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Artist Antoni Malinowski has been commissioned to produce a major wall painting in the foyer of the new Mathematical Institute in Oxford, the Andrew Wiles Building. To celebrate and introduce that work Antoni and a series of distinguished speakers will demonstrate the different impacts and perceptions of colour produced by the micro-structure of the pigments, from an explanation of the pigments themselves to an examination of how the brain perceives colour.

Speakers:

Jo Volley, Gary Woodley and Malina Busch, the Pigment Timeline Project, Slade School of Fine Art, University College London

‘Pigment Timeline’

Dr. Ruth Siddall - Senior Lecturer in Earth Sciences, University College London

‘Pigments: microstructure and origins?’  

Antoni Malinowski

‘Spectrum Materialised’ 

Prof. Hannah Smithson Associate Professor, Experimental Psychology, University of Oxford and Tutorial Fellow, Pembroke College

‘Colour Perception‘

11.30am, Lecture Theatre 1

Mathematical Institute, University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

No booking required

Dave Hewett: Canonical solutions in wave scattering

By a "canonical solution" I have in mind a closed-form exact solution of the scalar wave equation in a simple geometry, for example the exterior of a circular cylinder, or the exterior of an infinite wedge. In this talk I hope to convince you that the study of such problems is (a) interesting; (b) important; and (c) a rich source of (difficult) open problems involving eigenfunction expansions, special functions, the asymptotic evaluation of integrals, and matched asymptotic expansions.

We revisit the optimal exit problem by adding a moral hazard problem where a firm owner contracts out with an agent to run a project. We analyse the optimal contracting problem between the owner and the agent in a Brownian framework, when the latter modifies the project cash-flows with an hidden action. The analysis leads to the resolution of a constrained optimal stopping problem that we solve explicitly.

Most networks and graphs encountered in empirical studies, including internet and web graphs, social networks, and biological and ecological networks, are very sparse.  Standard spectral and linear algebra methods can fail badly when applied to such networks and a fundamentally different approach is needed.  Message passing methods, such as belief propagation, offer a promising solution for these problems.  In this talk I will introduce some simple models of sparse networks and illustrate how message passing can form the basis for a wide range of calculations of their structure.  I will also show how message passing can be applied to real-world data to calculate fundamental properties such as percolation thresholds, graph spectra, and community structure, and how the fixed-point structure of the message passing equations has a deep connection with structural phase transitions in networks.

Eigenvectors of square matrices are central to linear algebra. Eigenvectors of tensors are a natural generalization. The spectral theory of tensors was pioneered by Lim and Qi around 2005. It has numerous applications, and ties in closely with optimization and dynamical systems.  We present an introduction that emphasizes algebraic and geometric aspects

I will review Bott's classical periodicity result about topological K-theory (with period 2 in the case of complex K-theory, and period 8 in the case of real K-theory), and provide an easy sketch of proof, based on the algebraic periodicity of Clifford algebras. I will then introduce the `higher real K-theory' of Hopkins and Miller, also known as TMF. I'll discuss its periodicity (with period 576), and present a conjecture about a corresponding algebraic periodicity of `higher Clifford algebras'. Finally, applications to physics will be discussed.

In 1995, celebrated Russian mathematician V.I. Arnold conjectured that, contrary to common belief, convex, homogeneous solids with just two static balance points ("weebles without a bottom weight") may exist. Ten years later, based on a constructive proof, the first such object, dubbed "Gömböc", was built. In the process leading to the discovery, several curious properties of the shape emerged and evidently some tropical turtles had evolved similar shells for the purpose of self-righting.

This Public Lecture will describe those properties as well as explain the journey of discovery, the mathematics behind the journey, the parallels with molecular biology and the latest Gömböc thinking, most notably Arnold's second major conjecture, namely that the Gömböc in Nature is not the origin, rather the ultimate goal of shape evolution.

Please email @email to register.

There has been a great deal of attention paid to "Big Data" over the last few years.  However, often as not, the problem with the analysis of data is not as much the size as the complexity of the data.  Even very small data sets can exhibit substantial complexity.  There is therefore a need for methods for representing complex data sets, beyond the usual linear or even polynomial models.  The mathematical notion of shape, encoded in a metric, provides a very useful way to represent complex data sets.  On the other hand, Topology is the mathematical sub discipline which concerns itself with studying shape, in all dimensions.  In recent years, methods from topology have been adapted to the study of data sets, i.e. finite metric spaces.  In this talk, we will discuss what has been
done in this direction and what the future might hold, with numerous examples.