| School of Mathematical Sciences Colloquium Series | |
Adventures with group theory: counting
and constructing polynomial invariants for applications in quantum
entanglement and molecular phylogenetics
by
Dr Peter Jarvis
Date: Friday, June 8, 2012
Time:
15:10 Location: B.21 Ingkarni
Wardli
Abstract: In many
modelling problems in mathematics and physics, a standard challenge is
dealing with several repeated instances of a system under study. If
linear transformations are involved, then the machinery of tensor
products steps in, and it is the job of group theory to control how the
relevant symmetries lift from a single system, to having many copies.
At the level of group characters, the construction which does this is
called PLETHYSM. In this talk all this will be contextualised via two
case studies: entanglement invariants for multipartite quantum systems,
and Markov invariants for tree reconstruction in molecular
phylogenetics. By the end of the talk, listeners will have understood
why Alice, Bob and Charlie love Cayley's hyperdeterminant, and they
will know why the three squangles -- polynomial beasts of degree 5 in
256 variables, with a modest 50,000 terms or so -- can tell us a lot
about quartet trees!
The Colloquium will be followed by a reception for our speaker in
the Staff Tea Room with wine and nibbles to which all are invited.