# AUMS Student Talks

AUMS has been running student talks - informal talks, given by students, pitched at an undergraduate level. The talks act as an opportunity for students to see some maths that they may not otherwise see during their degree. They also act as a platform for students to practice giving presentations, which is an important skill for all students to have, especially those planning to do Honours (and beyond).

If you would like to suggest a topic for a talk you'd like to see, let us know either via our Facebook page, or contact us via email.

## Upcoming Talks Show/Hide

## Past Talks (2016)

**Speaker:** Daniel Kon

**Title:** The Unsuccessful Search for a 3D Mandelbrot Set

**Date:** Friday 28 October, 5pm

**Location:** LG28, Lower Napier, the Universty of Adelaide

**Abstract:** The Mandelbrot set is a famous two dimensional fractal—an object, generated from a mathematical formula, which has infinite detail and fascinating self-similar structures. What is the three dimensional equivalent of this set? How can we know if we've found such a thing?

In this talk I explore the world of three dimensional fractals, working through the computational steps required to render images of them. Many have applied these processes to search for candidate fractals that are worthy of being considered the successor of the Mandelbrot set.

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**Speaker:** Vanessa Glenny

**Title:** Latent Dirichlet Allocation

**Date:** Friday 14 October, 5pm

**Location:** LG28, Lower Napier, the Universty of Adelaide

**Abstract:** Topic modelling is an area of natural language processing concerned with finding hidden structures, or 'topics', in large amounts of text. These statistical models are used for finding information in things such as news articles, books and movie scripts.

This talk will introduce Latent Dirichlet Allocation, arguably the most famous and widely used of topic models.

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**Speaker:** Nathan Companez

**Title:** Proving the Five Colour Theorem

**Date:** Friday 9 September, 5pm

**Location:** LG28, Lower Napier, the Universty of Adelaide

**Abstract:** Graph theory is the study of relation between objects. While this definition sounds far too vague to be useful, graph theory has proven to have many applications, especially in the field of computer science. More importantly, though, it is full of interesting proofs

This talk will show that elegant and powerful proofs in graph theory do not require a deep background in the subject. Specifically, the five colour theorem will be proved without requiring any previous knowledge or results. The five colour theorem states that any map requires only five colours in order to ensure that no two adjacent countries share a colour.

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**Speaker:** Nicolas Rebuli

**Title:** Introduction to Mathematical Epidemiology

**Date:** Monday 22 August, 5pm

**Location:** LG29, Lower Napier, the Universty of Adelaide

**Abstract:** A common ethos of mathematicians of all levels is that mathematics is the ultimate tool for understanding and resolving problems which arise in the real world. However, throughout my undergraduate degree I often wondered where these problems came from, if any had the potential to make an impact on society, and what level of mathematics would be required to model them faithfully. For example, the game Craps can be analysed using techniques taught in second year, but who plays Craps?!

In this talk I will introduce you to my area of research and convince you that it has the potential to make a positive impact on society. My research is in the area of Mathematical Epidemiology, which focuses on modelling the spread of infectious diseases for the purpose of predicting the probability of future states of the spread of the disease. I will introduce you to some popular epidemiological models which use techniques taught in second and third year. Namely, computer-based simulation, ordinary differential equations, discrete-time Markov chains, and continuous-time Markov chains. I will also describe some of my own research and how it ties in with the afforementioned models.

To demonstrate how these models can be used to investigate data from the real world I will investigate the simulated outbreak of a particularly horrifying disease, commonly referred to as zombieitis.

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**Speaker:** Russell Edson

**Title:** Draw Fractals with Barnsley's Chaos Game

**Date:** Tuesday 16 August, 5pm

**Location:** LG29, Lower Napier, the Universty of Adelaide

**Abstract:** Fractals are mathematical structures with beautiful visual complexity, whose patterns can often be described using very little information. They appear everywhere in computer graphics and digital art, since many natural phenomena like trees and mountains can be generated with high detail using fractal descriptions. Fractals are also important objects in chaos theory: the strange attractors of chaotic dynamical systems are fractals.

