Week 12.10.2026 – 18.10.2026

We will discuss how to bootstrap string theory in AdS, using N=4 SYM as a concrete example. The first lecture will review the basic ingredients of AdS/CFT: the definitions of AdS and CFT, the correspondence between Kaluza–Klein modes and single-trace operators, and the relation between string scattering in AdS and correlation functions of Kaluza–Klein modes in the CFT. The second lecture will focus on the stress-tensor multiplet four-point function, including its conformal block expansion, the constraints imposed by superconformal Ward identities, and its formulation in Mellin space. The third lecture will introduce the flat-space limit, explain how it acts on the conformal block expansion, and discuss the spectrum of single-trace operators that survives at strong coupling. In the final lecture, we will go beyond the flat-space limit and study the first AdS correction. We will introduce a worldsheet ansatz for this correction and show how matching it to the conformal block expansion fixes the correction completely.

The level sets of the Gaussian free field give rise to natural long-range percolation models whose critical behaviour is particularly well understood. We will give precise meaning to studying this model in dimensions between two and three, with dimension two playing the role of the lower critical dimension.
This setting unveils a rich family of delicate scaling laws that fall outside the conventional scaling theory. Despite this anomalous behaviour, we show that the classical critical scaling relations nevertheless remain valid in a generalised sense.
Based on joint work with Pierre-Francois Rodriguez.

Recently, data-driven methods based on path signatures have gained prominence in mathematical finance. They rely on universal approximation theorems stating that continuous functionals on path space can be approximated uniformly on compact sets by linear functionals of the signature. In financial applications, this has led to the use of Stratonovich-signatures, although Itô integration is often the natural modeling framework.

In this talk, we establish a universality result for signatures of non-geometric rough paths. By augmenting the path with its rough path bracket, we obtain a quasi-shuffle structure that provides the algebraic basis for universality. For continuous semimartingales, this yields a universal approximation property for Itô signatures.

This talk is based on joint work with A. P. Kwossek and D. J. Prömel.

Please register here: https://forms.gle/7zfqxHjCDSdDesmy7

The recent discovery of a known infinite-dimensional algebra, w(1+infinity), among the asymptotic symmetries of four-dimensional asymptotically flat spacetimes has been interpreted as key evidence in support of a bottom-up approach to flat-space (a.k.a. celestial) holography.  In particular, since a holographic theory must realize the symmetries of its associated gravitational dual, large universal symmetries in principle impose fairly stringent constraints on a holographic correspondence. Of course, concrete progress relies crucially on the precise strength of the constraints from symmetry. Thus in pursuit of this larger goal, in this seminar, I will present a precise avatar of the universal  w(1+infinity) symmetry algebra that persists in the absence of gravity and in particular is realized in generic interacting four-dimensional conformal field theories.  The generators of the algebra are light-ray operators formed from null integrals of the stress tensor that generalize the average null energy operator.  I will discuss potential implications for conformal field theories in spacetime dimensions greater than two and celestial holography.

Please register here: https://forms.gle/7zfqxHjCDSdDesmy7

I will address the question: In what situations are perturbative quantum gravity effects important at distances much longer than the Planck scale? Among other examples, I will calculate the `quantum width' of the black hole horizon.

Synthesising multiple sources of data and information is beneficial in biostatistical applications because it can provide more precise estimates and reduces the risk of biases introduced by using only partial data. However, this can be challenging when combining different types, quality or scales of data. I will give a brief overview of my contributions to three Bayesian methodological aspects. First, if for each data source we have a separate Bayesian model, but these have quantities in common, how can we combine these in a single Bayesian analysis? Second, if some parts of the data/model are regarded as less reliable, how can we formulate "cut posteriors" that prevent unreliable components contaminating the reliable components? Third, if some information is in the form of prior information about an observable quantity, how can we "translate" this into an informative parameter prior?