cept for some co— title: “Programme with abstracts” format: html tbl-colwidths: [20,80] —
All classes and talks take place in the Wolfson lecture room (4W 1.7) on the lower ground floor of building 4 West, except for some computer labs. See the Campus map here. See also the Programme overview.
Week 1
| From 15.00 |
Check-in (East accommodation centre) |
| 16:15 |
Tea (4W Atrium) |
| 19:15 - 20:00 |
Dinner (Lime tree) |
| 9:30 - 12:00 |
Keating: Knot theory, knot practice |
|
Abstract: Knot theory is a vibrant area of modern mathematics; it has a rich history, and far-fetching connections, many of them to other areas of science. This mini-course will provide an introduction to the subject from a mathematician’s perspective. We will start with some basic definitions and properties. We will then explore, first, some links with low-dimensional topology; and second, connections with algebra. We will emphasise examples throughout. |
| 12:00 - 13:30 |
Lunch (atrium) |
| 13:30 - 16:00 |
Keating (continued) |
| 16:15 - 17:15 |
Lawson: Information in large data: Lessons from population genomics on relating mathematical models to algorithmic scaling |
|
Abstract: One of the key challenges in applying mathematics is to figure out what the question should be. This talk distils population genetics into mathematical statements of how to represent data. We will see how answering questions directly - how to store a matrix - lead to good, but incomplete answers. We will see how understanding the mathematical generative process leads to drastically better algorithms for storage and analysis, exploiting sparsity with the “positional Burrows-Wheeler Transform”. The takehome message - of choosing data representations based on mathematical understanding rather than brute-force - points towards improvements in many disciplines, including the AI analysis of free text. |
| 19:15 - 20:00 |
Dinner (Lime tree) |
| 9:30 - 12:00 |
Keating (continued) |
| 12:00 - 13:30 |
Lunch (outlets*) |
| 13:30 - 16:00 |
Touloupou: Statistical inference for epidemic models |
|
Abstract: |
| 16:15 - 17:15 |
Green: Fourier analysis in additive number theory, and its generalisations |
|
Abstract: Fourier analysis arose historically from questions in applied mathematics, but it has also been very successful at studying pure mathematical problems, for instance to do with representing numbers as sums of squares or sums of primes. I will discuss this a little bit, and then move on to give a hint of more recent developments in which Fourier analysis has been generalised in order to attack problems that the classical theory was unable to handle. |
| 17.30-19.45 |
Outdoor games (Medical centre sports field)
The student union have kindly loaned us a variety of games for us to use on the lacrosse pitch to the south of 10W. (Note that while we have the sports pitch booked until 8pm, our dinner at the Lime tree is also only served until 8pm.) |
| 19.15-20.00 |
Dinner (Lime tree) |
| 9:30 - 12:00 |
Touloupou (continued) |
| 12:00 - 13:30 |
Lunch (outlets*) |
| 13:30 - 16:00 |
Touloupou (continued) |
|
Computer lab (CB 5.13) |
| 16:15 - 17:15 |
TBD |
| 18:00-21:00 |
Pizza and board games (Claverton rooms, upstairs in 2W) |
| 9:30 - 12:00 |
Sousi: Random walks, electrical networks and uniform spanning trees |
|
Abstract: A random walk is called recurrent if it returns to its starting point infinitely many times with probability one. Otherwise it is called transient. How do we determine whether a walk is transient or recurrent? One way is by viewing the graph as an electrical network and calculating effective resistances. This course will start by developing the theory of electrical networks and the connection to random walks. Kirchhoff in 1847 was the first one to find a connection of spanning trees to electrical networks. Spanning trees in a connected graph are basic objects of great interest in combinatorics and computer science. In this course we will study what a typical spanning tree looks like and we will discuss elegant sampling algorithms using random walks due to Aldous, Broder and Wilson from the 1990’s. These connections have yielded many insights on the geometry of uniform spanning trees; this is a topic of intense current research. |
| 12:00 - 13:30 |
Lunch (outlets*) |
| 13:30 - 16:00 |
Sousi (continued) |
| 16:15 - 17:15 |
Tripaldi: SubRiemannian geometry in real life: how to parallel park your car |
|
Abstract: A nonholonomic system is a type of mechanical system that cannot move in an arbitrary direction, and is instead constrained by its physical structure and the environment. Examples of such systems include cars, rockets, and wheeled mobile robots.
