# Special Semester on Mathematical Thinking

## Monday, 5th Nov 2018 — Friday, 31st May 2019

The next CARMA special semester programme is on the theme of Mathematical Thinking, examining the conceptual and neurological basis of mathematical thought and creativity, different aspects of which are associated with brain structures evolved for different purposes. It will explore links to machine learning, which plays a critical role as a model for cognition, as well as cognitive psychology, neuroscience, philosophy and pure and applied mathematics, through a series of workshops and other events. Please visit the semester's webpage for details. Events will also be listed on the events page of the CARMA website.

# Special Semester on Mathematical Thinking

## Thursday, 28th Mar 2019

SR202, SR Building

# Matt Skerritt

(School of Mathematical and Physical Sciences, The University of Newcastle)

# An Introduction to Assisted Theorem Proving with “Coq”

I introduce and demonstrate the Coq assisted theorem prover.

# CARMA Colloquium

## Thursday, 4th Apr 2019

SR202, SR Building

# Professor Yann Bugeaud

(Mathématiques , Université de Strasbourg)

# On the decimal expansion of $\log (2019/2018)$ and $e$

It is commonly expected that $e$, $\log 2$, $\sqrt{2}$, among other « classical » numbers, behave, in many respects, like almost all real numbers. For instance, their decimal expansion should contain every finite block of digits from $\{0, \ldots , 9\}$. We are very far away from establishing such a strong assertion. However, there has been some small recent progress in that direction. Let $\xi$ be an irrational real number. Its irrationality exponent, denoted by $\mu (\xi)$, is the supremum of the real numbers $\mu$ for which there are infinitely many integer pairs $(p, q)$ such that $|\xi - \frac{p}{q}| < q^{-\mu}$. It measures the quality of approximation to $\xi$ by rationals. We always have $\mu (\xi) \ge 2$, with equality for almost all real numbers and for irrational algebraic numbers (by Roth's theorem). We prove that, if the irrationality exponent of $\xi$ is equal to $2$ or slightly greater than $2$, then the decimal expansion of $\xi$ cannot be `too simple', in a suitable sense. Our result applies, among other classical numbers, to badly approximable numbers, non-zero rational powers of ${{\rm e}}$, and $\log (1 + \frac{1}{a})$, provided that the integer $a$ is sufficiently large. It establishes an unexpected connection between the irrationality exponent of a real number and its decimal expansion.

# Symmetry in Newcastle

## Friday, 5th Apr 2019

(Location to be decided)

Schedule:

12-1: Talk 1
1-2: Lunch
2-3: Talk 2
3-3.30: Tea
3.30-4.30: Talk 3
Evening: Dinner

## Dr Arnaud Brothier

(University of NSW)

## Dr Lawrence Reeves

(The University of Melbourne)

## Dr Richard Garner

(Macquarie University)

# International Workshop on Water Waves and Floating Bodies

## Sunday, 7th Apr 2019 — Wednesday, 10th Apr 2019

Noah's On the Beach [Newcastle, NSW]

The 34th International Workshop on Water Waves and Floating Bodies (IWWWFB) will be held in Newcastle in 2019. Please visit the workshop website for more information.

# CARMA Colloquium

## Thursday, 11th Apr 2019

SR202, SR Building

This talk will take place at 2pm, not the standard time.

# A/Prof Alessandro Toffoli

(The University of Melbourne)

# Sailing through a polar cyclone to witnes the fierceness of the Southern Ocean: there and back again

Sea ice acts as a refrigerator for the world. Its bright surface reflects solar heat, and the salt it expels during the freezing process drives cold water towards the equator. As a result, sea ice plays a crucial role in our climate system. Antarctic sea-ice extent has shown a large degree of regional variability, in stark contrast with the steady decreasing trend found in the Arctic. This variability is within the ranges of natural fluctuations, and may be ascribed to the high incidence of weather extremes, like intense cyclones, that give rise to large waves, significant wind drag, and ice deformation. The role exerted by waves on sea ice is still particular enigmatic and it has attracted a lot of attention over the past years. Starting from theoretical knowledge, new understanding based on experimental models and computational fluid dynamics is presented. But exploration of waves-in-ice cannot be exhausted without being on the field. And this is why I found myself in the middle of the Southern Ocean during a category five polar cyclone to measure waves…

# CARMA Colloquium

## Thursday, 18th Apr 2019

SR202, SR Building

# Dr Scott Lindstrom

(Hong Kong Polytechnic University)

# Optimisation models for data science and machine learning

We discuss various optimisation-based approaches to machine learning. Tasks include regression, clustering, and classification. We discuss frequently used terms like 'unsupervised learning,' 'penalty methods,' and 'dual problem.' We motivate our discussion with simple examples and visualisations.

# CARMA Colloquium

## Wednesday, 24th Apr 2019

SR202, SR Building

# A/Prof Duangkamon Baowan

(Department of Mathematics, Mahidol University)

# Calculus of variations and the bending of carbon nanostructures

Calculus of variations is utilized to minimize the elastic energy arising from the curvature squared while maximizing the van der Waals energy. Firstly, the shape of folded graphene sheets is investigated, and an arbitrary constant arising by integrating the Euler–Lagrange equation is determined. In this study, the structure is assumed to have a translational symmetry along the fold, so that the problem may be reduced to a two dimensional problem with reflective symmetry across the fold. Secondly, both variational calculus technique and least squared minimization procedure are employed to determine the joining structure involved a C60 fullerene and a carbon nanotube, namely a nanobud. We find that these two methods are in reasonable overall agreement. However, there is no experimental or simulation data to determine which procedure gives the more realistic results.

# CARMA Workshop on Computer-Aided Proof

## Wednesday, 5th Jun 2019 — Friday, 7th Jun 2019

NewSpace (City Campus)

Computers are playing an increasingly important role in the creation and verification of mathematical proofs. This role is expected to become central in the future of mathematics. This workshop will bring together experts in computer proof assistants, formal proof verification systems, formal foundations of mathematics and related topics. The intended audience will be working mathematicians and graduate students, who are not necessarily experts in formal mathematics. Please visit the workshop website for more information.