School of Mathematical Sciences 2017 / 2018 SUMMER VACATION RESEARCH PROJECTS Summer Vacation Period 20 November 2017 to 26 February 2018 Applications are open for the 2017 / 2018 AMSI and Monash summer vacation scholarships

Please contact the supervisor for more details, prerequisites and to obtain the required formal letter of support, before applying. How to apply .................................................................................................................................... 2 Applied and Computational Mathematics .................................................................................... 3 1.

Splitting integer linear programs with a Lagrangian axe ..................................................... 3

2.

Aggregation decomposition methods in a mining application ............................................. 3

3.

Simulating Lava Flows using Smoothed Particle Hydrodynamics ...................................... 3

4.

Numerical Optimization Methods for Big Data Analytics..................................................... 4

5.

Mathematics and Optimisation for Cryogenic Electron Microscopy .................................... 4

6.

Numerical Optimisation Applied to Monte-Carlo Algorithms for Finance ............................ 4

7.

MHD modelling of the evolution of proto-spicules in the solar chromosphere .................... 4

Pure Mathematics ........................................................................................................................ 5 8.

Functionals of higher-order derivatives of curvature for surfaces ....................................... 5

9.

Parallelogram polyominoes, partitions and polynomials ..................................................... 5

10.

How many ways are there to cover a sphere? .................................................................... 5

11.

Knots, polynomials and triangulations ................................................................................ 5

12.

Gravitational Waves: a mathematical analysis ................................................................... 6

13.

Exploring combinatorial geometry ....................................................................................... 6

14.

Fourier restriction estimates ................................................................................................ 7

15.

3D axisymmetric Navier-Stokes equation. .......................................................................... 7

16.

Some topics in nonlinear dispersive equations ................................................................... 7

Statistics and Stochastic Process ................................................................................................ 8 17.

The percolation on cellular automata .................................................................................. 8

18.

Inference of biological systems using approximate Bayesian computation ........................ 8

1

How to apply What does this AMSI/Monash scholarships offer me?  the chance to work on a real research project for six weeks  travel and accommodation to attend the AMSICONNECT student conference in Melbourne  a six-week award of $450/week (total $2,700) Eligibility These scholarships are open to students who:  are currently enrolled at an AMSI Member university  are in their third year doing a major in the mathematical sciences (outstanding second year students with the support of their department may apply)  have a strong academic record  intend to go on to honours and/or postgraduate study in the mathematical science