## MSI Honours Conference September 2016

The MSI Honours Conference is one of the exciting annual events in MSI. It is the time for the Honours students to showcase their research projects and share with us their discoveries.

The event is open and free to all members of MSI.

## Professor Peter Hall workshop

Download the event timetable (PDF, 48KB)

The Mathematical Sciences Institute (MSI) and the Research School of Finance, Actuarial Studies and Statistics (RSFAS) at The Australian National University (ANU) are organising a one day workshop to honour and commemorate Professor Peter Hall who passed away on the 9^{th} January 2016.

## Electric-Magnetic duality

This talk will be on the subject of Electric-Magnetic duality, explaining in particular the paper by Goddard-Nuyts-Olive which introduced the ideas of a such a duality, and ending with the definition of the Langland dual.

## Exact sequences and homology

The techniques of homology are a powerful tool in many areas of algebra, including algebraic geometry and topology. In this talk I will define the notions of exact sequences and chain complexes, prove some basic homological facts, including the snake lemma, and introduce the key computational tool of the long exact sequence of homology. Some basic knowledge of groups and rings will be assumed.

## Analytic Semigroups

This talk will introduce operator semigroup theory, discuss the class of analytic semigroups, and outline some applications of this theory to PDE, specifically regularity theory. A semigroup is a family of operators $t \to T(t):X \to X$ that we can interpret as evolution of a system over time. Any semigroup is uniquely generated by some operator A, and more interesting semigroups are generated by unbounded operators. Given suitable conditions on A, we can generate an analytic semigroup using the Cauchy Integral Formula from complex analysis.

## Electric-Magnetic duality

This talk will be on the subject of Electric-Magnetic duality, explaining in particular the paper by Goddard-Nuyts-Olive which introduced the ideas of a such a duality, and ending with the definition of the Langland dual.

## Vote Counting as Mathematical Proof

Paper-based elections are gradually being replaced with electronic alternatives, creating the need for a new kind of election scrutiny in order to have trust in the outcome. By viewing vote-counting rules as analogous to proof rules in mathematical logic, I will explain how we can formalise vote-counting protocols in the setting of constructive type theory, and how the Curry-Howard isomorphism means we can 'extract' a provably correct vote-counting program from a proof of the existence of winning candidates.

## Analyzing stochastic models for chemical master equation

Continuous Markov Chain is used in classical stochastic model for chemcial reactions. CME (chemcial master equation) is a differential equation for the probability of a certain state at certain time. In this talk, i will focus on the primilarily relationships between the model and the chemical reactions. Examples will be introduced.

## Discontinuous Galerkin Method For the Advection Equation

There are many methods available to approximate the solution of partial differential equations. Some methods work well for elliptic problems, others are better adapted to hyperbolic equations. I will first look at two classical methods, the finite element method and the finite volume method, and I will use the advection equation to demonstrate the advantages and disadvantages for each method when approximating hyperbolic equations.