Junior Analysis Seminar: Optimal Line Packings with Heisenberg Symmetry

December 3, 2021, 2:10-3:00pm | Carver 294

Speaker: Herionexy Mounier

Title of the Talk : Optimal Line Packings with Heisenberg Symmetry

Abstract : Zauner’s Conjecture has been a subject of study in Frame Theory for several years. It states that for any complex Hilbert space of dimension d, there exists a d x d^2 equiangular tight frame (ETF). However, we proved a consequence of this conjecture by showing the existence of some particular ETFs. This was done by considering an orbit of some action of the Heisenberg group of a finite abelian group over the set of d x d matrices with complex entries. In this talk, I will introduce the concept of an ETF, together with the main result of this research.