# Lunchtime Seminar Series

## Lunchtime Seminar Series

A series of talks presented by staff from the Department of Mathematics, on topics of broad general interest. The talks will be aimed at the lower undergraduate level and should be accessible to anyone who has experience with first year mathematics and an interest in seeing the wide range of possibilities the study of mathematics affords.

Talks take place 1pm-2pm on Tuesdays during semester 1 and 2.

Contact: Richard Garner (richard.garner@mq.edu.au)

#### Session 1, 2017

Talks take place in C5A 310, 1pm-2pm

• Tuesday 23 May:  Christopher Cooper "Several Slices of Pi"
• RECIPE FOR PI
Take one of each odd natural number.
Square each of them and take their reciprocals.
Mix together and bake in an infinite sum.
Garnish by multiplying by 8 and taking the square root.
This will make one delicious pi.

The geometric definition of pi is the ratio of the circumference of a circle to its diameter. This is fine, unless you happen to be a disembodied angel, an intelligent being with no concept of the spatial world ("what is a circle?"). The definition in terms of an infinite series would be more satisfactory in that case.

We'll also discuss some other definitions of pi: the biblical definition in 1 Kings 7:23, the statistician's definition in terms of throwing sticks on the floorboards, and finally the astronomer's definition based on the brightness of the moon.

Finally we'll ask whether we should reject pi and become Tauists instead.

• Tuesday 9 May:  Steve Lack, "Counting and Measurement"
• Abstract:  The traditional approach to counting is to use whole numbers, and the traditional approach to measurement is to use real numbers. I’ll argue that counting sometimes leads to negative numbers and that measurement should often be done with polynomials. To do this requires a tiny modification to the rulers we use, as I shall also explain.

• Tuesday 11 April:  Emily Riehl, "A solution to the stable marriage problem"
• Abstract: Consider what might called the “matchmaker’s dilemma”: A matchmaker wishes to arrange (opposite-sex) marriages in a dating pool of single men and single women in such a way that no unmatched couple would prefer to elope together rather than remain with their assigned partners.  (There is a mathematical reason that this theory requires a heteronormative framework that will be discussed). Is it always possible, given any numbers of men and women, each with their own personal preferences, to arrange marriages that are stable in this way?

We’ll discuss this problem, an algorithmic solution, its sexist implications, and a real-world application that demonstrates that the theorems proven here aren’t simply another case of “mathematical make-believe.”

• Tuesday 28th March:  Richard Garner, "Cataloguing the Alhambra"

Abstract: Islamic art provides a cornucopia of intricate and beautiful geometric patterns; particularly interesting to mathematicians are those made by sticking polygons together in a repeating pattern which tiles the plane. For a long time people have sought ways of cataloguing these patterns, but it was not until the 1980's that the definitive way of doing so was found by Delaney and Dress. In this talk I will give an interactive introduction to these "Delaney-Dress symbols" and to the rich world of patterns that they can encode.

#### Session 2, 2016

Talks take place in C5A 315, 1pm-2pm

• Tuesday 30th August: Chris Cooper, "The many faces of a cube"
• Tuesday 13th September: Richard Garner, "On dithering, uncertainty and loping basslines"
• Tuesday 4th October: Jim Denier, "Fluid Mechanics: what’s Maths got to do with it?"
• Tuesday 18th October: Steve Lack, tbc
• Tuesday 1st November: William Chen, "There is no integer between 0 and 1, and Schmidt chocolate cake theorem"