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# 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)
Title: Abstract regular polytopes from orthogonal groups
Abstract: 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.

Jomar Kevin D. Sta. Ana (Matrix Analysis and Linear Algebra Group)
Title: Sums of $$H$$-selfadjoint, $$H$$-skewadjoint, and $$H$$-unitary matrices
Abstract: 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 $$H$$-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.