Triangle Seminars

Abstract:
Let us say that two conjugacy classes of a group commute if they contain representatives that commute. When G is a finite group with a normal subgroup N such that G/N is cyclic, one can use this definition, together with Hall's Marriage Theorem, to describe the distribution of the conjugacy classes of G across the cosets of N. I will give an overview of this result, and then talk about some more recent work on commuting conjugacy classes in symmetric and general linear groups. This talk is on joint work with John Britnell.

Abstract:
After briefly reviewing the notion of geometries characterised by SU(3) structures, I will discuss a particular class
known (in String Theory) as non-Kahler. I will explain how this arises both in Type II and Heterotic Supergravities.
Two explicit constructions of these geometries will be discussed. One is a one-parameter solution corresponding
to fivebranes wrapped on the two-sphere of the resolved conifold, that can be thought of as a non-Kahler analog of the conifold.
The other is a general construction of one-parameter non-Kahler deformations of Calabi-Yau manifolds with a U(1)
isometry, where the non-Abelian Yang-Mills field of the Heterotic is non-trivial. The presentation will be loosely based
on the two papers: arXiv:0906.0591 and arXiv:1010.4031.

Abstract:
Understanding the phases of string theory in the strong curvature
and high temperature regime, which is inaccessible to the field theory approximation, may provide insights about the physics of the very early Universe. Cosmological solutions can be described at the perturbative string level, arising as quantum or thermal instabilities of an initially flat background. Two major obstacles that typically prevent a perturbative treatment of the backreaction are the Hagedorn/tachyonic divergences that occur in such strong curvature and/or high temperature regions and the initial gravitational singularity (Big Bang), that always appears in the field theory approach. In this talk, I will present recent progress in tackling these problems within the framework of perturbative string theory. In particular, I will consider a special toy model whose high degree of symmetry may help uncover the stringy mechanism that protects the cosmological evolution from Hagedorn or gravitational type singularities.

Abstract:
Supersymmetric invariants, their symmetries and various approaches to contructing them are discussed. Their role in investigating the onset of UV divergences is outlined. In particular, it is argued that D=4 N=8 supergravity is finite up to, and including, 6 loops.