IMath Webinar Series: Maria Carmen Amarra, Ph.D. and Eloise Misa

You are all invited to attend the first seminar of this semester’s IMath Webinar Series on Monday, October 3, 2022, 2:00pm. Dr. Amarra (of the Discrete Geometry and Combinatorics Group) and Ms. Misa (of the Matrix Analysis and Linear Algebra Group) will be our speakers.

Maria Carmen V. Amarra, Ph.D. (Discrete Geometry and Combinatorics Group)
Title: Block-transitive, \(s\)-chain imprimitive designs
Abstract: A block design consists of a finite set of elements called points, and a collection of subsets of points with a fixed size, called blocks. An automorphism of a block design is a permutation of the point set which preserves the block set. In this talk, we will define an \(s\)-chain imprimitive action on a set, and show a construction of block designs which admit an automorphism group that acts transitively on blocks and \(s\)-chain imprimitively on points. This is joint work with Alice Devillers and Cheryl Praeger.

Eloise Misa (Matrix Analysis and Linear Algebra Group)
Title: Sums and products of nilpotent elements in a matrix centralizer
Abstract: For an arbitrary square matrix \(S\), denote by \(C(S)\) the centralizer of \(S\), and by \(C(S)_N\) the set of all nilpotent elements in \(C(S)\). We use the Weyr canonical form to study the sums and products of matrices in \(C(S)_N\). In this talk, we give necessary and/or sufficient conditions such that \(A \in C(S)\) is a sum or a product of nilpotent matrices in \(C(S)\).