
CARMASponsored Seminar Series: Colloquia, Seminars and More.

[Note: events are listed by ascending date.]
 CARMA COLLOQUIUM
 Speaker: Professor Yann Bugeaud, Mathématiques , Université de Strasbourg
 Title: On the decimal expansion of $\log (2019/2018)$ and $e$
 Location: Room SR202, SR Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 4^{th} Apr 2019
 Abstract:
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, nonzero 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.
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 CARMA COLLOQUIUM
 Speaker: A/Prof Alessandro Toffoli, The University of Melbourne
 Title: Sailing through a polar cyclone to witnes the fierceness of the Southern Ocean: there and back again
 Location: Room SR202, SR Building (Callaghan Campus) The University of Newcastle
 Time and Date: 2:00 pm, Thu, 11^{th} Apr 2019
 Abstract:
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 seaice 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 wavesinice 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…
 This talk will take place at 2pm, not the standard time.
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 CARMA COLLOQUIUM
 Speaker: Dr Scott Lindstrom, Hong Kong Polytechnic University
 Title: Optimisation models for data science and machine learning
 Location: Room SR202, SR Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 18^{th} Apr 2019
 Abstract:
We discuss various optimisationbased 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.
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 CARMA COLLOQUIUM
 Speaker: A/Prof Duangkamon Baowan, Department of Mathematics, Mahidol University
 Title: Calculus of variations and the bending of carbon nanostructures
 Location: Room SR202, SR Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Wed, 24^{th} Apr 2019
 Abstract:
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.
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