A randomly trapped random walk on a graph is a simple continuous time random walk in which the holding time at a given vertex is an independent sample from a probability measure determined by the trapping landscape, a collection of probability measures indexed by the vertices.

This is a time change of the simple random walk. For the constant speed continuous time random walk, the landscape has an exponential distribution with rate 1 at each vertex. For the Bouchaud trap model it has an exponential random variable at each vertex but where the rate for the exponential is chosen from a heavy tailed distribution. In one dimension the possible scaling limits are time changes of Brownian motion and include the fractional kinetics process and the Fontes-Isopi-Newman (FIN) singular diffusion. We extend this analysis to put these models in the setting of resistance forms, a framework that includes finitely ramified fractals. In particular we will construct a FIN diffusion as the limit of the Bouchaud trap model and the random conductance model on fractal graphs. We will establish heat kernel estimates for the FIN diffusion extending what is known even in the one-dimensional case.

A classification of simple flops on smooth threefolds in terms of the length invariant was given by Katz and Morrison, who showed that the length must take the value 1,2,3,4,5, or 6. This classification was produced by understanding simultaneous (partial) resolutions that occur in the deformation theory of A, D, E Kleinian surface singularities. An outcome of this construction is that all simple threefold flops of length l occur by pullback from a "universal flop" of length l. Curto and Morrison understood the universal flops of length 1 and 2 using matrix factorisations. I aim to describe how these universal flops can understood for lengths >2 via noncommutative algebra.

Gaussian fields are prevalent throughout mathematics and the sciences, for instance in physics (wave-functions of high energy electrons), astronomy (cosmic microwave background radiation) and probability theory (connections to SLE, random tilings etc). Despite this, the geometry of such fields, for instance the connectivity properties of level sets, is poorly understood. In this talk I will discuss methods of extracting geometric information about levels sets of a planar Gaussian field through discrete observations of the field. In particular, I will present recent work that studies three such discretisation schemes, each tailored to extract geometric information about the levels set to a different level of precision, along with some applications.

 Monte Carlo methods are one of the main tools of modern statistics and applied mathematics. They are commonly used to approximate integrals, which allows statisticians to solve many tasks of interest such as making predictions or inferring parameter values of a given model. However, the recent surge in data available to scientists has led to an increase in the complexity of mathematical models, rendering them much more computationally expensive to evaluate. This has a particular bearing on Monte Carlo methods, which will tend to be much slower due to the high computational costs.

This talk will introduce a Monte Carlo integration scheme which makes use of properties of the integrand (e.g. smoothness or periodicity) in order to obtain fast convergence rates in the number of integrand evaluations. This will allow users to obtain much more precise estimates of integrals for a given number of model evaluations. Both theoretical properties of the methodology, including convergence rates, and practical issues, such as the tuning of parameters, will be discussed. Finally, the proposed algorithm will be illustrated on a Bayesian inverse problem for a PDE model of subsurface flow.

Abstract:  Anyone who has worked in $\beta$N will not be surprised to learn that some of the algebraically defined subsets of $\beta N$ are not topologically simple, even though their algebraic definition may be very simple.  I shall show that the following subsets of $\beta N$ are not Borel: $N^*+N^*$; the smallest ideal of $\beta N$; the set of idempotents in $\beta N$; any semiprincipal right ideal in $\beta N$; the set of idempotents in any left ideal in $\beta N$.

The "Weyl fermion" was discovered in a topological semimetal in
2015. Its mathematical characterisation turns out to involve deep and subtle
results in differential topology. I will outline this theory, and explain
some connections to Euler structures, torsion of manifolds,
and Seiberg-Witten invariants. I also propose interesting generalisations
with torsion topological charges arising from Kervaire semicharacteristics
and ``Quaternionic'' characteristic classes.

In this talk, I will talk about my current approach to model customer movements and in particular congestion inside supermarkets using queuing networks. As the research question for my project is ‘How should one design supermarkets to minimize congestion?’, I will then talk about my current progress in understanding how the network structure can affect this dynamics.

There are several conjectures in the literature suggesting that absolute Galois groups of fields tend to be "as free as possible," given their "almost-abelian" data.
This can be made precise in various ways, one of which is via the notion of "1-formality" arising in analogy with the concept in rational homotopy theory.
In this talk, I will discuss several examples which illustrate this phenomenon, as well as some surprising diophantine consequences.
This discussion will also include some recent joint work with Guillot, Mináč, Tân and Wittenberg, concerning the vanishing of mod-2 4-fold Massey products in the Galois cohomology of number fields.