Centre for Research in Mathematics

Higher homotopy, higher groupoids

Steve Lack (Macquarie University)
Monday, 15 October 2012, 15:30-16:30

SCEM AccessGrid (KWD-Y.2.39, PTA-EB.1.32, CTN-26.1.50) presented from Parramatta

Topology is a branch of geometry in which objects are regarded as being the same if one can be transformed into the other by bending or stretching (tearing and glueing are not allowed). It is sometimes also called "rubber sheet geometry". Homotopy theory is a part of topology in which the geometric objects (called spaces) are studied via algebraic ones, such
as groups and groupoids.

In this talk, I shall describe groupoids, and how to associate to any space a groupoid, called the fundamental groupoid, which can be seen as measuring the "one-dimensional holes" in the space. I shall then go on to describe higher-dimensional analogues of groupoids, and how they can be used to measure the higher-dimensional holes in spaces.

The Breaking of JN-25

SCEM AccessGrid (KWD-Y.2.39, PTA-EB.1.32, CTN-26.1.50) presented from Kingswood

JN-25 was the name given by the Allies to the main operational code used by the Imperial Japanese Navy (IJN) during World War II. It was broken into almost immediately after its introduction in mid-1939 by John Tiltman, one of the greatest World War II British code breakers. It continued to be broken throughout the war, and yielded by far the majority of useful signals intelligence regarding IJN operations available to the Allies. At the same time, the Imperial Japanese Army (IJA), using the same cryptographic systems, maintained their security until early 1943, when only one important system was broken. All others defied
attack.

The talk will describe the coding system used, why the IJN was insecure, and how this was exploited.