Triangle Seminars
Tuesday, 9 Feb 2010
Knot invariants, knot homology and geometric representation theory
Geordie Williams
(Oxford University)
Abstract:
I will start by giving an introduction to polynomial knot invariants, as well as to Khovanov's more recent idea of knot homology. The goal is to find bi- and tri-graded vector spaces whose graded Euler characteristics are classical polynomial knot invariants (like the Jones or HOMFLYPT polynomial). I will then explain how HOMFLYPT homology can be given a transparent construction using some heavy machinery from geometric representation theory. This gives a bridge between link homology and techniques which have been developed for studying the characters of finite groups of Lie type.
I will start by giving an introduction to polynomial knot invariants, as well as to Khovanov's more recent idea of knot homology. The goal is to find bi- and tri-graded vector spaces whose graded Euler characteristics are classical polynomial knot invariants (like the Jones or HOMFLYPT polynomial). I will then explain how HOMFLYPT homology can be given a transparent construction using some heavy machinery from geometric representation theory. This gives a bridge between link homology and techniques which have been developed for studying the characters of finite groups of Lie type.
Posted by: KCL
Wednesday, 10 Feb 2010
tba
Atish Dabholkar
(Paris)
Abstract:
I will report on some recent progress on defining and computing finite
size effects in the entropy of black holes with highly nontrivial
agreements between thermodynamics and statistical mechanics. I will
describe a number of puzzles and their resolutions along with some exact
computations, and then briefly discuss the role of mock modular forms
and Borcherds-Kac-Moody superalgebras in this context.
I will report on some recent progress on defining and computing finite
size effects in the entropy of black holes with highly nontrivial
agreements between thermodynamics and statistical mechanics. I will
describe a number of puzzles and their resolutions along with some exact
computations, and then briefly discuss the role of mock modular forms
and Borcherds-Kac-Moody superalgebras in this context.
Posted by: KCL
tba
Atish Dabholkar
(Paris)
Massive 3D supergravities
Paul Townsend
(DAMTP, Cambridge)
Abstract:
Non-zero mass is compatible with unbroken gauge invariance in
three spacetime dimensions (3D). A systematic procedure for the
construction of massive gauge theories will be illustrated by new massive
gravity, which propagates unitarily two massive spin 2 modes in a
Minkowski vacuum. The supergravity extension of this model will be
presented along with new results on supersymmetric AdS vacua. The extension to a new N=8 3D supergravity will be discussed, as will be the AdS3CFT2 correspondence and possible connections to string/M-theory.
Non-zero mass is compatible with unbroken gauge invariance in
three spacetime dimensions (3D). A systematic procedure for the
construction of massive gauge theories will be illustrated by new massive
gravity, which propagates unitarily two massive spin 2 modes in a
Minkowski vacuum. The supergravity extension of this model will be
presented along with new results on supersymmetric AdS vacua. The extension to a new N=8 3D supergravity will be discussed, as will be the AdS3CFT2 correspondence and possible connections to string/M-theory.
Posted by: IC