The University of Oxford MPLS Enterprise and Innovation Fellows are hosting a quantum entrepreneurship discussion event with Ramy Shelbaya, CEO and Co-Founder of Oxford University spin-out Quantum Dice
The event is on Tuesday 22nd November, at 5:30 pm, in the Simpkins Lee Seminar Room, Beecroft Building, Department of Physics. Click "Going" on the Facebook event for updates.
Random forests and the OSp(1|2) nonlinear sigma model
Abstract
Given a finite graph, the arboreal gas is the measure on forests (subgraphs without cycles) in which each edge is weighted by a parameter β greater than 0. Equivalently this model is bond percolation conditioned to be a forest, the independent sets of the graphic matroid, or the q→0 limit of the random cluster representation of the q-state Potts model. Our results rely on the fact that this model is also the graphical representation of the nonlinear sigma model with target space the fermionic hyperbolic plane H^{0|2}, whose symmetry group is the supergroup OSp(1|2).
The main question we are interested in is whether the arboreal gas percolates, i.e., whether for a given β the forest has a connected component that includes a positive fraction of the total edges of the graph. We show that in two dimensions a Mermin-Wagner theorem associated with the OSp(1|2) symmetry of the nonlinear sigma model implies that the arboreal gas does not percolate for any β greater than 0. On the other hand, in three and higher dimensions, we show that percolation occurs for large β by proving that the OSp(1|2) symmetry of the non-linear sigma model is spontaneously broken. We also show that the broken symmetry is accompanied by massless fluctuations (Goldstone mode). This result is achieved by a renormalisation group analysis combined with Ward identities from the internal symmetry of the sigma model.
Hi Mathematical Institute colleagues!
I am Tim LaRock, a postdoctoral researcher here in maths, as well as the representative for the MI to the Oxford branch of the University and College Union (UCU), the trade union that represents academic workers across the UK. I also serve as the co-Secretary for Membership and Recruitment on our local committee.
Congratulations to James who won the award from the American Mathematical Society for work with Jack Thorne (University of Cambridge). The citation praises "their astonishing proof of a landmark, sought-after case of the Langlands Conjectures: namely the symmetric power functoriality for holomorphic modular forms".
Genentech, part of Roche (the second largest pharmaceutical company in the world) have a postdoctoral position using artificial intelligence in drug development involving neuralODEs.
More details here or contact Yixuan Sun (@email); for more information.
A Hele-Shaw Newton's cradle and Reciprocity in Fluids
Abstract
A Hele-Shaw Newton's cradle: Circular bubbles in a Hele-Shaw channel. (Daniel Booth)
We present a model for the motion of approximately circular bubbles in a Hele-Shaw cell. The bubble velocity is determined by a balance between the hydrodynamic pressures from the external flow and the drag due to the thin films above and below the bubble. We find that the qualitative behaviour depends on a dimensionless parameter and is found to agree well with experimental observations. Furthermore, we show how the effects of interaction with cell boundaries and/or other bubbles also depend on the value of this dimensionless parameter For example, in a train of three identical bubbles travelling along the centre line, the middle bubble either catches up with the one in front or is caught by the one behind, forming what we term a Hele-Shaw Newton's cradle.
Reciprocity in Fluids (Matthew Cotton)
Reciprocity is a useful, and often underused, way to calculate integrated quantities when a to solution to a related problem is known. In the remaining time, I will overview these ideas and give some example use cases
The Mathematical Institute is seeking to appoint a Departmental Lecturer in Applied Mathematics. The appointment will be in collaboration with Christ Church, and is full time for a fixed period until 31st March 2025. The department anticipates a starting date of 1st April 2023 or as soon as possible thereafter. You will be based in the Oxford Centre for Industrial and Applied Mathematics (OCIAM).
The Newton Gateway to Mathematics is pleased to be working with the United Kingdom Health Security Agency (UKHSA), who are seeking 7 PhD Students with strong backgrounds in data analysis, statistics, mathematics, biological sciences, or social research, to join their Early Career Researcher (ECR) programme as ECR Analysts - Advanced Epidemiological Modellers, for 3 months.