We’ll have an open discussion about the ways in which Mathematics is very euro-centric and how we can act, as students and educators, to change this.
Placing M-theory on a non-compact Calabi-Yau threefold allows us to construct low energy field theories in 5d with minimal supersymmetry, in a limit in which gravity is decoupled. We venture into this topic by introducing all the building blocks we hope to capture in a 5d SCFT. Next, from the geometric perspective we realise the 5d gauge theory data from the objects within the Calabi-Yau geometry, given by curves, divisors, rulings, and singularities. After seeing how the geometry captures all the possible field theory data, we illustrate how to build some simple 5d SCFTs by placing M-theory on toric Calabi-Yau threefolds.
Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.
Part of a Carrollian day in wonderland 9.15am-5pm.
The main challenges in constructing a holographic correspondence for asymptotically flat spacetimes lie in the null nature of the conformal boundary and the non-conservation of gravitational charges in the presence of bulk radiation. In this talk, I shall demonstrate that there exists a systematic and mathematically robust approach to understanding and deriving the associated flux-balance laws from intrinsic boundary geometric considerations — an aspect of crucial importance for flat-space holography, as I shall argue during the presentation.
For self-containment, I shall begin by reviewing key aspects of the geometry at null infinity, which has been termed conformal Carroll geometry. Reviving Ashtekar’s old statement, I shall emphasise that boundary affine connections possess degrees of freedom that precisely serve as the sources encoding radiation from a holographic perspective. I shall conclude by deriving flux-balance laws in an effective field theory framework at the boundary, employing novel techniques that introduce “hypermomenta” as responses to fluctuations in the boundary connection. The strength of our formalism lies in its ability to perform all computations in a manifestly coordinate- and Weyl-invariant manner within the framework of Sir Penrose’s conformal compactification.
Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.
In this talk, I will discuss a conjecture of Penrose, which asserts a lower bound on the mass of a spacetime in terms of the area of a suitable horizon. Whilst Penrose presented a physical motivation for this inequality in the 1970s, the only proofs heavily rely upon PDE arguments, and in particular the use of geometric flows. I hope to show in this talk, through this concrete example (and without unpleasant technical details!), how ideas from geometric PDE theory can be helpful in obtaining results in physics.
Come chill out after a busy term and play some board games with us. We'll provide some games but feel free to bring your own!
A question we get asked all the time! We'll also be discussing the numerous ways our identities as Mathematicians are shaped by being a minority. Free lunch provided.
I will introduce basic concepts from category theory that are relevant to the study of generalized symmetries. Then, I will focus on constructions known as equivariantization and de-equivariantization, which allow one to move between categories with a group G-action and those with a Rep(G)-action. I will also discuss their relation to the concept of gauging, if time permits.
Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.
Anomalies in quantum systems are present when a classical symmetry is broken by quantum effects. They give rise to physical predictions and constraints. This talk will focus on the mathematical features of anomalies of continuous, ordinary, symmetries. In the first part, we will review the topological nature of anomalies, in particular the connection to the Atiyah-Singer index theorem and its non-perturbative path-integral computation by Fujikawa. We will then discuss how anomalies and their associated (topological) Chern-Simons polynomials are related to BRST cohomology via the Stora-Zumino chain of descent equations, explaining the connection to the two-step descent procedure reviewed in the talk by Alice Lüscher last term.
Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.