CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Michael Coons, CARMA, The University of Newcastle Title: Minimal growth of some structured $\pm 1$-sequences Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Wed, 16th Mar 2016 Abstract: In this talk, I will outline my interest in, and results towards, the Erdős Discrepancy Problem (EDP). I came about this problem as a PhD student sometime around 2007. At the time, many of the best number theorists in the world thought that this problem would outlast the Riemann hypothesis. I had run into some interesting examples of some structured sequences with very small growth, and in some of my early talks, I outlined a way one might be able to attack the EDP. As it turns out, the solution reflected quite a bit of what I had guessed. And I say 'guessed' because I was so young and naïve that my guess was nowhere near informed enough to actually have the experience behind it to call it a conjecture. In this talk, I will go into what I was thinking and provide proof sketches of what turn out to be the extremal examples of EDP. [Permanent link] CARMA SEMINAR Speaker: Dr Michael Coons, CARMA, The University of Newcastle Title: The benefits of a regular outlook Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 2:00 pm, Tue, 20th Oct 2015 Abstract: I will talk a bit about the benefits of a regular outlook. [Permanent link] CARMA COLLOQUIUM Speaker: Dr Michael Coons, CARMA, The University of Newcastle Title: Variations on a theme of Mahler Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 25th Sep 2014 Abstract: I will survey some recent and not-so-recent results surrounding the areas of Diophantine approximation and Mahler's method related to variations of the Chomsky-Schützenberger hierarchy. [Permanent link] AUSTRALIAN MATHEMATICAL SCIENCES STUDENT CONFERENCE Keynote Lecture Speaker: Dr Michael Coons, CARMA, The University of Newcastle Title: My life in \$mathmode\$ Location: Room V07, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 10:00 am, Wed, 2nd Jul 2014 Abstract: I will survey my career both mathematically and personally offering advice and opinions, which should probably be taken with so many grains of salt that it makes you nauseous. (Note: Please bring with you a sense of humour and all of your preconceived notions of how your life will turn out. It will be more fun for everyone that way.) [Permanent link] CARMA OANT SEMINAR Speaker: Dr Michael Coons, CARMA, The University of Newcastle Title: The rational-transcendental dichotomy of Mahler functions Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Mon, 15th Oct 2012 Abstract: In this talk, we will show that a D-finite Mahler function is necessarily rational. This gives a new proof of the rational-transcendental dichotomy of Mahler functions due to Nishioka. Using our method of proof, we also provide a new proof of a Pólya-Carlson type result for Mahler functions due to Randé; that is, a Mahler function which is meromorphic in the unit disk is either rational or has the unit circle as a natural boundary. This is joint work with Jason Bell and Eric Rowland. [Permanent link] CARMA COLLOQUIUM Speaker: Dr Michael Coons, CARMA, The University of Newcastle Title: A functional introduction to Mahler's method Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 9th Aug 2012 Abstract: Let $F(z)$ be a power series, say with integer coefficients. In the late 1920s and early 1930s, Kurt Mahler discovered that for $F(z)$ satisfying a certain type of functional equation (now called Mahler functions), the transcendence of the function $F(z)$ could be used to prove the transcendence of certain special values of $F(z)$. Mahler's main application at the time was to prove the transcendence of the Thue-Morse number $\sum_{n\geq 0}t(n)/2^n$ where $t(n)$ is either 0 or 1 depending on the parity of the number of 1s in the base 2 expansion of $n$. In this talk, I will talk about some of the connections between Mahler functions and finite automata and highlight some recent approaches to large problems in the area. If time permits, I will outline a new proof of a version of Carlson's theorem for Mahler functions; that is, a Mahler function is either rational or it has the unit circle as a natural boundary. [Permanent link]