Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Στούμπος Κωνσταντίνος
Supervisors info:
Απόστολος Γιαννόπουλος Καθηγητής (Επιβλέπων), Αριστείδης Κατάβολος Καθηγητής, Παντελής Δοδός Επίκ. Καθηγητής
Original Title:
Φασματική αραιοποίηση και το πρόβλημα Kadison-Singer
Translated title:
Spectral Sparcification and the Kadison Singer problem
Summary:
The subject of this master thesis is to study the Kadison-Singer problem and to
present the method of interlacing families of polynomials, which Marcus,
Spielman
and Srivastava invented and used in order to give a solution.
The method is based on techniques of linear algebra, combinatorics and complex
analysis and it is elementary and powerfull. This method has also been used by
the
same authors to give a solution to a problem of spectral graph theory about
Ramanujan graphs. The above application is contained in the last part of this
thesis.
Keywords:
Interlacing families of polynomials, Real stable polynomials, Mixed characteristic polynomial, Expander families of graphs, Ramanujan graphs
