# IMath Webinar Series: Maria Carmen Amarra, Ph.D. and Jomar Kevin Sta. Ana

You are all invited to attend the fourth webinar of this semester’s IMath Webinar Series on Monday, May 16, 2022, 2:30pm. Dr. Amarra (of the Discrete Geometry and Combinatorics Group) and Mr. Sta. Ana (of the Matrix Analysis and Linear Algebra Group) will be our speakers.

** Maria Carmen V. Amarra, Ph.D.** (Discrete Geometry and Combinatorics Group)

**Abstract regular polytopes from orthogonal groups**

*Title:***Abstract regular polytopes are incidence structures which are generalizations of regular polygons and polyhedra. In this talk I will give a brief overview of the theory of abstract regular polytopes and present partial results on the construction of abstract regular polytopes whose automorphism group is an orthogonal group over a finite field of odd characteristic.**

*Abstract:*** Jomar Kevin D. Sta. Ana** (Matrix Analysis and Linear Algebra Group)

**Sums of \(H\)-selfadjoint, \(H\)-skewadjoint, and \(H\)-unitary matrices**

*Title:***Let \(H\) be an \(n\)-by-\(n\) nonsingular Hermitian matrix and let \(A^H := H^{-1}A^*H\). An \(n\)-by-\(n\) complex matrix \(A\) is said to be**

*Abstract:**\(H\)-selfadjoint*if \(A^H = A\); \(A\) is

*\(H\)-skewadjoint*if \(A^H = -A\); and \(A\) is

*\(H\)-unitary*if \(A^H A = I_n\). We give sufficient conditions for an arbitrary \(n\)-by-\(n\) complex matrix to be written as a sum of an \(H\)-selfadjoint and an \(H\)-unitary matrix, and as a sum of an \(H\)-skewadjoint and an \(H\)-unitary matrix.