Dr Simon Willerton
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Teaching:
| MAS156 | Mathematics (Electrical and Aerospace) | Information | Home page (also MOLE) |
| MAS344 | Knots and Surfaces | Information | Home page |
| MAS400 | Project Presentation in Mathematics and Statistics | Information |
Research:
| Interests: | quantum topology, algebraic topology |
| Research groups: | Topology, Differential Geometry, Category Theory |
| Publications: | Preprint page, ArXiv, MathSciNet |
Roles:
Convener of Staff-Student Forum, Programme Leader: with study in Australia or North America
Biography:
Dr. Willerton obtained his PhD from the University of Edinburgh in
1997, where he also held a temporary lectureship. He held a Royal
Society Research Fellowship in Melbourne and an EU Marie Curie
Fellowship in Strasbourg before returning to the UK as a Research
Associate at Heriot-Watt University. After a Visiting Professorship
at the University of California, San Diego, he joined Sheffield
University as a lecturer in 2002.
Since then he has held visiting positions at UC San Diego, UC Riverside and the Autonomous University of Barcelona.
He was awarded a Senate Award for Excellence in Teaching and Learning in 2009
for his work with Eugenia Cheng on using YouTube in teaching mathematics and was promoted to Senior Lecturer in 2010.
Research interests:
Dr. Willerton is interested in various ideas in low-dimensional topology
coming from quantum physics, and in their relationship to geometry and
algebraic topology.
In particular, methods from quantum field theory give rise to new invariants of knots and three-manifolds - these are the so-called quantum and Vassiliev (or finite-type) invariants. A large part of the motivation for Dr. Willerton's work is to understand these invariants from a topological or geometric point of view. For instance, the Kontsevich integral is a construction which takes a knot and gives back a sort of Feynman diagram expansion: this embodies a rich algebraic structure that is reminiscent of certain objects from algebraic topology, but it is not clear at the moment how to relate these.
Well-studied examples of quantum invariants arise when one fixes a Lie group. Motivated in part by trying to understand the Kontsevich integral, Dr. Willerton has considered (with collaborators in San Diego and Oxford) the less well-studied invariants which arise when one fixes a hyper-Kahler manifold. This work has revealed unexpected algebraic structures in the derived category of coherent sheaves on a complex manifold.
The theory of gerbes is a related interest of Dr. Willerton. Gerbes can be thought of as the next step beyond line bundles. Ideas from this area feed into K-theory, string theory and the quantum invariants mentioned above.
In recent times Dr Willerton has been interested in the connections between metric spaces and category theory. This has lead in particular to him studying measures of biodiversity.
In particular, methods from quantum field theory give rise to new invariants of knots and three-manifolds - these are the so-called quantum and Vassiliev (or finite-type) invariants. A large part of the motivation for Dr. Willerton's work is to understand these invariants from a topological or geometric point of view. For instance, the Kontsevich integral is a construction which takes a knot and gives back a sort of Feynman diagram expansion: this embodies a rich algebraic structure that is reminiscent of certain objects from algebraic topology, but it is not clear at the moment how to relate these.
Well-studied examples of quantum invariants arise when one fixes a Lie group. Motivated in part by trying to understand the Kontsevich integral, Dr. Willerton has considered (with collaborators in San Diego and Oxford) the less well-studied invariants which arise when one fixes a hyper-Kahler manifold. This work has revealed unexpected algebraic structures in the derived category of coherent sheaves on a complex manifold.
The theory of gerbes is a related interest of Dr. Willerton. Gerbes can be thought of as the next step beyond line bundles. Ideas from this area feed into K-theory, string theory and the quantum invariants mentioned above.
In recent times Dr Willerton has been interested in the connections between metric spaces and category theory. This has lead in particular to him studying measures of biodiversity.