Collection Number C21002
Collection Date -
Collection Type Conference/School
Can the 32C-dimensional algebra RCHO offer anything new for particle physics? Indeed it can. Here we identify a sequence of complex structures within RCHO which sets in motion a cascade of breaking symmetries: Spin(10) -> Pati-Salam -> Left-Right symmetric -> Standard model + B-L (both pre- and post-Higgs-mechanism). These complex structures derive from the octonions, then from the quaternions, then from the complex numbers. It should be noted that this pattern would not have been obvious within the standard formalism.
The concepts of quantum information theory play an important role in two seemingly distinct areas of physics: For studying the quantum properties of black holes as well as for devising quantum computing algorithms. Quantum entanglement and computational complexity may be mapped to geometric quantities. This is intimately related to the holographic principle, according to which the information stored in a volume is encoded on its surface, as is the case for black holes. In the talk I will describe the essential new concepts that relate quantum information to geometry and gravity.
I will discuss some of the mathematical puzzles that arise from the causal set approach to quantum gravity. In this approach, any causal continuum spacetime is said to be emergent from an underlying ensemble of locally finite posets which represents a discretisation of the causal structure. If the discrete substructure is to capture continuum geometry to sufficient accuracy, then it must be "approximately" close to it. How can we quantify this closeness? This discreteness, while also preserving local Lorentz invariance, leads to a fundamental non-locality.
In this talk we will introduce generalized hyperpolygons, which arise as Nakajima-type representations of a comet-shaped quiver, following recent work joint with Steven Rayan. After showing how to identify these representations with pairs of polygons, we shall associate to the data an explicit meromorphic Higgs bundle on a genus-g Riemann surface, where g is the number of loops in the comet. We shall see that, under certain assumptions on flag types, the moduli space of generalized hyperpolygons admits the structure of a completely integrable Hamiltonian system.
The physics of General Relativity is deeply intertwined with the mathematics of Lorentzian differentiable manifolds. The latter provide excellent models of spacetime across a vast range of physical scales, encoding gravitational interactions into the curvature properties of smooth metric spaces. However, describing geometry in terms of the infinitesimal line element "ds" does not seem appropriate in the quantum regime near the Planck scale.
Astrid Eichhorn University of Southern Denmark
Colleen Delaney Indiana University
Roberta Iseppi University of Southern Denmark
Lisa Glaser Universität Wien
Mahumm Ghaffar Memorial University of Newfoundland
Eilind Karlsson Technische Universität München (TUM)
Evelyn Yoczira Lira Torres Queen Mary - University of London (QMUL)
Sharmia Gunasekaran Memorial University of Newfoundland
In this talk we will introduce categories, a notion that packages mathematical objects of any kind and provides an abstract language to study them. We will build up our way towards so-called modular tensor categories, which roughly speaking are categories with a tensor product, duals, and quite a bit of extra categorical structure. They arise in (rational) conformal field theory and its study poses many interesting questions on their classification, internal structure and generalizations. I will give an overview of these questions and some current lines of research in this topic.