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Priority Research Centre for Computer-Assisted
Research Mathematics and its Applications

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CARMA-Sponsored Events: Colloquia, Seminars, Workshops, Conferences and More.

Details of upcoming events are listed on this page.

Upcoming CARMA Events

  • Special Semester on Mathematical Thinking
  • Location:
  • Dates: Mon, 5th Nov 2018 - Fri, 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.
  • [Permanent link]

  • Speaker: Dr Michael Coons, CARMA, The University of Newcastle
  • Title: Mahler's methods: theorems, speculations and variations
  • Location: TBAThe University of Newcastle
  • Time and Date: 4:00 pm, Thu, 7th Mar 2019
  • Abstract:

    Mahler's method in number theory is an area wherein one answers questions surrounding the transcendence and algebraic independence of both power series $F(z)$, which satisfy the functional equation $$a_0(z)F(z)+a_1(z)F(z^k)+\cdots+a_d(z)F(z^{k^d})=0$$ for some integers $k\geqslant 2$ and $d\geqslant 1$ and polynomials $a_0(z),\ldots,a_d(z)$, and their special values $F(\alpha)$, typically at algebraic numbers $\alpha$. The most important examples of Mahler functions arise from important sequences in theoretical computer science and dynamical systems, and many are related to digital properties of sets of numbers. For example, the generating function $T(z)$ of the Thue-Morse sequence, which is known to be the fixed point of a uniform morphism in computer science or equivalently a constant-length substitution system in dynamics, is a Mahler function. In 1930, Mahler proved that the numbers $T(\alpha)$ are transcendental for all non-zero algebraic numbers $\alpha$ in the complex open unit disc. With digital computers and computation so prevalent in our society, such results seem almost second nature these days and thinking about them is very natural. But what is one really trying to communicate by proving that functions or numbers such as those considered in Mahler's method?

    In this talk, highlighting work from the very beginning of Mahler's career, we speculate---and provide some variations---on what Mahler was really trying to understand. This talk will combine modern and historical methods and will be accessible to students.

  • [Permanent link]

  • International Workshop on Water Waves and Floating Bodies
  • Location: , Noah's On the Beach Newcastle, NSW
  • Dates: Sun, 7th Apr 2019 - Wed, 10th Apr 2019
  • 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.
  • [Permanent link]

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