower, Maybee, and O’Connell ) formalism, which makes this connection precise by showing how classical dynamics can be derived directly from quantum scattering amplitudes. This on-shell viewpoint offers a simple and transparent way ...
Fields satisfying conservation conditions are among the simplest spinning multiplets in conformal field theory. Paradoxically, their kinematics are significantly more difficult to fix than their non-conserved counterparts. This is because, in addition to the conformal Ward identities, the conservation laws must be imposed at each point, and such direct calculations ...
For a Lagrangian quantum field theory, the equations determining its
n-point correlation functions non-perturbatively form an infinite
set of coupled, non-linear integral equations. This hierarchy
simplifies drastically once conformal symmetry is imposed: it
diagonalises when expressed through conformal partial waves. I will
trace this connection following Mack's group-theoretic approach ...
I will give a general overview of our current understanding of the symmetries of renormalization group fixed points in quantum field theory and why they are interesting, including scale, conformal and Weyl invariance. I will describe the distinction between these symmetries, as well as what is generally known about when ...
What happens when a large amount of charge explodes? Where will all this charge go, and how will it get there? A way to answer these questions while doing minimal damage to university buildings is offered by light-ray operators: weighted integrals, along a null geodesic, of local QFT operators. In ...
I will talk about anomalous symmetries and RG flows to gapped phases. I will spend some time reviewing 3d Abelian TQFTs, their symmetries and anomalies. If time permits, we can study factorization and structure theorems.
Tannaka duality was developed in the late 1930’s in order to reconstruct a complex Lie group from its category of representations. Its generalisation, more often simply called “reconstruction theory,” has now become a fundamental part of representation theory — in particular, representation theory of categories and higher categories. It was ...
In this talk we will review the proof of the Atiyah-Singer index theorem in flat space using Fujikawa's method for calculating the chiral anomaly. We will also discuss some applications of the theorem in physics, from calculating gauge anomalies using the method of descent to the Neilsen-Ninomiya theorem which ...
Examples of granular materials exist in abundance, from rice and cereal to sand and rocks. These particulate systems seem simple; they consist of dry, rigid grains that interact by contact forces. However, granular materials present many questions to address, such as how force distributes heterogeneously among grains and how flow ...
In this talk, I will discuss the two apparently distinct issues of dark matter and polarization modes of gravitational waves (GWs) in the framework of modified gravity. Both of these two phenomena have been extensively investigated within the so-called standard Lambda CDM model. At the same time, it is known ...
Monte Carlo sampling is a ubiquitous method for numerically estimating high-dimensional integrals. Unfortunately, standard methods for Monte Carlo sampling sometimes become highly inefficient for certain problems, for example in important limits of lattice QCD simulations that are used to study the Standard Model. I will discuss my ongoing work to ...
Ordered structures that tile the plane in an aperiodic fashion - thus lacking translational symmetry - have long been considered in the mathematical literature. A general method for the construction of quasicrystals is known as cut-and-project (CNP for short), where an irrational slice 'cuts' a higher-dimensional space endowed with a lattice and ...
Twists of supersymmetric field theories are a rich source of theories which depend topologically and/or holomorphically on different directions of spacetime. A key characteristic of these theories is that they can be placed on curved manifolds on which their untwisted ancestors could not have been defined. In certain cases ...
Energy conditions are attempts to summarise the properties of realistic descriptions of matter, encapsulating for example the idea that energy densities should be positive. Being such general statements, they can have very profound consequences, for example ruling out wormholes and superluminal travel. However, the classical energy conditions are all violated ...
The conformal bootstrap is a framework which aims to classify conformal field theories in diverse dimensions via symmetry and consistency arguments. In this talk, I will provide an introduction to the key ideas underlying this approach. Following this, the discussion will focus on the new structures and complications that arise ...
Active constituents burn fuel to sustain individual motion, giving rise to collective effects that are not seen in systems at thermal equilibrium, such as phase separation with purely repulsive interactions. There is a great potential in harnessing the striking phenomenology of active matter to build novel controllable and responsive materials ...
The singularity theorems developed by Roger Penrose and Stephen Hawking are profound and fundamental results in General Relativity. They proved that spacetime singularities would form under general physical conditions relevant to gravitational collapse and expanding universes, without the assumption of high degrees of symmetry that had been present in previous ...
In this talk I provide some of the key mathematical ingredients of the effective field theory formalism which is used to describe diffractive cross sections. This is intended as a deeper dive into the theoretical setup that leads to the final result presented in my colloquium. In particular I discuss ...
The Lie group SL(2,C) is the simply-connected cover of the Lorentz group. Understanding its representation theory is therefore vital to understanding Lorentz-invariant theories. The standard irreps that one encounters in QFT are indexed by two half integers, which correspond to left and right chirality. These irreps have one ...
Theoretical research on gravitational waveforms from compact binary inspirals (of the kind observed for example at LIGO) has been reinvigorated in recent years by an influx of ideas and techniques from collider physics, especially techniques used to understand the Standard Model at the Large Hadron Collider. I will explain the ...
Einstein's equations imply that a gravitationally collapsed object forms an event horizon. But what lies on the other side of this horizon? In this talk, we question the reality of the conventional solution (the black hole), and point out another, topologically distinct solution: the black mirror. In the black ...
Despite its age and numerous successes, the principle of holography is often misconstrued either as a mere offshoot of string theory or as being based on a series of mysterious identifications of black hole physics with thermodynamics. In particular, any intuition one could hope to gain from these perspectives is ...
This talk provides insight into how topological solitons emerge within the framework of nuclear physics. The lack of understanding how the properties of baryons and nuclei arise from first principles in Quantum Chromodynamics (QCD) has led to the development of various Effective Field Theories (EFTs). Among these, the Skyrme theory ...
In this seminar, I will give an introduction to catastrophe theory and derive Thom’s “seven elementary catastrophes” in the physicist’s (rather than mathematician’s) language. Starting from critical points and structural stability, I will derive the characteristic geometries of the caustics and discuss how they arise in various ...
We revisit the cosmological perturbations in minimal single-field inflation, focusing on subtleties arising from total time derivatives (boundary terms) in their action and the corresponding slow-roll unsuppressed phase in the wave functional. While these total derivatives do not contribute to field correlators, they can significantly influence processes related to momentum-space ...
In this talk I seek to present the mystery of vanishing Love in a Black Hole. It is well-known that Black Holes exhibit no Tidal response - characterised by their 'Love Numbers' - however to date there remains no completely satisfying explanation as to why. This talk will largely be pedagogical, focusing ...
Abstract: We discuss the structure of 2-> N scattering in QCD and gravity in high energy Regge asymptotics and outline remarkable similarities between the two. In the QCD case, the rapid growth of the N-gluon amplitude, described by the BFKL equation, leads to the emergence of nonperturbative classical lumps that ...
Given a gauge Lie algebra, it is natural to seek representations for four-dimensional spacetime fermions that are anomaly-free and chiral. Even for irreducible representations, where the problem reduces to studying su(n) for n≥3, solutions seem to be few and far between: a trial-and-error scan by Eichten, Kang and ...
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