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Combinatorics and Optimization Seminar

March 15, 2012 at 11:30 AM to 12:30 PM

Location:4369 HP Herzberg Laboratories
Cost:Free

Speaker: Prof. Aiden Bruen

Title:  Euler’s problem, Bruck’s embedding theorem, quantum information

theory and a theorem of Gallucci.

Abstract:  It was Euler who first posed the “problem of the 36 officers”

,solved by Tarry in 1901.  Since then the question of determining the

maximum number of mutually orthogonal latin squares [mols] of a given

order n has been central .  Interest in the problem has recently

increased because of a putative connection with a basic question in

quantum information theory.  R.H.Bruck showed that a “large “ set of

mols can be embedded in a complete set.  In this lecture we provide a

construction for a “fairly large” but unimbeddable system of mols.  This

is the largest known such system.  The main tool in the construction is

a classical result in line geometry known as Gallucci’s theorem but

which goes back to Dandelin circa 1826.

Short Biography:  Aiden A Bruen was born in Galway, Ireland. He read

mathematics for his B.Sc and M.Sc at University College, Dublin.  He

took his PhD in incidence geometry at the University of Toronto under

the supervision of F.A.Sherk.  At Toronto he also worked with Professors

Coxeter,Ellers and Lehman. Prior to his arrival at Calgary  he was on

staff at Los Alamos.  Currently he is an Adjunct Professor in the ECE

department. He works in finite geometries, codes, cryptography and other

topics in discrete mathematics