In this talk, we will see Barnsley's chaos game. This simple algorithm plots fractals as the attractors of iterated function systems. We will also see the collage theorem, which tells us how to construct an iterated function system with an attractor that approximates a fractal we want to draw. The combination of the collage theorem with the chaos game empowers us to draw many interesting fractals!

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**Speaker:** John McCarthy

**Title:** The Poincaré Conjecture and the Classification of Spaces

**Date:** Friday 5 August, 5pm

**Location:** LG28, Lower Napier, the Universty of Adelaide

**Abstract:** In 1904 Henri Poincaré conjectured that 3-dimensional spaces without holes were equivalent to the 3-dimensional sphere. The Poincaré conjecture became one of the most important problems in geometry and topology during the 20th century. In the year 2000 it was chosen to be a Millenium Prize problem by the Clay Mathematics Institute, with a $1 million prize offered for a solution. In 2003, the enigmatic Russian mathematician Grigori Perelman found a solution, but declined the Millenium Prize offered to him in 2006. Perelman's solution arose from the joining of geometry with analysis, and had far-reaching applications to the classification of all possible 3-dimensional spaces

In this talk we will investigate the statement of the Poincaré conjecture and Perelman's proof, and explore the implications for the classification of all closed 3-dimensional spaces.

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**Speaker:** Adam Hamilton

**Title:** Games, Infinity and Other Surreal Things

**Date:** Friday May 27th, 5pm

**Location:** LG28, Lower Napier, the Universty of Adelaide

**Abstract:** The surreal number system belongs to the family of mathematical objects called Things You Probably Haven't Heard Of And Will Almost Certainly Never Use. In this talk we define this number system and wrap our heads round the completely different set of axioms that govern it as well as seeing how this completely new number system can be used to solve problems in Combinatorial Game Theory.

**Speaker:** Alexander Tam

**Title:** The Unreasonable Effectiveness of Applied Mathematics

**Date:** Friday May 13th, 5pm

**Location:** LG28, Lower Napier, the Universty of Adelaide

**Abstract:** Applied mathematics is one of the three disciplines in which a mathematics student can major at the University of Adelaide. While mathematics is a subject based on abstract logic, applied mathematics is somewhat paradoxically referred to as "the useful kind of maths" or "the maths of the real world". Unfortunately, these terms do not provide much insight into what applied mathematics actually is. This talk will discuss how the development of mathematical ideas readily enables mathematical modelling, the process that underpins all applied mathematics. The modelling framework will be used on a problem of bacterial growth, showing how a small number of simple assumptions leads to surprisingly complex patterns.

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**Speaker:** Jayden Redden

**Title:** The Mathematics of Juggling:

Parabolas, Space-Time Diagrams, Elementary Catching and bit of Group Theory

**Date:** Friday April 8th, 5pm

**Location:** LG28, Lower Napier, the Universty of Adelaide

**Abstract:** A brief look at the physics and mathematics that model the art of flying balls, a deeper look at the underlying structure inherent in juggling patterns, and how mathematics can lead to new ways of juggling. Using the theory of siteswap notation we can show the existence and uniqueness of juggling patterns. Can we form a Group from these patterns under a binary operation and create routines?

This talk explores the marriage of both art and science, how artists can intuitively understand deep mathematical and physical properties and how mathematicians can explore and architect these ideas to bring rigour and structure that the artists can to use to surprise and delight audiences.

**Speaker:** Michael Hallam

**Title:** What is a Manifold?

**Date:** Friday April 1st, 5pm

**Location:** LG29, Lower Napier, the Universty of Adelaide

**Abstract:** Manifolds play key roles in many areas of modern mathematics and physics. They provide a general setting for calculus and the study of differential equations, geometric notions such as shape and curvature, and are foundational in general relativity and string theory. The aim of this talk is to explain what manifolds are to an undergraduate without the background needed to understand the technical definition.

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**Speaker:** Diclehan Erdal

**Title:** Perfect Numbers

**Date:** Friday March 11th, 5pm

**Location:** LG28, Lower Napier, the Universty of Adelaide

**Abstract:** Perfect numbers have been studied since antiquity and they represent some of the earliest work in the field of number theory. Major figures who worked with them seriously include Euclid, Descartes, Euler and Sylvester. This talk aims at exploring the history of perfect numbers, as well as looking at elementary results concerning them.

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