Triangle Seminars
Monday, 10 Mar 2008
Conformal field theory and Frobenius algebras
Ingo Runkel
(KCL)
Abstract:
Two-dimensional conformal field theory can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. Generalising what one finds for 2d topological field theories, a solution to these constraints can be obtained from a symmetric special Frobenius algebra in the appropriate braided monoidal category.
Two-dimensional conformal field theory can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. Generalising what one finds for 2d topological field theories, a solution to these constraints can be obtained from a symmetric special Frobenius algebra in the appropriate braided monoidal category.
Posted by: IC
Tuesday, 11 Mar 2008
Topological quantum computation from non-abelian anyons
Paul Fendley
(University of Virginia, USA)
Abstract:
I discuss how systems with non-abelian anyons can be used to build a topological quantum computer. Operations are performed by braiding the anyons, because the outcome of braiding is a purely topological property, such quantum computers should be robust against local errors. I will give
several examples of how such anyons arise in fractional quantum Hall systems and in quantum loop models. Mathematical byproducts of this work are algebraic proofs and extensions of Tutte's identities for the chromatic polynomial (the zero-temperature Potts-model partition
function).
I discuss how systems with non-abelian anyons can be used to build a topological quantum computer. Operations are performed by braiding the anyons, because the outcome of braiding is a purely topological property, such quantum computers should be robust against local errors. I will give
several examples of how such anyons arise in fractional quantum Hall systems and in quantum loop models. Mathematical byproducts of this work are algebraic proofs and extensions of Tutte's identities for the chromatic polynomial (the zero-temperature Potts-model partition
function).
Posted by: KCL
Wednesday, 12 Mar 2008
QCD bound states and AdS/CFT correspondence
📍 London
Konstadinos Siampos
(University of Patras)
Abstract:
I will review the computation of the quark-antiquark potential within the AdS/CFT correspondence. I will explain in detail the conformal case and apply this machinery in more general backgrounds, where multivalued potentials
appear and stability issues have to be considered in order to isolate the physical branches of the potential. Finally I will extend this idea in the case of dyons and baryons. Mechanical analogues of the above configurations will be
given.
I will review the computation of the quark-antiquark potential within the AdS/CFT correspondence. I will explain in detail the conformal case and apply this machinery in more general backgrounds, where multivalued potentials
appear and stability issues have to be considered in order to isolate the physical branches of the potential. Finally I will extend this idea in the case of dyons and baryons. Mechanical analogues of the above configurations will be
given.
Posted by: KCL
On Brauer diagram categories, representations, and spin-chain spectra
Paul Martin
(Leeds)
Triadophilia: A Special Corner in the Landscape
Yang-Hui He
(Oxford University)
Abstract:
We point out a special corner in the space of Calabi-Yau compactifications where standard-like models tend to emerge. We show how these scenarios are inter-related via a mathematical process of transgression of bundles, a generalisation of the conifold transition. Perhaps our world is special and we live in this oasis within the multitude of vacua.
We point out a special corner in the space of Calabi-Yau compactifications where standard-like models tend to emerge. We show how these scenarios are inter-related via a mathematical process of transgression of bundles, a generalisation of the conifold transition. Perhaps our world is special and we live in this oasis within the multitude of vacua.
Posted by: IC
Thursday, 13 Mar 2008
Supersymmetry Relations and (N)MHV-Amplitudes in Superstring Theory
Stephan Stieberger
(Munich)
Friday, 14 Mar 2008
Sasaki-Einstein Geometry.
James Sparks
(Oxford University)
Abstract:
Sasakian geometry is the odd-dimensional cousin of Kahler geometry. Although the two are very closely related, there are some interesting differences. I will give an introduction to Sasakian, and in particular Sasaki-Einstein, geometry, and review some of the developments in this subject over the last few years. In particular I'll cover explicit constructions, toric Sasakian geometry, and obstructions. Some of these results also provide new insights into Kahler geometry - for example, I'll describe very simple new obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.
Sasakian geometry is the odd-dimensional cousin of Kahler geometry. Although the two are very closely related, there are some interesting differences. I will give an introduction to Sasakian, and in particular Sasaki-Einstein, geometry, and review some of the developments in this subject over the last few years. In particular I'll cover explicit constructions, toric Sasakian geometry, and obstructions. Some of these results also provide new insights into Kahler geometry - for example, I'll describe very simple new obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.
Posted by: IC