People

Christopher Strachey Professor of ComputingTel: 01865 283558I have been working on highlevel methods for quantum computation and information. I pioneered categorical quantum mechanics with Bob Coecke. More recently, I have been working on a unified sheaftheoretic approach to nonlocality and contextuality. This has led to a number of developments, including a novel classification of mulitpartite entangled states, cohomological characterizations of nonlocality and contextuality, a novel characterization of nosignalling involving signed measures (negative probabilities), and a unifying principle for Bell inequalities. There are also striking connections with a number of topics in computer science, including relational database theory, computational complexity and dependence logic. This is ongoing work, with a number of collaborators including Adam Brandenburger, Lucien Hardy, Shane Mansfield, Rui Soares Barbosa, Ray Lal, Phokion Kolaitis, Georg Gottlob, and Jouko Vaananen.

Dr Bruce BartlettResearch FellowTel: 01865 615167Email:Bruce.Bartlett@maths.ox.ac.ukMy work is in quantum topology  that is, the application of ideas from quantum mechanics to study lowdimensional manifolds and vice versa. I use higher categories as a conceptual tool. This work has applications to and is informed by ideas from topological quantum computing and anyon models in condensed matter physics.

Professor of Quantum Foundations, Logics and StructuresTel: 01865 273829I am interested in the Foundations of Physics, in particular the structures involved, with a strong structural bias towards Logic, Order and Category Theory, and their applications e.g. arXiv. Other work includes information domains e.g. arXiv, dynamic epistemic logic e.g. arXiv, and more recently, compositional distributional models of meaning e.g. arXiv. I currently have twelve PhD students; links to them are below. I jointly lead a multidisciplinary research group, the Quantum Group. More details on my research and links to publications and talks are on my informal webpage.

Associate Professor of MathematicsTel: 01865 273563My research is in algebraic and geometric topology, particularly in the homotopy theory of topological and quantum field theory. My recent research projects focus on the topology and algebra of fusion categories, conformal nets and local field theory, the geometry of elliptic cohomology, and cornered HeegaardFloer homology. At QMAC, I am investigating the use of topological defects in designing algorithms for quantum computation, and analyzing the topological structure of quantum entanglement.

Research FellowTel: 01865 283513Email:chris.heunen@cs.ox.ac.ukI work on the mathematical foundations of physics, especially quantum mechanics, and its logical aspects. My weapons of choice are category theory, functional analysis, and order theory; specifically, monoidal categories, operator algebras, and orthomodular lattices. I suppose you could say that my ultimate goal is to really understand the category of Hilbert spaces, in particular categorical aspects of a choice of basis.

University Lecturer in Pure MathematicsTel: 01865 273546My research area is geometric representation theory. Representation theory is the study of symmetries. There are many different kinds of symmetries and they are formalized by algebraic structures. Historically representation theory was part of algebra. In the 1970s and 1980s it was discovered that the tools and perspective of geometry can be used to solve and understand problems in representation theory. Geometry is very powerful because it deals with understanding global and complicated objects by their local (and simple) nature. This led to solving of conjectures using geometric tools (the theory of Dmodules) where there are no known purely algebraic solutions. It also led to the development of new theories such as the geometric Langlands programme. My work is also related to quantum field theory.

Professor of PhysicsTel: 01865 273954Email: s.simon1 at physics dot ox dot ac dot ukSteve Simon is a theoretical physicist who is interested in topological matter — physical systems that are realizations of topological quantum field theories (TQFTs). He is also interested in the possible application of TQFTs to quantum computation. He is an expert in fractional quantum Hall effect, perhaps the best studied physical TQFT.

Professor of MathematicsTel: 01865 273572Email: Ulrike.Tillmann@maths.ox.ac.ukUlrike Tillmann has been a leader in understanding the geometry of cobordism categories and has thereby made transformational contributions to the classification of topological field theories. She contributes to the Centre cuttingedge knowledge of mathematical formulations of field theory and a broad intuition about the geometry of cobordism structures.

Research FellowTel: (018656)10775Email: jamie.vicary@cs.ox.ac.ukMy work is on highlevel mathematical structures that can account for phenomena in quantum theory, and in theories of interacting systems more broadly, including topics such as quantum algorithms, quantum foundations, concurrency and topological quantum field theory. I am particularly interested in higher category theory as a language to help explore these ideas.