LisMath Seminar 

28/11/2018, 17:00 — 18:00 — Room P9, Mathematics Building
Salvatore Baldino, Instituto Superior Técnico

String theory and integrability

The goal of this seminar is to introduce the concept of integrability, showing how it can be applied to obtain solutions for dynamical systems. We will then apply the tools that we build in the first part of the talk to attack a problem that is relevant in topological string theory, the problems of the KP and KdV hierarchy. We will introduce those problems in a self-contained way, explore the use of the technique of the Lax pairs to solve them and finally we will see how those solutions are of use in matrix models, that appear in minimal string theories of interest.

Bibliography:

[1] E. Witten, Two-dimensional gravity and intersection theory on moduli space, Survey in Differential Geometry, 243-310 (1990)

[2] R. Dijkgraaf, Intersection theory, integrable hierarchies and topological field theory

[3] P. van Moerbecke, Integrable foundations of string theory, In: Lec- tures on Integrable Systems, ed by O. Babelon, P. Cartier, Y. Kosmann- Schwarzbach (World Sci. Publishing, River Edge, NJ, 1994) pp 163-267

[4] R. Dijkgraaf, E. Witten, Developments in topological gravity

See also

[S_Baldino]_String_Theory_and_Integrability.pdf