Public Lecture in English

The lecture provides an overview of the question of whether the shape of fullerenes – carbon molecules composed of pentagons and hexagons – can be determined from their spectrum, based on Mark Kac's problem »Can you hear the shape of a drum?« It shows how the analysis of random eigenvalues of regular lattices, in particular the hexagonal lattice (graphene) and its dual triangular lattice, leads to explicit descriptions of spectral distributions by interpreting closed paths as moment sequences of suitable random variables.

In addition, the transfer of this framework to nanotubes, which are described as »rolled-up« graphene sheets by a chiral vector ((p,q)), is discussed. It is shown that the corresponding spectral distributions converge to those of the infinite hexagonal lattice in the limit (p+q → ∞), thus establishing a mathematical bridge between finite structures and the idealized graph model.

Finally, current advances and open problems in the spectral geometry of fullerenes are discussed. Using local weak convergence, a conjecture is formulated according to which large random fullerenes approximate the spectral distribution in a suitable way.

Speaker:

Prof. Dr. Evgeny Spodarev from the University Ulm