Public lectures given by

 Prof. Sir Michael V. Berry

 and

Prof. Gary W. Gibbons

 organized by the Pál Csonka PhD School in the framework of the project

TÁMOP-4.2.2/B-10/1-2010-0009

9th May 2013, 10:00 - 11:45

Hungarian Academy of Sciences, Large lecture room

Széchenyi István tér 9., 1051 Budapest

Prof. Sir Michael V. Berry:

Quantum, chaos, and the singing of the primes

The Riemann hypothesis can be interpreted as stating that the prime numbers contain music, whose component frequencies are the Riemann zeros. The question Frequencies of what? leads to tantalizing connections with the energy levels of quantum systems whose corresponding classical motion is chaotic, and the analogy suggests directions for seeking the elusive dynamical syste whose corresponding quantum eigenvalues are the zeros. At the level of statistics, predictions for the Riemann zeros based on semiclassical quantum asymptotics (with primes as periods of classical trajectories) have reached a high degree of accuracy and refinement. For the zeros themselves, the Riemann-Siegel formula and its improvements lead to new ways of calculating quantum levels.

Prof. Gary W. Gibbons:

Black holes: from Astrophysics to String theory

This talk will be an overview and history of black holes from

John Michell's original prediction in 1784 to the present day aimed at the non-specialist. Although usually thought of as a major part of modern relativistic astrophysics, both observational and theoretical, which of course they are, black holes currently also play a central role in quantum gravity: the theoretical attempt to unify Quantum Mechanics and Einstein's General Relativity. A sort of inside out black hole caused by cosmic repulsion due to dark energy is responsible for quantum fluctuations in an inflationary stage of the early universe which grew to make the stars and galaxies we see today. These developments have also provoked experimenter's to try to design analogues which could be built in the laboratory.