Triangle Seminars
Monday, 17 Nov 2008
Towards noncommutative toric geometry
Alistair Craw
(Glasgow)
Abstract:
Toric varieties have proved to be a fabulous testing ground for questions in algebraic geometry and string theory for many years. I will describe work in progress with Greg Smith that lays the foundation for a noncommutative analogue. As applications, I will provide a multigraded version of Beilinson's theorem on the derived category of projective space and I will propose a concrete link to dimer models.
Toric varieties have proved to be a fabulous testing ground for questions in algebraic geometry and string theory for many years. I will describe work in progress with Greg Smith that lays the foundation for a noncommutative analogue. As applications, I will provide a multigraded version of Beilinson's theorem on the derived category of projective space and I will propose a concrete link to dimer models.
Posted by: IC
Tuesday, 18 Nov 2008
Integrable models from PT-symmetric deformations
Andreas Fring
(City University London)
Abstract:
I will give a brief account of some examples of non-Hermitian Hamiltonian systems with real spectra, which have appeared in the literature over the last four decades. I will discuss the spectral properties of these type of Hamiltonians and explain how their reality results from PT-symmetry, quasi-Hermiticity, pseudo-Hermiticity
or supersymmetry. Subsequently I review the general technicalities needed to formulate a consistent quantum mechanical system in this context by constructing an appropriate metric and domain. I will provide
some Lie algebraic examples.
Taking PT-symmetry as a guiding principle one may construct
deformations of integrable models, such as Calogero-Moser-Sutherland models, the Korteweg-deVries or Burgers equation. It turns out that some of these deformations are supersymmetry preserving. Others even leave the integrabilty in tact and therefore lead to new types
of integrable system.
I will give a brief account of some examples of non-Hermitian Hamiltonian systems with real spectra, which have appeared in the literature over the last four decades. I will discuss the spectral properties of these type of Hamiltonians and explain how their reality results from PT-symmetry, quasi-Hermiticity, pseudo-Hermiticity
or supersymmetry. Subsequently I review the general technicalities needed to formulate a consistent quantum mechanical system in this context by constructing an appropriate metric and domain. I will provide
some Lie algebraic examples.
Taking PT-symmetry as a guiding principle one may construct
deformations of integrable models, such as Calogero-Moser-Sutherland models, the Korteweg-deVries or Burgers equation. It turns out that some of these deformations are supersymmetry preserving. Others even leave the integrabilty in tact and therefore lead to new types
of integrable system.
Posted by: KCL
Wednesday, 19 Nov 2008
Supergravity and ''exceptional'' generalised geometry
📍 London
Daniel Waldram
(IC)
Complexified classical mechanics - an introduction
Daniel Hook
(Imperial College London)
Abstract:
Several recent papers have investigated the extention of classical PT-Symmetric Hamiltonians to the classical domain. This approach to classical mechanics will be introduced as a generalisation of the familiar classical mechanics learnt at high school. The properties of these systems are often surprising and specific graphical studies can be quite beautiful. Familiar classical systems will be studied and brand new results will be presented including an exploration of chaotic systems.
Several recent papers have investigated the extention of classical PT-Symmetric Hamiltonians to the classical domain. This approach to classical mechanics will be introduced as a generalisation of the familiar classical mechanics learnt at high school. The properties of these systems are often surprising and specific graphical studies can be quite beautiful. Familiar classical systems will be studied and brand new results will be presented including an exploration of chaotic systems.
Posted by: KCL
Higgsing Worldvolume M2 Theories
Constantinos Papageorgakis
(TIFR, Mumbai)
Abstract:
I will be reviewing the details of a novel form of the Higgs mechanism, present in the context of the Bagger-Lambert and ABJM proposals for the worldvolume description of multiple parallel M2 branes. I will also discuss some of its implications as well as describe related applications. The latter will focus on the determination of four-derivative corrections to the Bagger-Lambert A_4-theory for all values of the Chern-Simons level k.
I will be reviewing the details of a novel form of the Higgs mechanism, present in the context of the Bagger-Lambert and ABJM proposals for the worldvolume description of multiple parallel M2 branes. I will also discuss some of its implications as well as describe related applications. The latter will focus on the determination of four-derivative corrections to the Bagger-Lambert A_4-theory for all values of the Chern-Simons level k.
Posted by: IC
Thursday, 20 Nov 2008
Dynamical supersymmetry breaking, duality and unification
Valentin V. Khoze
(Durham University)
Friday, 21 Nov 2008
London Mathematical Society Graduate Student Meeting
📍 London
Neil Lambert. David Tong.
Abstract:
Neil Lambert (KCL) 'From D-branes to M-branes', David Tong (DAMTP) 'Quantum vortex strings' plus several presentations by PhD students on their work. Ends at 14:15. See www.mth.kcl.ac.uk/'tilde'anderl/LMSpremeeting/
Neil Lambert (KCL) 'From D-branes to M-branes', David Tong (DAMTP) 'Quantum vortex strings' plus several presentations by PhD students on their work. Ends at 14:15. See www.mth.kcl.ac.uk/'tilde'anderl/LMSpremeeting/
Posted by: KCL
London Mathematical Society Annual Meeting
📍 London
Graeme Segal. Michael Green.
Abstract:
Graeme Segal FRS (Oxford) 'Noncommutative geometry and quantum field theory' and Michael Green FRS (Cambridge) '2007 Naylor Lecture: Some dualities of string theory and quantum gravity'. Ends at 18:00. See www.mth.kcl.ac.uk/'tilde'anderl/LMSpremeeting/
Graeme Segal FRS (Oxford) 'Noncommutative geometry and quantum field theory' and Michael Green FRS (Cambridge) '2007 Naylor Lecture: Some dualities of string theory and quantum gravity'. Ends at 18:00. See www.mth.kcl.ac.uk/'tilde'anderl/LMSpremeeting/
Posted by: KCL