Triangle Seminars
Tuesday, 2 Mar 2010
2-vector spaces: an introduction to higher-dimensional category theory
Eugenia Cheung
(Sheffield University)
Abstract:
Category theory is used to study structures in various branches of mathematics, and higher-dimensional category theory is being developed to study higher-dimensional versions of those structures. Examples include higher homotopy theory, higher stacks and gerbes, extended topological quantum field theories, concurrency, type theory, and higher-dimensional representation theory. In this talk we will present two general methods for categorifying things, that is, for adding extra dimensions: enrichment and internalisation. We will show how these have been applied to the definition and study of 2-vector spaces, with 2-representation theory in mind. This talk will be introductory. In particular, it should not be necessary to be familiar with any category theory, although it will of course help
Category theory is used to study structures in various branches of mathematics, and higher-dimensional category theory is being developed to study higher-dimensional versions of those structures. Examples include higher homotopy theory, higher stacks and gerbes, extended topological quantum field theories, concurrency, type theory, and higher-dimensional representation theory. In this talk we will present two general methods for categorifying things, that is, for adding extra dimensions: enrichment and internalisation. We will show how these have been applied to the definition and study of 2-vector spaces, with 2-representation theory in mind. This talk will be introductory. In particular, it should not be necessary to be familiar with any category theory, although it will of course help
Posted by: KCL
Wednesday, 3 Mar 2010
On the universality classes of Strongly Coupled Doped systems
Elias Kiritsis
(Crete)
Abstract:
Effective Holographic Theories are employed in order to classify
and study the critical dynamics at low temperature of quantum field
theoritec systems in 2 and 3 spacial dimensions at finite charge density.
The relevant dynamics variables involve the energy momentum tensor, a scalar
relevant or marginal operator and the charge density current.
A wealth of scaling phases are found with interesting and sometimes
counterintuitive properties.
Effective Holographic Theories are employed in order to classify
and study the critical dynamics at low temperature of quantum field
theoritec systems in 2 and 3 spacial dimensions at finite charge density.
The relevant dynamics variables involve the energy momentum tensor, a scalar
relevant or marginal operator and the charge density current.
A wealth of scaling phases are found with interesting and sometimes
counterintuitive properties.
Posted by: IC
Effective Strings and Emergent Gravity
Erik Verlinde
(University of Amsterdam)
Abstract:
I present arguments that suggest that string theory should be viewed as an effective framework just like quantum field theory. The open/closed string and UV/IR correspondence indicate that gravity is emergent. I introduce the concept of entropic force and discuss it's subtleties. Next I present the case for the entropic origin of gravity and outline a route toward its derivation. Finally, I discuss some of the possible implications on this new view on gravity.
I present arguments that suggest that string theory should be viewed as an effective framework just like quantum field theory. The open/closed string and UV/IR correspondence indicate that gravity is emergent. I introduce the concept of entropic force and discuss it's subtleties. Next I present the case for the entropic origin of gravity and outline a route toward its derivation. Finally, I discuss some of the possible implications on this new view on gravity.
Posted by: QMW
Thursday, 4 Mar 2010
Random Matrices and the Riemann zeta-function
Jon Keating
(Bristol)
Abstract:
The Riemann zeta-function, which encodes information about the primes, is the subject of one of the most important problems in mathematics: the Riemann Hypothesis. In the past few years connections have emerged with random matrix theory/matrix models. I shall review these connections.
The Riemann zeta-function, which encodes information about the primes, is the subject of one of the most important problems in mathematics: the Riemann Hypothesis. In the past few years connections have emerged with random matrix theory/matrix models. I shall review these connections.
Posted by: QMW