In this talk, we’ll explore how the constraints of nonholonomic motion shape control strategies, using the parallel parking problem as a guiding example. Along the way, we’ll see how subRiemannian geometry encodes feasible trajectories and how tools from control theory and differential geometry help us navigate this constrained world. |
| 19:15 - 20:00 |
Dinner (Lime tree) |
| 9:30 - 12:00 |
Sousi (continued) |
| 12:00 - 13:30 |
Lunch (outlets*) |
| 14:15 - 16:15 |
Walking tour of Bath |
|
Departing at 14:15 from Abbey Churchyard (outside the Roman Baths and Pump Room, in front of the City of Bath’s Mayor’s Honorary Guides noticeboard). |
| 16:45 - 18:00 |
Roman Baths |
|
If you wish to join the group visit to the Roman Baths, then please pay £15 by Tuesday evening.
|
| Gather from 16:30 at the main entrance from the Abbey Churchyard. We will need to enter no later than 16:45. |
|
| 10.30 |
Coach departing to Avebury (from East car park) |
|
Visit at Avebury. We’ll bring a packed lunch. We have a guided tour 12.30-13.30. The rest of the time you cn explore the sotne circle, manor gardens and museum. |
| 15.00 |
Coach departing from Avebury |
| 10:00 - 11:00 |
Skyline walk |
|Group walk along a portion of the Bath skyline walk, leaving at 10am from the 4W atrium, arriving to Prior Park around 11am |
11:00 | Entry to Prior Park|
| To enter Prior Park with the group (as opposed to buying a ticket yourself) either come along on the preceding walk or meet at the main entrance to Prior Park (from Ralph Allen Drive) at 11am. You can then stay as long as you like. There is a cafe offering sandwiches and cakes (but no hot food), or you can bring something for a picnic. |
Week 2
| 9:30 - 12:00 |
Speight: Topological solitons |
|
Abstract: Topological solitons are smooth, spatially localized solutions of nonlinear field theories, which owe their existence and stability to topological considerations: they cannot be removed or destroyed by any continuous deformation of the system’s fields (for example, time evolution). They occur across many branches of physics, most notably condensed matter physics, where they model, inter alia, magnetic flux tubes in superconductors and magnetization bubbles in ferromagnets.
An intriguing possibility is that they might actually represent elementary particles (protons, neutrons, electrons, or something more exotic - and so far unobserved - such as magnetic monopoles). They sit very naturally within Einstein’s theory of Special Relativity and already (before “quantization”) exhibit many fundamentally particle-like properties (conserved topological “quantum numbers”, and antimatter counterparts, for example). If such fundamental solitons do exist, they would account elegantly for some otherwise mysterious facts about the universe. Perhaps more important for mathematicians, their study involves a fascinating mixture of differential geometry, mathematical analysis and computer simulations.
This minicourse will introduce a selection of the most important ideas underlying the study of topological solitons by focussing on simple examples in one and two spatial dimensions. I will assume familiarity with linear algebra, multivariable calculus, including vector calculus (div, grad, curl, Stokes’s Theorem etc), complex analysis and some basic notions from Newtonian mechanics (kinetic energy, potential energy, force etc). No background in topology or advanced differential geometry will be assumed. |
| 12:00 - 13:30 |
Lunch (outlets*) |
| 13:30 - 16:00 |
Speight (continued) |
| 16:15 - 17:15 |
Horton: Neutron transport from a probabilistic perspective |
|
Abstract: Neutron transport describes the dynamics of neutrons undergoing fission in environments such as nuclear reactors. Understanding the growth rate of the number of neutrons in the reactor and their long-term spatial distribution is crucial for reactor design and safety. In this talk, we will discuss how to model neutron transport via a branching process and how this can be helpful to understand such properties. |
| 19:15 - 20:00 |
Dinner (Lime tree) |
| 9:30 - 12:00 |
Speight (continued) |
| 12:00 - 13:30 |
Lunch (4W Atrium) |
| 13:30 - 16:00 |
Luckins: Free boundary problems in phase-change and porous media |
|
Abstract: Many examples of partial-differential-equation (PDE) models that you will have encountered in your degree so far are posed on prescribed domains. A free-boundary problem is a PDE model posed on a domain where at least part of the boundary moves, and where the position and speed of the moving boundary must be determined as part of the model solution. Free-boundary problems are more complicated to solve and analyse mathematically due to their inherent nonlinearity, and are particularly tricky in scenarios where the free-boundary becomes unstable, but they are crucial to understand as they appear in many important real-world problems. In this minicourse, we will explore two classical examples of free-boundary problems: (i) melting/freezing problems and (ii) fluid flows in porous media, and discuss their modern applications in modelling sea ice, heat batteries, metallurgy, and carbon sequestration. |
| 16:15 - 17:15 |
Spence: Numerical analysis of wave scattering problems |
|
Abstract: |
| 19:15 - 20:00 |
Dinner (Lime tree) |
| 9:30 - 12:00 |
Luckins (continued) |
| 12:00 - 13:30 |
Lunch (outlets*) |
| 16:15 - 17:15 |
PhD student talks |
| 19:15 - 20:00 |
Dinner (Lime tree) |
| 20:15 - 21:15 |
N is a number |
|
Documentary about Paul Erdős. James Davenport can answer questions about “Uncle Paul”. |
| 9:15 - 12:00 |
Shelton: Resummation of divergent series expansions and the Stokes phenomenon |
|
Abstract: |
| 12:00 - 13:30 |
Lunch (outlets*) |
| 13:30 - 16:00 |
Shelton (continued) |
| 16:15 - 17:15 |
Leary: Recognising contractible spaces |
|
Abstract: |
| 18:30 |
Dinner (Pearl of India) |
| 9:30 - 12:00 |
Shelton (continued) |
| 12:00 - 13:30 |
Lunch (outlets*) |
- Use vouchers in any outlet on campus