We will explore three pieces of analytic theory connected with crystals and crystallographic symmetries.

# Videos

## The Australian Mathematical Science Institute and the IRMACS Centre Present:

A Workshop on Computational and Analytical Mathematics - Video Recordings

Crandall, Richard

Analysis of brain-synapse coordinates in actual mouse-brain tissue has recently revealed that the synapses are not randomly distributed. So is there a pattern? In a sense, yes; in another sense, no. The lecture will touch upon such as: Fractal sets and their fractional dimensions, how to construct fractals that agree with real-world laboratory...

Mclellan, Karyn

This talk will extend some ideas from both Viswanath's and Rittaud’s work on random Fibonacci sequences. First, we will look at second order linear recurrence sequences whose coefficients belong to the set *TeX Embedding failed!* and form periodic cycles. We will analyze the growth of such sequences and develop criteria for...

Noble, Rob

The weighted Delannoy numbers give a weighted count of lattice paths starting at the origin and using only minimal east, north and northeast steps. Full asymptotic expansions exist for various diagonals of the weighted Delannoy numbers. In the particular case of the central weighted Delannoy numbers, certain weights give rise to asymptotic...

Lewis, Adrian

Concrete optimization problems, while often nonsmooth, are not pathologically so.

The class of "semi-algebraic" sets and functions - those arising from polynomial

inequalities - nicely exemplifies nonsmoothness in practice. Semi-algebraic sets

(and their generalizations) are common, easy to recognize, and richly structured,...