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The classical Schur-Horn theorem characterizes the set of diagonals of the unitary orbit of a self-adjoint matrix in terms of a set of linear inequalities called majorization. In 2002 Kadison discovered a characterization of the diagonals of orthogonal projections on infinite dimensional Hilbert spaces. Since Kadison's breakthrough there has been a great deal of work by several authors to extend the Schur-Horn theorem to all self-adjoint operators on infinite dimensional Hilbert spaces. In this talk we discuss our recent contributions to this effort.
We give an overview of Riemann surfaces and present a sketch of a proof on necessary conditions for which a Riemann surface may be represented as an algebraic curve over the algebraic numbers. This result is known as Belyi's theorem from 1979. We then describe an application of this theorem: to form bipartite graphs on Riemann surfaces known as dessins d'enfants, French for "children's drawings".
In collaboration with the Statistics Department, EECS, and CGRB,
the Mathematics Department will host the 2015 Milne Lecture.
This year’s speaker is Michael Waterman http://dornsife.usc.edu/labs/msw/
Notably Mike is an OSU Alumnus who graduated with a major in Mathematics !
He will present the Milne lecture on the first day of Spring term, March 30,
and a follow up seminar on Wednesday April 1. Watch for follow up postings on
the Math Department Colloquium and Mathematical Biology Seminar postings.
The 2015 Milne Lecture Committee...