Local Conditions of Crystal Structures

• 主讲人：Nikolay Dolbilin (Steklov Mathematical Institute of RAS)
• 举办方： Beijing-Moscow Mathematics Colloquium
• 时间： 2023-07-02 17:00 - 2023-07-02 18:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/5B9CB00F9249BA5A27BACFBF7366AD1D
Valid Until: 2027-07-31 23:59

 

Abstract: We will give an overview of the Local Theory of regular systems and also its connection with studies of quasicrystals and of arbitrary Delone/Delaunay set. The Local Theory of regular systems relates to the foundations of Geometric Crystallography.

The mathematical model of an ideal crystal (its atomic structure) is a discrete subset X in a finite-dimensional Euclidean space that is invariant with respect to some crystallographic group G of isometries of the Euclidean space. In other words, a crystal X is the union of a finite number of G-orbits.

A single-point orbit is termed a regular system. Our attention will be focused on the lower and upper bounds for the regularity radius, which is the minimum size of clusters whose pairwise equivalence at all points of a Delone set provides the regularity of the set.

 

Bio: Nikolay Dolbilin is a leading researcher at the Steklov Mathematical Institute of the Russian Academy of Sciences and a part-time professor at Moscow State University. He also had long-term professor positions in mathematical centers and universities in Hungary, Germany, Japan, USA.

Among scientific results are the following: the proof of a local criterion of regularity and development of the local theory of regular systems, the first complete proof of the celebrated Kac-Ward formula for the statistical sum for the Ising model, studies on the theory of parallelohedra (the concepts of the contact face and its index, a theorem on the sum of indices of contact faces).

Besides, Nikolay Dolbilin paid much attention to the issues of mathematical education. He was an invited speaker at ICME-2000 at Tokyo/Makuhari, a member of the International Programm Committee of ICME-2004 in Copenhagen, a member of EC ICMI in 2003-2007.