Week starting Monday 21 May 2018
Gross, et. al. defined an index for bosonic “locality preserving” unitaries which measures net transport of quantum information (left or right). This index has a fermionic generalization (due to Fidkowski et.al.) important in Floquet physics. I will discuss a generalization of this index to higher dimensions where it assumes the form of an incompressible flow. I feel that this generalization is ½-interesting: Some new idea needs to be added to find cool applications, perhaps to knot or manifold invariants. I will seek the advice of the audience.
In 1968 Waldhausen gave a beautiful proof that the three sphere has a unique (up to isotopy) Heegaard decomposition into two genus g handlebodies. I’ll show you Waldhausen’s proof and sketch one or two others. We'll then proceed to generalizations to other 3-manifolds, and parametric versions, e.g. the Powell conjecture (on which there is a recent arXiv posting with M. Scharlemann).
Young maths enthusiasts from across the region are invited to battle it out in a test of mind and muscles at ANU Maths Day.
In teams of five, year 12 students take part in mathematical challenges designed to build teamwork skills and promote a love of maths. The day is divided into four challenges:
- a group of story problems
- a swiss 'find the rule' problem
- a cross number puzzle
- and the day’s highlight, the relay – a test of brainpower and physical stamina.
ANU Maths Day has been running in the ACT since 1982. The University's competition includes contestants from schools in Canberra, Wollongong, the South Coast, Southern Highlands and Sydney. The day gives the students a chance to meet another 160 like-minded young people who are into mathematics, which is particularly important for people from smaller schools.
ANU Maths Day isn’t all about being the cleverest or the brightest. Activities are formulated to ensure that everyone can have a go and have fun while taking part in some healthy and rigorous competition.
Registrations will are open!
Sample questions & solutions
We will discuss recent work joint with Jacob Bridgeman and Corey Jones on domain walls between topological phases.
Session 9 of the Canberra Mathematics Enrichment programme.