I will discuss the various completed, ongoing, and planned mathematics visualisation projects within CARMA's SeeLab visualisation laboratory.

Bio: Michael Assis was awarded a PhD in Statistical Mechanics at Stony Brook University in 2014, and then took a postdoctoral fellowship at the University of Melbourne. In 2017 he held a computational mathematics postdoctoral position within CARMA, and earlier this year he worked to develop CARMA's Seelab mathematics visualisation laboratory together with David Allingham.

Given a sequence of integers, one would like to understand the pattern which generates the sequence, as well as its asymptotics. If the sequence is viewed as the coefficients of the series expansion of a function, called its generating function, many questions regarding the sequence can be answered more easily. If the generating function satisfies a linear ODE or a nonlinear algebraic DE, the differential equation can be found if enough terms in the sequence are given. In this talk I'll discuss my implementation in C of such a search, applications, and a systematic search of the entire Online Encyclopedia of Integer Sequences (OEIS) for generating functions.

I will discuss how to relate regular origami tilings to vertex models in statistical mechanics. The Miura-ori origami pattern has found many uses in engineering as an auxetic metamaterial. I analyze the effect of crease assignment defects on the long-range order properties of the Miura-ori and 4 other foldable lattices. These defects are known to affect the material's compressibility properties, so my exact results help to understand how easy it is to tune an origami metamaterial to have desired compressibility properties by introducing a set density of defects. I have found that certain origami patterns are more easily tunable than others, and conversely, the long-range ordering of some are more stable with respect to defect formation. I have also found analytical expressions for the locations of phase transition points with respect to crease assignment ordering as well as layer ordering.