In my talk I will give a basic introduction to the finiteness properties of groups and their relation to subgroups of direct products of groups. I will explain the relation between such subgroups and fibre products of groups, and then proceed with a discussion of the n-(n+1)-(n+2)-Conjecture and the Virtual Surjections Conjecture. While both conjectures are still open in general, they are known to hold in special cases. I will explain how these results can be applied to prove that there are groups with arbitrary (non-)finiteness properties.

Coding theory revolves around the question of what can be accomplished with only memory and redundancy. When we ask what enables the things that transmit and store information, we discover codes at work, connecting the world of geometry to the world of algorithms.

This talk will focus on those connections that link the real world of Euclidean geometry to the world of binary geometry that we associate with Hamming.

I will talk about a result on meromorphic continuation of Euler products over primes p of definable p-adic or motivic integrals, and applications to zeta functions of groups. If time permitting, I'll state an analogue for counting rational points of bounded height in some adelic homogeneous spac

One of the greatest challenges in developing renewable energy sources is finding an efficient energy storage solution to smooth out the inherently fluctuating supply. One cheap solution is lead-acid batteries, which are used to provide off-grid solar energy in developing countries. However, modelling of this technology has fallen behind other types of battery; the state-of-the-art models are either overly simplistic, fitting black-box functions to current and voltage data, or overly complicated, requiring complex and time-consuming numerical simulations. Neither of these methods offers great insight into the chemical behaviour at the micro-scale.

In our research, we use asymptotic methods to explore the Newman porous-electrode model for a constant-current discharge at low current densities, a good estimate for real-life applications. In this limit, we obtain a simple yet accurate formula for the cell voltage as a function of current density and time. We also gain quantitative insight into the effect of various parameters on this voltage. Further, our model allows us to quantitatively investigate the effect of ohmic resistance and mass transport limitations, as a correction to the leading order cell voltage. Finally, we explore the effect on cell voltage of other secondary phenomena, such as growth of a discharge-product layer in the pores and reaction-induced volume changes in the electrolyte.

In this talk we consider the limiting behaviour of the strong solution of the Navier--Stokes equation as the viscosity goes to zero, on a three--dimensional region with curved boundary. Under the Navier and kinematic boundary conditions, we show that the solution converges to that of the Euler equation (in suitable topologies). The proof is based on energy estimates and differential--geometric considerations. This is a joint work with Profs. Gui-Qiang Chen and Zhongmin Qian, both at Oxford. 

Let X be a smooth, complete geometrically connected curve defined over a one variable function field K over a finite field. Let G be a subgroup of the points of the Jacobian variety J of X defined over a separable closure of K with the property that G/p is finite, where p is the characteristic of K. Buium and Voloch, under the hypothesis that X is not defined over K^p, give an explicit bound for the number of points of X which lie in G (related to a conjecture of Lang, in the case of curves). In this joint work with Pazuki, we extend their result by requiring just that X is non isotrivial.