Numerical semi-groups and applications

04.04.2023, 15:00  –  Online Seminar
Arbeitsgruppenseminar Analysis

Abdallah ASSI (University of Angers)

A numerical semigroup  (NSG for short) is a monoid S of the set N of non negative integers such that the group generated by S in Z is Z (that is, S is stable under addition, 0 is an element of S, and the GCD of the elements of S is 1). Given a NSG S, there exists a finite number of elements, a_1,...,a_n, of S such that S=a_1N+....+a_nN. Moreover,  there exists an integer in N\S, denoted F(S), such that  every integer > F(S) is in S. We call F(S) the Frobenius number of S. Then we can associate with S many numerical invariants, and this gives rise  to many combinatorial problems and conjectures. In addition, NSGs appear in many areas in mathematics, in particular they give us an arithmetic tool in the problem of classification of singularities of plane algebraic curves. The purpose of this talk is to give a review of the results, problems, conjectures, and applications related to this field.

Please keep in mind that the fourth session will take place on May 16th 2023 at 3pm (CET) with a talk by Joseph AYOUB (University of Zurich).

This talk is part of the colloquium "Mathematics in Lebanon and beyond," of the partnership between the University of Potsdam and two universities in Beirut, the Lebanese University (UL) and the American University of Beirut (AUB). The colloquium will serve as a meeting place for scientific exchange, bringing together mathematicians and physicists from the Lebanese diaspora, friends of Lebanon from around the world, and researchers based in Lebanon.

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