Prof. Dr. Evgeny Spodarev (Ulm University, Germany)
【Title】
Spectral properties of fullerenes
【Abstract】
Fullerenes $C_n$ are 3-simple convex compact polytopes with $n$ vertices, $n\ge 20$ even, $n\neq 22$, 12 pentagons and $n/2-10$ hexagons as facets. They are mathematical models of famous carbon molecules which find wide applications in modern nanotechnologies. For the synthesis of $C_60$, R. Curl, H. Kroto and R. Smalley got a Nobel prize in chemistry (1996). Since the number of distinct fullerene isomers (which are combinatorially non—equivalent versions of $C_n$) grows as $O(n^9)$ for large $n$, their enumeration and classification is a non-trivial mathematical problem. We propose a solution to this problem using the Newton polynomials of the spectra of their dual graphs of hexagons. It appears that the degree of such polynomials has a logarithmic growth order with respect to $n$. The spectral linear ordering of characters of $C_n$ for different $n$ as well as the distribution of a random eigenvalue of Laplace-type matrices for the graphene, regular triangulation of the plane and infinite nanotubes with chiral vector $(p,q)$ will be touched upon as well.
Joint work with A. Bille (Skoltech, Moscow/Ulm University), V. Buchstaber (Steklov Mathematical Institute, Moscow) and S. Coste (INRIA, Paris)
【Reference】
A. Bille, V. Buchstaber, E. Spodarev, "Spectral clustering of combinatorial fullerene isomers based on their facet graph structure", J. Math. Chemist., 59 (2021), 264-288. https://doi.org/10.1007/s10910-020-01193-4
