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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. In the winter term 2008 we plan two meetings, one on 22 October, the other on 26 November. There will probably be two further meetings in January and February 2009. While the topic for the first meeting is fixed (see below), the further schedule will be discussed at the end of the first meeting.
For confirmation please contact Jonathan Woolf on (0151) 794 4052 or Thomas Mohaupt on (0)151 795 5177.
Thomas Mohaupt - "From T-duality to Mirror Symmetry"
I will discuss the motion of strings on circles and on elliptic curves/two-tori, which provide the simplest examples of what physicists call T-duality and mirror symmetry. I will also motivate the concept of a stringy Kähler moduli space, and try to make contact with Jon's discussion of spaces of stability conditions, where elliptic curves were used as an example. The talk will be self-contained, and should be accessible to PG students.Thomas Mohaupt - "From T-duality to Mirror Symmetry (Part2)"
I will continue my previous seminar, but will try to keep it self-contained. Strings on elliptic curves/two-tori will be covered in detail, and I'll explain how the so-called special geometry of the moduli space connects to Bridgeland's work on stability conditions.Vicente Cortes (University of Hamburg) - "Holonomy of pseudo-Riemannian Cones"
We consider metric cones over pseudo-Riemannian manifolds. It is shown how explicit geometric information about the base manifold can be obtained from rather general properties of the holonomy representation of the cone. For instance, we give a general structure result for cones with decomposable holonomy and more specific results under various global assumptions. In particular we prove a generalisation of Gallot's theorem, which states that the Riemannian cone over a simply connected complete Riemannian manifold is decomposable if and only if the base manifold is the standard sphere and the cone is flat. In the case of indecomposable but reducible holonomy we specialise to the two extremal cases: the Lorentzian case and the case of split signature. (This part is based on math.dg:0707.3063) Then we discuss some new results about manifolds with Killing spinors (based on math.dg:0902.4536).Jon Woolf - "Stability conditions for elliptic curves"
Mirian Tsulaia - "Mirror symmetry for the quintic (hypersurface in P^4)"
Your contribution is welcome!