Triangle Seminars
Monday, 12 Jun 2006
Excited Giant Gravitons
Robert de Mello Koch
(SIAS)
A surgery for generalized complex 4-manifolds
Gil Cavalcanti
(Oxford)
Abstract:
One of the few known obstructions for a 1-connected 4-
manifold to admit a symplectic structure is given by Taubes theorem:
if b_+ is greater than two, then such a manifold has a nonvanishing Seiberg–Witten
invariant. It is only natural to ask whether the same holds for
generalized complex manifolds, as introduced by Hitchin, which are a
simultaneous generalization of symplectic and complex manifolds.
I will introduce a surgery for generalized complex manifolds whose input
is a symplectic 4-manifold containing a symplectic 2-torus with trivial
normal bundle and whose output is a 4-manifold endowed with a
generalized complex structure exhibiting type change along a 2-torus.
I will use this surgery to produce an example of a generalized complex
manifold with vanishing Seiberg–Witten invariants and hence which does
not admit complex or symplectic structures.
One of the few known obstructions for a 1-connected 4-
manifold to admit a symplectic structure is given by Taubes theorem:
if b_+ is greater than two, then such a manifold has a nonvanishing Seiberg–Witten
invariant. It is only natural to ask whether the same holds for
generalized complex manifolds, as introduced by Hitchin, which are a
simultaneous generalization of symplectic and complex manifolds.
I will introduce a surgery for generalized complex manifolds whose input
is a symplectic 4-manifold containing a symplectic 2-torus with trivial
normal bundle and whose output is a 4-manifold endowed with a
generalized complex structure exhibiting type change along a 2-torus.
I will use this surgery to produce an example of a generalized complex
manifold with vanishing Seiberg–Witten invariants and hence which does
not admit complex or symplectic structures.
Posted by: IC
Tuesday, 13 Jun 2006
Complex Quartic Hamiltonians
Carl Bender
(Washington University in St. Louis)
Thursday, 15 Jun 2006
Properties of the type II effective action
Jorge Russo
(University of Barcelona)
Abstract:
The exact string coupling dependence of higher derivative
terms in the type IIA and type IIB effective action is highly constrained by a combination of duality symmetries and by results from perturbative string theory. For example, we show that terms of the form D to the 2k times R to the 4th in type IIA theory should receive no perturbative contributions beyond genus k (k greater than 0). We also propose that the exact modular functions of general type IIB higher derivative terms are determined by a Poisson equation on the fundamental domain of the moduli space.
The exact string coupling dependence of higher derivative
terms in the type IIA and type IIB effective action is highly constrained by a combination of duality symmetries and by results from perturbative string theory. For example, we show that terms of the form D to the 2k times R to the 4th in type IIA theory should receive no perturbative contributions beyond genus k (k greater than 0). We also propose that the exact modular functions of general type IIB higher derivative terms are determined by a Poisson equation on the fundamental domain of the moduli space.
Posted by: IC
Friday, 16 Jun 2006
Continued fractions, non-commutative boundaries and Einstein equations
📍 London
Yuri Manin
(Northwestern University)
Abstract:
This is a Hardy lecture of the LMS. It is embedded into a wider program. Please consult the webpage http://www.lms.ac.uk/meetings/16june06.html for details.
This is a Hardy lecture of the LMS. It is embedded into a wider program. Please consult the webpage http://www.lms.ac.uk/meetings/16june06.html for details.
Posted by: KCL