Mon, 21 Jan 2019
14:15
L4

Orientations for gauge-theoretic moduli problems

Yuuji Tanaka
(Oxford University)
Abstract

This talk is based on joint work with Dominic Joyce and Markus Upmeier. Issues we'd like to talk about are a) the orientability of moduli spaces that
appear in various gauge-theoretic problems; and b) how to orient those moduli spaces if they are orientable. We begin with briefly mentioning backgrounds and motivation, and recall basics in gauge theory such as the Atiyah-Hitchin-Singer complex and the Kuranishi model by taking the anti-self-dual instanton moduli space as an example. We then describe the orientability and canonical orientations of the anti-self-dual instanton moduli space, and other
gauge-theoretic moduli spaces which turn up in current research interests.

 

Thu, 09 May 2019

16:00 - 17:30
L3

Self-similarly expanding regions of phase change yield cavitational instabilities and model deep earthquakes

Professor Xanthippi Markenscoff
(UC San Diego)
Further Information

Department of Mechanical and Aerospace Engineering University of California, San Diego La Jolla, CA 92093-0411 

@email 

Abstract

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Abstract

The dynamical fields that emanate from self-similarly expanding ellipsoidal regions undergoing phase change (change in density, i.e., volume collapse, and change in moduli) under pre-stress, constitute the dynamic generalization of the seminal Eshelby inhomogeneity problem (as an equivalent inclusion problem), and they consist of pressure, shear, and M waves emitted by the surface of the expanding ellipsoid and yielding Rayleigh waves in the crack limit. They may constitute the model of Deep Focus Earthquakes (DFEs) occurring under very high pressures and due to phase change. Two fundamental theorems of physics govern the phenomenon, the Cauchy-Kowalewskaya theorem, which based on dimensional analysis and analytic properties alone, dictates that there is zero particle velocity in the interior, and Noether’s theorem that extremizes (minimizes for stability) the energy spent to move the boundary so that it does not become a sink (or source) of energy, and determines the self-similar shape (axes expansion speeds). The expression from Noether’s theorem indicates that the expanding region can be planar, thus breaking the symmetry of the input and the phenomenon manifests itself as a newly discovered one of a “dynamic collapse/ cavitation instability”, where very large strain energy condensed in the very thin region can escape out. In the presence of shear, the flattened very thin ellipsoid (or band) will be oriented in space so that the energy due to phase change under pre-stress is able to escape out at minimum loss condensed in the core of dislocations gliding out on the planes where the maximum configurational force (Peach-Koehler) is applied on them. Phase change occurring planarly produces in a flattened expanding ellipdoid a new defect present in the DFEs. The radiation patterns are obtained in terms of the equivalent to the phase change six eigenstrain components, which also contain effects due to planarity through the Dynamic Eshelby Tensor for the flattened ellipsoid. Some models in the literature of DFEs are evaluated and excluded on the basis of not having the energy to move the boundary of phase discontinuity. Noether’s theorem is valid in anisotropy and nonlinear elasticity, and the phenomenon is independent of scales, valid from the nano to the very large ones, and applicable in general to other dynamic phenomena of stress induced martensitic transformations, shear banding, and amorphization.

 

Thu, 14 Feb 2019
16:00
C4

TQFTs with values in holomorphic symplectic varieties

Maxence Mayrand
(Oxford University)
Abstract

I will describe a family of 2d TQFTs, due to Moore-Tachikawa, which take values in a category whose objects are Lie groups and whose morphisms are holomorphic symplectic varieties. They link many interesting aspects of geometry, such as moduli spaces of solutions to Nahm equations, hyperkähler reduction, and geometric invariant theory.

Wed, 21 Nov 2018
11:00
N3.12

The Monoidal Marriage of Stucture and Physics

Nicola Pinzani
(University of Oxford)
Abstract

What does abstract nonsense (category theory) have to do with the apparently opposite proverbial concreteness of physics? In this talk I will try to convey the importance of understanding physical theories from a compositional and structural perspective, where the fundamental logic of interaction between systems becomes the real protagonist. Firstly, we will see how different classes of symmetric monoidal categories can be used to model physical processes in a very natural and intuitive way. We will then explore the claim that category theory is not only useful in providing a unified framework, but it can be also used to perfect and modify preexistent models. In this direction, I will show how the introduction of a trace in the symmetric monoidal category describing QIT can be used to talk about quantum interactions induced by cyclic causal relationships.

Tue, 26 Feb 2019

12:00 - 13:15
L4

Higgsplosion: excitements and problems

Alexander Belyaev
(Southampton University)
Abstract

A recent calculation of the multi-Higgs boson production in scalar theories
with spontaneous symmetry breaking has demonstrated the fast growth of the
cross section with the Higgs multiplicity at sufficiently large energies,
called “Higgsplosion”. It was argued that “Higgsplosion” solves the Higgs
hierarchy and fine-tuning problems. The phenomena looks quite exciting,
however in my talk I will present arguments that: a) the formula for
“Higgsplosion” has a limited applicability and inconsistent with unitarity
of the Standard Model; b) that the contribution from “Higgsplosion” to the
imaginary part of the Higgs boson propagator cannot be re-summed in order to
furnish a solution of the Higgs hierarchy and fine-tuning problems.

Based on our recent paper https://arxiv.org/abs/1808.05641 (A. Belyaev, F. Bezrukov, D. Ross)

 

Fri, 25 Jan 2019

10:00 - 11:00
L5

Coresets for clustering very large datasets

Stephane Chretien
(NPL)
Abstract

Clustering is a very important task in data analytics and is usually addressed using (i) statistical tools based on maximum likelihood estimators for mixture models, (ii) techniques based on network models such as the stochastic block model, or (iii) relaxations of the K-means approach based on semi-definite programming (or even simpler spectral approaches). Statistical approaches of type (i) often suffer from not being solvable with sufficient guarantees, because of the non-convexity of the underlying cost function to optimise. The other two approaches (ii) and (iii) are amenable to convex programming but do not usually scale to large datasets. In the big data setting, one usually needs to resort to data subsampling, a preprocessing stage also known as "coreset selection". We will present this last approach and the problem of selecting a coreset for the special cases of K-means and spectral-type relaxations.

 

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