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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 (30-40 minute) and accessible talk by a member of one of the divisions followed by discussion. They occur monthly on Monday afternoons, 4:00-5:00 alternately in G117 and Room 514.
For confirmation please contact Jonathan Woolf on (0151) 794 4052 or Thomas Mohaupt on (0)151 795 5177.
In the academic year 2007/08, we plan to have a series of talks investigating the topic of stability conditions in mathematics and physics. As always, participants are wellcome to contribute talks about any topic they find interesting.
Thomas Mohaupt - "A brief introduction to strings and branes"
I will start to explain the basic concepts of string theory. This will be continued in further talks until we make contact with Jon's lectures on stability conditions. In this context, physicists have introduced D-branes, which will be explained in the seminar. The related notion of Pi-stability will not (yet) be covered, but I will try to illuminate its central ingredient namely 'stringy corrections' aka 'alpha-prime' corrections. This will give us a first idea about the new features contributed by string theory to the study of geometrical and topological problems.Thomas Mohaupt -"A brief introduction to strings and branes (part II)"
I will continue where we stopped last time. Topics still to be covered include the quantum theory of strings, 'stringy corrections', conformal quantum field theories, and 'stringy' modifications of 'classical' geometry.Radu Tatar - "Quiver gauge theories "
In this lecture I introduce the field theories obtained on D-branes at singularities. The Dp-branes are p+1 hypersurfaces where the string can end. For D3-branes in flat space we get a D=4 field teory with a maximum amount of supersymmetry. For D3 brane at singularities, the amount of supersymmetry is reduced. The field theory can also be directly read from a quiver diagram which I shall introduce during my lecture.Jon Woolf - "Stability conditions"
Inspired by Douglas's work on Pi-stability of D-branes in string theory Bridgeland introduced a mathematical notion of stability condition on a triangulated category. When the category is the coherent derived category of an algebraic variety this notion generalises the classical notion of stability for vector bundles on a curve. In this talk I'll try to explain Bridgeland's definition, some simple examples and the relation to string theory. It's probably fair to warn the audience that I'll use lots of terms which I don't understand at all, in the hope that the audience can make some sense of them for me!Jon Woolf - "Stability conditions (cont'd)" & Thomas Mohaupt - "Supersymmetry and Stability"
In this 'double feature' Jon will illustrate the ideas introduced in his last talk by an example. Then Thomas will start to address the issue of stability from the physics side, by introducing supersymmetry and explaining the 'BPS bound', which, while being a straightforward consequence of the supersymmetry algebra, has profound implications.Your contribution is welcome!