On some problems in Combinatorial Number Theory

by Mr Alexey Semchenkov (SPbU)

Friday 25 Mar 2022, 12:00 → 14:00 Europe/Moscow

201 (SPbU Math & CS Dept)

Additive Combinatorics is an interdisciplinary subject that, roughly speaking, studies structural properties of sets in groups, related to operations + and \times. This area naturally involves tools of Number Theory, Combinatorics, Graph Theory, Ergodic Theory, Linear Algebra, Functional Analysis, and others.
To give listeners a flavour of what such a mixture of methods could look like, without too much deepening into the subject, we will consider the two following problems of Combinatorial Number Theory:
1) Given natural c > 1, how many n with n - \varphi(n) = c does exist?
2) Given large prime p, how many residues sequence 1!, 2!, 3!, ... produces modulo p ? Their solutions involve Incidence Geometry, Graph Theory, Combinatorics, and Algebraic Geometry.