Registration: At the end of the Honours conference, students and staff are invited for a pizza lunch provided by the MSI!
For catering purposes, please indicate if you are coming, and your dietary requirements, here: https://www.eventbrite.com/e/msi-honours-conference-s1-2019-tickets-62246399657
Satisfaction Guaranteed: The talks will be colloquium style. In particular, the first 20 minutes will be accessible to anybody who vaguely remembers the content of Algebra 2 and Analysis 2. They will run precisely on time.
Talk 1 (Monday 9:30): Bolin Han, Higher spin algebras and universal enveloping algebras
Higher spin algebras, arising from the study of the underlying global symmetries of massless higher-spin particles in physics, now become an interesting area in mathematics since people realised these algebras are deeply related to the theory of minimal representations. A well-studied special one-parameter family hs[lambda] is shown to be equivalent to a quotient of the universal enveloping algebra (UEA) of sl(2). In this talk, we review the results on hs[lambda] with some modifications and then construct new higher spin algebras from the UEA of sl(2) x V_2. In addition, we also study the centralisers in the UEA of sl(2) x V_m for other values of m in preparation to construct more higher spin algebras.
Supervisor: Peter Bouwknegt
Talk 2 (Monday 10:30): Christopher Williams, Self-Similar Models and How to Find Them: A Moment Theory Approach
How do you find a Cantor set?
How do you model a fractal object?
In this talk I will show traditional self-similar modelling techniques stemming from fractal image compression and present a new tool in the area through the use of self-similar measures.
Supervisor: Michael Barnsley
Talk 3 (Monday 1:30): Frederick Yuan, The Selberg trace formula and the Prime Orbit theorem
Supervisor: Andrew Hassell
Talk 4 (Monday 2:30): Kelly Maggs, Finding the Homotopy Type of 3D Images
3D Images contain a multitude of information from which we want to distill important features. Algebraic topology provides ready-made tools for constructing efficient and meaningful summaries of spaces.
A notable example is finding the persistent homology groups of a filtered space. In this talk, we discuss an analogous idea, replacing homology groups with homotopy groups.
This new perspective retains more information than its homological counterpart, but is significantly harder to compute. Fortunately, Discrete Morse Theory equips us with tools to greatly simplify calculations. In the case of the fundamental group, it can even be used to construct algorithms which explicitly compute our algebraic invariants.
Supervisors: Kate Turner and Vanessa Robins
Talk 5 (Tuesday 9:30): Owen Hearder, Quasilinear Stochastic Partial Differential Equations
Supervisor: Pierre Portal
Talk 6 (Tuesday 10:30): Yutong Ma, Randomized Kaczmarz Method