In this talk, I will discuss a connection between the ANEC (Averaged Null Energy Condition) operator and monotonicity of the renormalization group. In particular, I will show how the 2d c-theorem and 4d a-theorem can be derived using the ANEC. This derivation relies on contact terms appearing in specific ANEC correlators. I will also review a new infinite set of constraints that can be derived from the ANEC in 2d QFT. This program hints at a more general role for light-ray operators in QFT, which I will argue for.

By the end of their degree, we expect our students to be independent learners who can read and understand mathematical texts (e.g. textbooks/papers) and study to understand the course material rather than trying to learn the exam. In practice, many of our students do not meet this expectation, in large part because we rarely teach these skills directly ��� they form part of the so-called hidden curriculum.

In this talk, I will present some activities I employed during an undergraduate calculus course which aimed to address these issues. I will also discuss how I borrow tools and techniques from my experience as a qualified English as a foreign language teacher to design my teaching sessions. Part of this was developed jointly with David Sheard (KCL).

In this talk, we will focus on the group of Hamiltonian diffeomorphisms (and area-preserving homeomorphisms) of the 2-sphere. A tremendous amount of progress has been made in the study of these groups in the last few years, but many problems remain, including the Equator Conjecture. An equator on the 2-sphere is a simple closed curve whose complementary components have equal area. The Equator Conjecture predicts that for any positive K, there are pairs of equators such that any Hamiltonian diffeomorphism sending one equator to the other must have Hofer norm larger than K. We will prove an alternative conjecture, by replacing "Hofer norm" with "quantitative fragmentation norm". To prove this, we construct new quasimorphisms defined on all area-preserving homeomorphisms on the 2-sphere, coming from methods inspired from mapping class groups and geometric group theory. Joint work with Yongsheng Jia.

The study of stochastic PDEs has known tremendous advances in recent years and, thanks to Hairer's theory of regularity structures and Gubinelli and Perkowski's paracontrolled approach, (local) existence and uniqueness of solutions of subcritical SPDEs is by now well-understood. The goal of this talk is to move beyond the aforementioned theories and present novel tools to derive the scaling limit (in the so-called weak coupling scaling) for some stationary SPDEs at the critical dimension. Our techniques are inspired by the resolvent method developed by Landim, Olla, Yau, Varadhan, and many others, in the context of particle systems in the supercritical dimension. Time allowing, we will explain how it is possible to use our techniques to study a much wider class of statistical mechanics models at criticality such as (self-)interacting diffusions in random environment.

It is joint work with Caroline Chessang, Tom Cowling and Ruth Keogh.

You are invited to a lunch panel discussion and Q&A with early carreer researchers in mathematics. During this event, our panel members are going to discuss opportunities and challenges that a female mathematician has to face nowdays and how these might affect a career path. Information about the Women in Number Theory and Geometry spring retreat and the work of Piscopia local community at King's College London will also be provided.

Registration: https://www.eventbrite.co.uk/e/women-in-maths-panel-discussion-tickets-803873827257?aff=oddtdtcreator

Lunch will be provided.

In this talk, we shall talk about two invariants associated with complete Nevanlinna-Pick (CNP) spaces. One of the invariants is an operator-valued multiplier of a given CNP space, and another invariant is a positive real number. These two invariants are called characteristic function and curvature invariant, respectively. The origin of these concepts can be traced back to the classical theory of contractions by Sz.-Nagy and Foias. We will begin by delving into this classical theory, gradually leading into our main subject matter.

Carroll symmetries were introduced many years ago by Levy-Leblond and Gupta as a possible contraction of the Lorentz symmetries in which effectively the speed of light is sent to zero. The name was inspired by the bizarre property that Carroll particles cannot move. After many years of silence Carroll symmetries have returned to the stage since they have been recognized as symmetries that do occur in several special situations such as the horizon of a black hole. In this presentation I will discuss some of the basic properties and mysteries of Carroll symmetries.

A few mathematicians had considerable influence during the covid-19 epidemic. Some mathematicians have focussed on designing and implementing mathematical models which only consider a single illness. Applied statisticians know that it is critical to first decide what the question is: "Minimise deaths from Covid-19?" or "Minimise deaths due to Covid-19 and our decisions this year?" or "Minimise the impact of Covid-19 on well-being over ten years?" The ethical status of an expert who gives a simple answer to the first question, without uncertainty or alternatives, will be examined.

Mathematical predictions were used to justify lockdowns even in countries where people would starve as a consequence. Some publications by influential mathematics groups were directly misleading or disparaging of African scientists. Some statisticians have tried to estimate the damage to children's education and wellbeing, and illness and deaths due lockdown.

I argue that such mathematical modelling cannot be justified within virtue, deontological, utilitarian or care ethics, though Zoroaster or Nietzsche might be invoked. It is always necessary to consider the wider context, and the probable consequences of actions, as explained in the International Statistics Institute Code of Professional Ethics. Assessment of the validity of model assumptions, data quality, adequacy of the fit of models and accuracy of predictions is essential, and essentially statistical.