Invertible Topological Field Theories
Abstract
Topological field theories (TFT's) are physical theories depending only on the topological properties of spacetime as opposed to also depending on the metric of spacetime. This talk will introduce topological field theories, and the work of Freed and Hopkins on how a class of TFT's called "invertible" TFT's describe certain states of matter, and are classified by maps of spectra. Constructions of field theories corresponding to specific maps of spectra will be described.
Spinning, stalling, and falling apart
Abstract
The birth of fixed-wing, powered flight in the first decade of the twentieth century brought with it significant potential for pilots to return to Earth by unintended, often fatal, means. I will discuss the nature of the contemporary mathematical and engineering debates associated with these facets of flight, and the practical steps taken to facilitate safer aircraft and more robust operating procedures.
With the passing of Landon T. Clay on 29 July, Oxford Mathematics has lost a treasured friend whose committed support and generosity were key factors in the recent development of the Mathematical Institute. The support of Landon and his wife Lavinia was the indispensible mainstay of the project to create the magnificent new home for Oxford Mathematics in the Andrew Wiles Building; the building is a symbol of the enduring legacy of their insightful, incisive support for mathematics and science.
It is an intriguing fact that the 3-dimensional world in which we live is, from a mathematical point of view, rather special. Dimension 3 is very different from dimension 4 and these both have very different theories from that of dimensions 5 and above. The study of space in dimensions 2, 3 and 4 is the field of low-dimensional topology, the research area of Oxford Mathematician Marc Lackenby.
Oxford Mathematician Nick Trefethen was recently awarded the George Pólya Prize for Mathematical Exposition by the Society for Industrial and Applied Mathematics (SIAM) "for the exceptionally well-expressed accumulated insights found in his books, papers, essays, and talks." Here Nick&n
As part of our series of research articles deliberately focusing on the rigour and intricacies of mathematics and its problems, Oxford Mathematician Nikolay Nikolov discusses his research in to Sofic Groups.
16:00
Existence of metrics maximizing the first eigenvalue on closed surfaces
Abstract
We prove that for closed surfaces of fixed topological type, orientable or non-orientable, there exists a unit volume metric, smooth away from finitely many conical singularities, that
maximizes the first eigenvalue of the Laplace operator among all unit volume metrics. The key ingredient are several monotonicity results, which have partially been conjectured to hold before. This
is joint work with Henrik Matthiesen.