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Representation theory involves studying mathematical objects by interpreting them in linear algebra: for example, we interpret group elements as matrices. It can be useful to abstract our linear algebra problem using a quiver, which is a directed graph where the […]

I shall explain Theorem (127) which determines the unique bijection BETWEEN the monomial basis called $(A_n)$- FC elements  AND the set of non-crossing diagrams of $n+1$ strings OF  our well-known Temperley-Lieb algebra, that respects the  diagrammatic multiplication by concatenation along […]

An opportunity to meet and discuss research ideas. More detail to follow.

We shall present a general method of constructing uncountable structures that are homogeneous with respect to their finitely generated substructures. The method is based on the category-theoretic Fraisse limits, using the monoid of self-embeddings of a countable homogeneous structure. Joint […]

We introduce an area formula for computing the spherical measure of an intrinsic graph of any codimension in an arbitrary homogeneous group. Our approach only assumes that the map generating the intrinsic graph is continuously intrinsically differentiable. The important novelty […]

Fix a sequence of countable structures $\mathcal{M}_n$, for $n$ in $ℕ$, in a given first-order language $\mathcal{L}$. The reduced product of $(\mathcal{M}_n)$, denoted $\prod_n\mathcal{M}_n/\mathrm{Fin}$ is the $\mathcal{L}$-structure obtained by quotienting the product of the $\mathcal{M}_n$ by the equivalence relation of […]

First, Robert Barham will introduce the systems of support available for undergraduate students.  The slides used will contain links and will be distributed afterwards.  Then Rukia Nuermaimaiti will direct a discussion around a number of hypothetical situations related to student […]

In this talk, I will discuss the ergodicity of the stochastic heat equation driven by centred Gaussian noise, which is white in time and coloured in space, satisfying the Dalang condition. I will also provide a sufficient condition for the […]

Dynamic covariance matrix models for multivariate normal data are a widely-applicable class of statistical models, meant to capture the covariate-dependent nature of the variance and dependence parameters. However, such models are rarely used in practice, partly due to the computational […]

TBA

TBA.

The entropy of a continuous random variable behaves, in some ways, similarly to the logarithm of the volume of a set. In particular, the Entropy Power Inequality (EPI) is widely considered as an information-theoretic analogue of the Brunn-Minkowski inequality. In […]

We study the probability that an AR(1) Markov chain $X_{n+1}=aX_n+\xi_{n+1}$, where $a$ is a constant, stays non-negative for a long time. Assuming that the i.i.d. innovations $\xi_n$ take only two values $\pm 1$ and $a \le \frac23$, we find the […]