Mon, 16 Jun 2014

14:15 - 15:15
Oxford-Man Institute

Topologies of nodal sets of band limited functions

IGOR WIGMAN
(Kings College London)
Abstract

This work is joint with Peter Sarnak.

It is shown that the topologies and nestings of the zero and nodal sets of random (Gaussian) band limited functions have universal laws of distribution. Qualitative features of the supports of these distributions are determined. In particular the results apply to random monochromatic waves and to random real algebraic hyper-surfaces in projective space.

Mon, 05 Nov 2012

12:00 - 13:00
L3

Global Aspects of F-theory on singular CY fourfolds

Sakura Schafer-Nameki
(Kings College London)
Abstract
F-theory compactifications on singular elliptic Calabi-Yau fourfolds provide an ideal framework to study supersymmetric Grand Unified Theories. Recent years have seen much progress in local F-theory model building. Understanding the global constraints for realizing local models are key in estabilishing a consistent F-theoretic realization. We will address these questions by analyzing the structure of the singular elliptic CY fourfolds, which form the geometric foundation for these compactification, as well as the construction of globally consistent G_4 flux.
Mon, 22 Nov 2010

12:00 - 13:00
L3

Constraining F-theory GUTs

Sakura Schafer-Nameki
(Kings College London)
Abstract
String theory phenomenology generically suffers from either too much flexibility (and lack of predictability) or from the a high specialization to case by case studies. I will discuss how F-theory GUT model building manages to get around these pitfalls, in particular, I will explain, how to systematically include global string consistency conditions, which are independent of the specific compactification, and which come with the benefit of highly constraining the class of GUT models that can arise from F-theory.
Mon, 08 Nov 2010

12:00 - 13:00
L3

Generalised Space-Time and Duality

Peter West
(Kings College London)
Abstract
I will review the conjectured E_{11} symmetry of strings and branes. I will explain how it is natural in the context of this symmetry to introduce a generalised space-time with a corresponding generalised geometry.
Mon, 07 Jun 2010

12:00 - 13:00
L3

The torsional conifold: fivebranes and the Klebanov-Strassler theory

Dario Martelli
(Kings College London)
Abstract
We study a gravity solution corresponding to fivebranes wrapped on the S^2 of the resolved conifold. By changing a parameter the solution continuously interpolates between the deformed conifold with flux and the resolved conifold with branes. Therefore, it displays a geometric transition, purely in the supergravity context. The solution is a simple example of torsional geometry and may be thought of as a non-Kahler analog of the conifold. By U-duality transformations we can add D3 brane charge and recover the solution in the form originally derived by Butti et al. This describes the baryonic branch of the Klebanov-Strassler theory. Far along the baryonic branch the field theory gives rise to a fuzzy two-sphere. This corresponds to the D5 branes wrapping the two-sphere of the resolved conifold in the gravity solution.
Thu, 06 Nov 2008
16:00
L3

"Annihilating Ideals for Class Groups of Number Fields"

David Solomon
(Kings College London)
Abstract

"Stickelberger's famous theorem (from 1890) gives an explicit ideal which annihilates the imaginary part of the class group of an abelian field as a module for the group-ring of the Galois group. In the 1980s Tate and Brumer proposed a generalisation of Stickelberger's Theorem (and his ideal) to other abelian extensions of number fields, the so-called `Brumer-Stark conjecture'.

I shall discuss some of the many unresolved issues connected with the annihilation of class groups of number fields. For instance, should the (generalised) Stickelberger ideal be the full annihilator, the Fitting ideal or what? And what can we say in the plus part (where Stickelberger's Theorem is trivial)?"

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