Triangle Seminars

Abstract:
These will be introductory lectures surveying GW, MNOP and GV invariants - all different ways of counting curves.

For a string theorist this involves seeing the curve as, respectively, the world sheet of a string, a D-brane, or a BPS thingummy.

I will describe a 4th way via stable pairs, which in effect means counting D-branes (or stable objects of the derived category, to mathematicians) after a change of stability condition.

Abstract:
An integrable shock, or discontinuity, is a type of 'defect' allowed, in the sense of not destroying the property of integrability, within (at least some) integrable field theories. A main example is the sine-Gordon model, or, more generally, the a-series of affine Toda field theories. Such 'defects' have interesting properties in the classical and quantum domains especially with regard to their interactions with solitons - or indeed with each other, if there is more than one of them and they are allowed to move. This talk will present a survey of recent results and describe some open problems.

Abstract:
In this talk I want to describe recent work on geometric (Berry) phases that arise in the quantum theory of certain D-brane states. After briefly reviewing the geometric phase in general theories, I will turn to supersymmetric systems of the type arising in D0-brane configurations in string theory. Interestingly, the resulting Berry phases are related to the four Hopf fibrations. I will show how this fact arises as a consequence of the close relationship between SUSY and the division algebras. The framework of string theory allows to draw some interesting physical consequences from these Berry phases, such as a new interpretation of the Berry phase in terms of gravitational precession and the surprising result that in certain configurations, D0 branes behave as anyons.