Lunchtime Seminar Series

Lunchtime Seminar Series

Lunchtime Seminar Series

A series of talks presented by staff from the Department of Mathematics and Statistics, 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 statistics and an interest in seeing the wide range of possibilities the study of mathematics and statistics affords.

Contact: Justin Tzou (justin.tzou@mq.edu.au)

Session 1, 2019

DETAILSTITLE & ABSTRACT

Tuesday 21 May:

Dr Hassan Doosti (Lecturer in Statistics, Macquarie University)

When: Tuesday 21st May 2019
Time: 12:00pm - 1:00pm
Where: 12 Second Way, room 310

Title:  Introduction to Quantile Regression

Abstract: In this talk, we will briefly introduce quantile regression and some of its applications. Whereas the ordinary regression models provide a grand summary for the averages of the distributions corresponding to the set of predictors, quantile regression aims at estimating the conditional quantiles of the dependent variable. Robustness against outliers of the regressand, higher efficiency for a wide range of error distributions and no distribution assumptions are main advantages of quantile regression. In the following figure, ordinary mean regression (left) does not show significant changes. However, some quantile regressions (right) show clear patterns, particularly for larger quantiles.

Tuesday 07 May:

Dr Richard Garner (Senior Lecturer in Pure Mathematics, Macquarie University)

When: Tuesday 7th May 2019
Time: 1:00pm - 2:00pm
Where: 12 Wally's Walk, level 8, room 801

Title: Deep Learning

( Abstract )

Tuesday 02 April:

Hugh Entwistle (Macquarie University, AMSI Vacation Scholar)

When: Tuesday 2nd April 2019
Time: 12:00noon - 1:00pm
Where: 14 SCO Avenue, Access Grid Room 146 (just off the grad hall)

Hugh Entwistle is currently one of our Statistics major students. He will be presenting on work that he did as an AMSI Vacation Scholar with Dr Georgy Sofronov of the Department of Mathematics and Statistics.

Title: "Convergence in the Central Limit Theorem"

( Abstract )

Session 2, 2018

Tuesday 16 October:  Dr Richard Garner, "Mathematics for Deleuzers"

In this talk I will give an idiosyncratic introduction to the philosophy of mathematics. One of the great dichotomies that has riven the philosophy of maths is between "realist" and "anti-realist" perspectives. That is, do mathematical objects really exist in some Platonic realm, and we merely discover them, or is mathematics just shuffling symbols around on a page, and so invented by us? I propose the answer "no" to this question. Having laid this thorny problem to rest, I will go on to address the much more profound question: why are assignments hard?

Tuesday 04 September:  Dr Paul Bryan, "Cantor tried to solve the heat equation and accidentally  invented set theory"

In the early 19th century, Fourier solved the heat equation, describing the flow of heat in a body by using infinite series of trigonometric functions. The question of whether expressing the solution in terms of such "Fourier series" was unique occupied a number of mathematicians throughout the 19th century. While attempting to solve this problem, Cantor discovered the need for a rigorous notion of sets of real numbers and indeed for real numbers themselves. In this talk, we will see how the uniqueness of Fourier series question lead Cantor to define ordinal numbers and a remarkable theorem of Cantor showing uniqueness of Fourier series for sets with "infinities upon infinities" of discontinuities!

Tuesday 21 August:  Dr Joshua Peate, "Finding the square root of a derivative, and why this is useful"

When learning mathematics, an early concept is that of the square root. The square root of two, for example, is defined as the number that if multiplied by itself gives back 2. Originally, you are told, you cannot square root a negative number, but then in university mathematics you are told you can, and in fact all of the imaginary numbers are defined through the square root of -1. But can we take this further and apply the concept of a square root to just anything? For example, can I find an operator, that if applied to a function twice, would result in the same as differentiating?

This talk will look at some specific examples of square roots and other parts of functional calculus, and how this type of thinking allows us to represent difficult mathematical problems in new ways. The talk will conclude with some comments on current research.

Session 1, 2018

Tuesday 01 May: Mr Ali Shariati,  "Statistical Inference Using Empirical Likelihood for Survival Data under Length-bias and Right-censorship"

A frequent problem statisticians face is the analysis of survival data. Survival data, known as time-to-event data, arises in various disciplines, such as reliability, engineering, economics, demography, biology, epidemiology and public health.

To study the natural history of a disease, survival data collected in a cohort of prevalent cases may be used to make statistical inference on survival functions. In such studies, we only observe subjects who have already been diagnosed with a condition or disease (e.g. HIV, cancer or dementia) but are yet to experience the failure event (e.g. AIDS, or death). Statistical procedures and methodology for assessment of interventions or treatments based on such data often involve different bias, the most important of which are right-censorship and length-bias.

In this talk, I will introduce some basic parameters to characterize the survival data. I will discuss the problem of making inference on survival parameters based on right-censored and length-biased data. I will propose an empirical likelihood procedure for analyzing such data. A simulation study is conducted to reveal the performance of the proposed methods. Several real examples are presented for better illustration. I will also demonstrate the usage of the methods proposed for engineering and reliability through some examples.

Tuesday 10 April: Prof. Ross Street,  "Trees, Permutations, Trigonometry, and Ploughing"

There are two kinds of “research”: one is finding out what was done, the other is discovering new facts for yourself. This talk involves a bit of both. Some years back, a colleague spoke of his interest in certain kinds of mathematical trees that he needed for some application of category theory to physics. He wanted to count the number of these trees with a given number of nodes. After our people used the internet to find that these numbers existed in the literature, I set two Vacation Scholars on further research of this first kind. The talk will outline their lovely results, including research of the second kind.

Tuesday 13 March: Justin Tzou, " Diffusion is not always a-smoothin' "

When a drop of ink spreads through a glass of water, when the smell of a perfume sprayed in one corner of a room makes its way to all corners, or when a disease that begins in a few isolated pockets overtakes entire regions, the underlying process at work is the ubiquitous phenomenon of diffusion. A result of random motion, diffusion acts to transport material (whether it be actual material such as atoms and molecules, or abstract material such as the prevalence of a disease) from regions with high concentration of material to those with low concentration. As such, one might assume that diffusion always drives a system toward a state in which concentrations of material are the same everywhere. If this was the case, why do bacteria colonies form in clumps, how can vegetation patterns persist, and, as was famously put by the math biologist Prof. J.D. Murray, how did the leopard get its spots? In this seminar, we take a brief journey through the mathematical underpinnings of diffusion-driven pattern formation, highlighted by the pioneering work of Alan Turing in 1952. Because of its prevalence in nature, the study of pattern formation is still currently an area of intense research in applied mathematics.

For past seminars, please go to our archive.

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