Welcome and Opening Remarks

Bianca Dittrich Perimeter Institute for Theoretical Physics

Theo JohnsonFreyd Perimeter Institute for Theoretical Physics

Sylvie Paycha Universität Potsdam

Katarzyna Rejzner University of York

Anne Taormina Durham Academy

Reiko Toriumi Okinawa Institute of Science and Technology (OIST)
Division algebraic symmetry breaking
Cohl Furey
Humboldt University of Berlin
Can the 32Cdimensional 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) > PatiSalam > LeftRight symmetric > Standard model + BL (both pre and postHiggsmechanism). 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.
State sum models with defects
Catherine Meusburger
FriedrichAlexanderUniversität ErlangenNürnberg
"We explain how to construct a TuraevViro state sum model with defect planes, defect lines and defect points. This is work in progress with John Barrett."
Quantum information and black holes
Johanna Erdmenger
University of Würzburg
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.
Researcher Presentations

Karen Yeats University of Waterloo

Sabine Harribey CPHT Centre de Physique Théorique de l’Ecole Polytechnique

Philine van Vliet Deutsches ElektronenSynchrotron (DESY)

Maria Elena TejedaYeomans University of Colima

Maryam Khaqan Emory University
Mathematical Puzzles from Causal Set Quantum Gravity
Sumati Surya
Raman Research Institute
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 nonlocality.
On generalized hyperpolygons
Laura Schaposnik
University of Illinois at UrbanaChampaign (UIUC)
In this talk we will introduce generalized hyperpolygons, which arise as Nakajimatype representations of a cometshaped 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 genusg 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.
Exploring spacetime beyond classicality
Renate Loll
Radboud Universiteit Nijmegen
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.
Researcher Presentations

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
A gentle introduction to (modular tensor) categories
Ana Ros Camacho
Cardiff University
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 socalled 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.