Patrick has been awarded the prize from the Society for Industrial and Applied Mathematics (SIAM) for his "broad, creative, and groundbreaking contributions to numerical solutions of partial differential equations, and the design and analysis of algorithms and software for scientific computing".
And ex-Oxford Mathematician Mason Porter has been awarded SIAM's George Pólya Prize for Mathematical Exposition.
The class of $t$-perfect graphs consists of graphs whose stable set polytopes are defined by their non-negativity, edge inequalities, and odd circuit inequalities. These were first studied by Chvátal in 1975, motivated by the related and well-studied class of perfect graphs. While perfect graphs are easy to colour, the same is not true for $t$-perfect graphs; numerous questions and conjectures have been posed, and even the most basic, on whether there exists some $k$ such that every $t$-perfect graph is $k$-colourable, has remained open since 1994. I will talk about joint work with Maria Chudnovsky, Linda Cook, James Davies, and Sang-il Oum in which we establish the first finite bound and show that a little less than 200 000 colours suffice.
In string theory, elementary particles correspond to the various oscillation modes of fundamental strings, whose dynamics in spacetime is described by a two-dimensional conformal field theory on the worldsheet of the propagating strings. While the theory enjoys several desirable features - UV-finiteness, the presence of the graviton in the closed-string spectrum, a pathway to unification - several aspects remain elusive or unsatisfactory, including the on-shell and perturbative nature of string scattering amplitudes and the presence of infrared divergences. String field theory - the formulation of string theory as a quantum field theory - provides a unique and complete framework for describing string dynamics, allowing for example to compute off-shell amplitudes and non-perturbative contributions, to regulate infrared divergences and to approach background independence. This talk will be concerned with the construction of string field theories. Following a brief review of string theory, I will introduce the string fields, and discuss the construction of a string field action and the associated Feynman diagrams. Finally, I will mention some applications before concluding.
Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.
Why do some memories last a lifetime while others fade away? A groundbreaking new study sheds light on this mystery by uncovering hidden patterns of brain activity that support long-term memory. Using a framework inspired by thermodynamics, scientists have developed a novel approach to understanding how different brain regions work together to shape cognition.
Recently, work has been done to understand higher-form symmetries in linear gravity. Just like Maxwell theory, which has both electric and magnetic U(1) higher form symmetries, linearised gravity exhibits analogous structure. The authors of
[https://arxiv.org/pdf/2409.00178] investigate electric and magnetic higher form symmetries in linearised gravity, which correspond to shift symmetries of the graviton and the dual graviton respectively. By attempting to gauge the two symmetries, the authors investigate the mixed ’t Hooft anomalies anomaly structure of linearised gravity. Furthermore, if a specific shift symmetry is considered, the corresponding charges are related to Roger Penrose's quasi-local charge construction.
Based on: [https://arxiv.org/pdf/2410.08720][https://arxiv.org/pdf/2409.00178][https://arxiv.org/pdf/2401.17361]
