Past Seminars

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Littlewood's Conjecture
Professor Andrew Pollington
Director for the Algebra, Number Theory and Combinatorics panel
National Science Foundation, Division of Mathematical Sciences
Start time: 12:00 pm
Date: Thursday 3 September 2009
Location: Prince Philip Theatre, Architecture and Planning Building (Ground Floor), The University of Melbourne

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Experimental Mathematics Meets Mathematical Physics
David H Bailey
Lawrence Berkeley Laboratory, USA
Start time: 3:15 pm
Date: Thursday 20 August 2009
Location: Old Geology Theatre 1, The University of Melbourne

High-precision arithmetic has been called the "electron microscope" of experimental mathematics. The general approach is to compute some mathematical expression to very high precision (typically several hundred digits) for some specific choice of parameters, then apply an integer relation algorithm such as "PSLQ" to find a relation linking this object or expression and other known mathematical entities. Relations and formulas that are numerically discovered in this manner must then be proven rigorously.

One particularly fruitful area for this methodology is the evaluation of definite integrals, such as those that arise in mathematical physics. Literally hundreds of new and intriguing results, specific and general, have been found in this manner, including results in Ising theory, quantum field theory and even computational biology. Progress in this arenas has been hampered by long run times required to evaluate high-dimensional integrals. However, with the increasing availability of highly parallel computer systems, many of these integrals can now be evaluated. Nonetheless, new techniques are required to further advance the state of the art.

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Wild emergence of complex organisation in a simple cellular automata
Tony Smith
Complex Systems Analyst, Meme Media
Start time: 3:15 pm
Date: Friday 1 May 2009
Location: Theatre 1, ICT Building (Ground Floor, 111 Barry Street, Carlton)

Six months intense study of the development from simple seeds with the Generations 345/3/6 cellular automata rule has revealed a vast new territory of emergent phenomena and a limitless supply of data on the behaviour of complex interactions extremely close to the elusive boundary of order and chaos. Viable seed patterns form a slowly growing chaotic core with outbound streams of 1/2 speed (space)ships headed NSEW. Around once per million live cells, one of several varieties of also 1/2 speed track/trail laying engines appears, surviving indefinitely within the ship streams. The tracks and trails exhibit resilience, even healing, and support a range of attached patterns moving at various fractional speeds. Those attached patterns and subsequent interactions with ships in the streams provide numerous different mechanisms for initiating new chaotic cores far from the original core. Most important reactions exhibit phase dependent variability making them computationally irreducible and attractive for statistical analysis despite being fully deterministic.

Further information and links:
Golly, an open source, cross-platform application for exploring the Game of Life and other cellular automata: http://golly.sf.net/
Current placeholder page for this project which is to be developed in the months to come: http://www.TheWildCA.com/
Some uneven commentary, pics and animations from the last six months: http://www.transforum.net/m.cgi?num=2779
As yet only one animation is on YouTube: http://www.youtube.com/watch?v=qh_DE_EXNGE
2003 essay on Border of Order–Edge of Chaos: http://www.meme.com.au/theoria/retreat.html
2004 evolving network project that is the only non CA amongst my six discrete system investigations: http://www.twistet.com/
Melbourne Emergence Meetup, 2nd Thursday of the month at The Corkman: http://emergence.meetup.com/24/

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Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions
Kostya Borovkov
The University of Melbourne
Start time: 3:15 pm
Date: Friday 13 March 2009
Location: Theatre 1, ICT Bldg (Ground Floor, 111 Barry Street, Carlton)

This talk will present a new monograph with the same title by A. A. Borovkov and K. A. Borovkov published in 2008 by Cambridge University Press (ISBN-13: 9780521881173, weight: 1.22 kg). This book focuses on the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. Large deviation probabilities are of great interest in numerous applied areas, typical examples being ruin probabilities in risk theory, error probabilities in mathematical statistics, and buffer-overflow probabilities in queueing theory. The classical large deviation theory, developed for distributions decaying exponentially fast (or even faster) at infinity, mostly uses analytical methods. If the fast decay condition fails, which is the case in many important applied problems, then direct probabilistic methods usually prove to be efficient. This monograph presents a unified and systematic exposition of the large deviation theory for heavy-tailed random walks. Most of the results presented in the book are appearing in a monograph for the first time. Many of them were obtained by the authors.

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The Mechanics of Nanoscale Devices
John Elie Sader
The University of Melbourne (Maths & Stats)
Start time: 3:15 pm
Date: Friday 12 September 2008
Location: Theatre 1, ICT Bldg (Rm:205-Flr:2, 111 Barry Street, Carlton)

Nanomechanical sensors are often used to measure environmental changes with extreme sensitivity. Controlling the effects of surfaces and fluid dissipation presents significant challenges to achieving the ultimate sensitivity in these devices. In this talk, I will give an overview of theoretical/experimental work we are undertaking to explore the underlying physical processes in these systems. The talk will be general and aimed at introducing some recent developments in the field of nanomechanical sensors.

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