With conference season fast approaching, we will be meeting up to discuss our experiences of going to conferences and how best to prepare for them as a minority in Mathematics.
Diffusion Limited Aggregation is a very simple mathematical model which describes a wide range of natural phenomena. Despite its simplicity, there is very little progress in understanding its large-scale structure. Since its introduction by Witten and Sander over 40 years ago, there was only one mathematical result. In 1987 Kesten obtained an upper bound on the growth rate. In this talk I will discuss DLA and some related models and the recent progress in understanding DLA. In particular, a new simpler proof of Kesten result which generalizes to other aggregation models.
We are pleased to announce that Oxford Mathematician Alison Etheridge has been elected as an international member of the National Academy of Sciences in the United States.
We present an inter-twining relation between operators on loop ensembles and connections.
We talk about the Hausdorff measure of level sets of the fields, say length of level lines of a planar field. Given two coupled stationary fields $f_1, f_2$ , we estimate the difference of Hausdorff measure of level sets in expectation, in terms of $C^2$-fluctuations of the field $F=f_1-f_2$. The main idea in the proof is to represent difference in volume as an integral of mean curvature using the divergence theorem. This approach is different from using the Kac-Rice type formula as the main tool in the analysis.
Franciscan nun Sister Irene O'Connor began singing when a teacher in Singapore in the 1960s. The following decade, together with producer Sister Marimil Lobregat, she recorded the 'Fire of God's Love' album which has become a cult classic for its psychedelic-folky sound. Have a listen. It might not be what you'd expect, but it is perhaps consoling.
