A number of interesting problems in physics can be phrased in terms of connection problems of ordinary differential equations. These are deeply connected to a class of

Riemann-Hilbert problems, of isomonodromy type,

which was recently solved using techniques from conformal field theory.

In this talk, I’ll summarize my efforts to understand the simplest non-trivial case, which comprises the connection problem for the Heun equation. These arise in a number of problems in physics, such as black hole scattering and the construction of

uniformizing maps in complex analysis.

The relevant tau function in this case is the famous

Painlevé transcendents of types V and VI,

which can be expanded in terms of

Nekrasov functions at c=1

or Fredholm determinants.

I will show that the accessory parameters of the Heun equation can be obtained from

zeros of the tau function,

and discuss analytical and numerical implementations of the method in order to calculate

quasi-normal modes of black holes.

## What Liouville, Painlevé e Virasoro have to say about black holes?

Research Group:

Bruno Carneiro da Cunha

Institution:

Federal University of Pernambuco

Schedule:

Tuesday, July 9, 2019 - 14:00

Abstract: