|
These meetings are designed to encourage interaction, both social and intellectual, between the mathematics divisions (pure, applied and statistics) and theoretical physics. They consist of a short and accessible talk by a member of one of the divisions, or by an invited guest, followed (or interrupted)
by discussion.
In the academic year 2009/2010 we plan to have a series of introductory talks
on topological field theories and topological strings, and to go a bit deeper
into the concept of spaces of stability conditions. The introductory talks on topologcial strings will follow Marcel Vonk's `A mini-course on topological strings' hep-th/0504147, in particular Sections 3-6. (Another review of the subject is Robert Dijkgraaf, `Les Houches Lectures on Fields, Strings and Duality' hep-th/9703136.)
There are some notes which have been made available by the speakers:
.
For confirmation please contact Jonathan Woolf on (0151) 794 4052 or Thomas Mohaupt on (0)151 795 5177.
Mirian Tsulaia - "Introduction to topological field theories and topological strings"
Abstract: We give a brief introduction to basics of Topological Field Theory and Topological String Theories. In particular, we give the axioms of cohomological field theories, discuss a construction of local and nonlocal physical operators and briefly describe some properties of correlation functions. We describe twisted N=(2,2) sigma models, introduce A and B models and describe some of their properties.Thomas Mohaupt - "One and a Half lectures on supersymmetry (Part 1)"
I will try to give a concise introduction to some concepts of supersymmetry from a mathematical perspective: super vector spaces, Lie superalgebras in general, and Poincare Lie superalgebras in particular.Thomas Mohaupt - "One and a Half lectures on supersymmetry (Part 1.5)"
Mirian Tsulaia - "Introduction to topological field theories and topological strings (Part II)"
Abstract: In this 'double feature' Thomas will wrap up his lecture and talk about super Minkowski space and the scalar superfield. Then Mirian will continue with a discussion of twisted N=(2,2) sigma models in general and of the A model and B model in particular.Jon Woolf - "Bridgeland stability conditions"
Abstract: One can associate a complex manifold of stability conditions to a complex projective variety. When the variety is Calabi-Yau a (naturally defined) quotient of this is conjectured to be the `stringy Kahler moduli space' of the variety. My aim is to explain how one constructs the space of stability conditions, and how to compute it for the case of an elliptic curve, i.e. a 1-dimensional Calabi-Yau variety. Plan: * Sketch of the construction and its conjectural connection with string theory. * (Very) brief introduction to coherent sheaves and their derived category. * Definition of stability conditions. * Computation of space of stability conditions for an elliptic curve. There are several rather abstract constructions, but I will try to motivate things as far as possible and give concrete examples.Jon Woolf - "Bridgeland stability conditions (Part 2)"
Jon will continue with his lecture on Bridgeland stability conditions.Thomas Mohaupt - "Central Charges, BPS states and stability in supersymmetric theories "
I will explain the concepts of central charges and BPS states in supersymmetric theories. While some similiarities with Jon's two lectures will become apparent, the seminar is essentially self-contained. Having introduces central charges and BPS states in a `kinematical' (=`algebraic') setting, we will move on to `dynamical' questions about the existence and stability of states, which will turn out to be rich and interesting. Time permitting I will give an outlook on how such dynamical problems have been `geometrized,' following work by Seiberg and Witten (and many others). This should be the proper setting for making contact with Jon's lectures on stability condition. Further exploration of this is left to the next term.Your contribution is welcome!