Honours Conference

S1 2024 Honours Conference

It is time to celebrate our Honours students and see what they have been up to!

schedule Date & time
31 May 2024 1:00pm - 31 May 2024 3:10pm
person Speaker
Lachlan Huang
Sud Hardikar
Prashant Rao
next_week Event series
Graduate Seminar
contact_support Contact
MSI Team
msi.hdr.sa@anu.edu.au
Galina Levitina
Galina.Levitina@anu.edu.au

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Description

We have three students who will present results of their Honours project. Each student will give a 30 minute talk followed by questions from the audience. The schedule for the talks can be found below. The titles and abstracts will be published next week.

Speakers:

Lachlan Huang

Sud Hardikar

Prashant Rao

Schedule:

Lachlan Huang13:00
Sud Hardikar13:45
Prashant Rao14:30

 

 

Schedule

event

schedule13:00

Computational solutions of the Grad-Shafranov equation

  • Speaker: Lachlan Huang

Toroidal magnetic confinement is the leading contender to tame a tokamak burning plasma for energy production. To leading order, all confinement, transport, and stability properties are determined by magnetic geometry. To a good approximation, the magnetic field in a toroidally symmetric tokamak is determined by solutions of the Grad-Shafranov equation (GSE). In this talk, a quick derivation of GSE will be presented. The uniqueness of the solution will be discussed. A direct method using Buneman's method will be presented. A Picard current field iteration numerical solver for the GSE is presented. Numerical results of its convergence, and computational costs will be presented. And a comparison to other kind of solver will be discussed. 

schedule13:45

A Representation-theoretic framework for Optimization

  • Speaker: Sud Hardikar

In 2010, Risi Kondor constructed a branch & bound algorithm to find exact solutions to the Quadratic Assignment Problem (QAP) by using the representation theory of the symmetric group. Remarkably, despite requiring a very intricate implementation the algorithm performed competitively in comparison to others of its time. Kondor notes his method can generalise to many other optimisation problems. In my thesis, I have proven extended variations of the key theorems relevant to this approach. In this talk, I will discuss a framework for how the representation theory of finite groups can be applied to solve any discrete optimisation problem.

schedule14:30

Discrete Approximations to 1-D Processes with Rough Generators

  • Speaker: Prashant Rao
Discretely approximating stochastic processes valued in the n-dimensional real numbers, whose generators have measurable coefficients, is an open problem if we allow any number of dimensions. The one-dimensional case, however, was solved by Etore and Lejay in 2007.
 
In this talk we introduce the problem and cover Etore and Lejay's solution. In particular, we will discuss the theory of G-convergence, which is somewhat obscure but is heavily relied upon in their paper.
 
First, we will see the problem can be reduced to showing bounds on certain probabilistic quantities. We will show how the Feynman-Kac formula allows us to express these quantities as solutions to elliptic PDEs when our coefficients our smooth. In our problem we only required the coefficients to be measurable, so we cannot immediately use this.
 
From here, we will dive into the theory of G-convergence, which we use to extend these results to the case of general measurable coefficients. We will introduce this theory, which involves functional analysis and semigroup theory, and we will show how this theory is applied to our problem to express the same probabilistic quantities as solutions to the same elliptic PDEs.
 
We will finish the talk by covering how we can use the one-dimensional notions of the speed measure and the scale function, which give us a formula for the Green's function, to prove our bounds.

Location

Seminar room 1.33, Mathematical Sciences Institute, #145 Hannah Neumann Building, Science Road, The Australian National University

-35.275387198178, 149.11925554276

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