Past Seminars

How to survive Real-World Projects as a Mathematician

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Speaker: Thorsten Koch
Institution: Zuse Institue Berlin (MATHEON)
Date: Wed 20 Oct 2010
Time: 4:15 pm
Location: Room 706, Doug McDonell Building, Building 168, University of Melbourne (see map for directions)

Abstract: This talks aims at sharing the experience from 10 years of successfully employing integer programming in industry projects with the audience. We will try to draw some general conclusions and using the projects of the author as examples to show some common pitfalls.
Bio: Thorsten is the team leader of the integer programming group at the Zuse Institue Berlin (MATHEON). Within this role he is responsible for managing many difficult and important projects, many of which are outlined on the ZIB website (http://www.zib.de/General/Adm/projects/projects/index.en.html). To view the slides of this talk, please click here.

Grassmann fields for spanning hyperforests

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Speaker: Andrea Bedini
Institution: MASCOS / Department of Mathematics and Statistics, University of Melbourne
Date: Mon 16 Aug 2010
Time: 3:15 pm
Location: Theatre 1, Alan Gilbert Building, University of Melbourne (building 104, cnr Grattan St and Barry St)

Abstract: The spanning-hyperforest model is a percolative model with the additional constraint of having no cycles where a weight is given to each connected component (tree). Its generating function can be expressed in terms of anti-commuting Grassmann fields, a representation which effectively generalizes Kirchhoff's matrix-tree theorem. Although the spanning-hyperforest model is naturally connected to the Potts model (in the $q \to 0$ limit), this novel representation uncover a new connection with super-symmetric vector models. Under the light of this "magnetic" interpretation we study the model on the complete graph, we identify a "low-temperature" phase characterized by the appearance of a giant connected component and delimited by a second order phase transition associated with the super-symmetry breaking.

Great is the Power of Steady Misrepresentation

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Speaker: Prof Ian Enting
Institution: MASCOS/Department of Mathematics and Statistics, The University of Melbourne
Date: Mon 2 Aug 2010
Time: 3:15 pm
Location: Theatre 1, Alan Gilbert Building (bldg 104), The University of Melbourne (cnr Grattan St and Barry St).

Abstract: The science of climate change has come under public attack through what has been described as asymmetric warfare. Public communication has been flooded with a deluge of misinformation. In parallel there have been attempts to distract, intimidate and gag climate scientists. In 2009 Ian Plimer's book, "Heaven+Earth - Global Warming: The Missing Science", claimed to demolish the theory of human-induced global warming due to the release of CO2 and other greenhouse gases. A careful reading of "Heaven + Earth" reveals extensive examples of fabricating numbers, distorted and misattributed graphics, misrepresentation of the content of cited references and a sprinkling of plagiarism. In spite of its blatant flaws, "Heaven+Earth" has gained considerable political traction in Australia.

Pdf version of the talk available here.

The asymptotic variance of departures from critically loaded queues

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Speaker: Yoni Nazarathy
Institution: EURANDOM, Technische Universiteit Eindhoven
Date: Fri 30 Jul 2010
Time: 3:15 pm
Location: Old Geology Theatre 1, University of Melbourne

Abstract: We study the departure process of the GI/G/1 queue and focus on the variance of the number of departures. This is typically a function which grows at an asymptotic linear rate with respect to time. Precise knowledge of this rate, helps obtain approximations for the distribution of departures over long intervals. It is quite easy to see that when the parameters of the system are such that the queue is under loaded, i.e. the inter-arrival times are longer than the service durations, the asymptotic variance equals that of the arrival process. Similarly, when the queue is overloaded, the asymptotic variance equals that of the service process. Our focus is on the critically loaded case where a complete different behavior occurs: We find that the asymptotic variance is (1-2/pi) multiplied by the sum of the asymptotic variances of the arrival and service processes.
Our result originates from a classic heavy traffic limit theorem of the departure process, yet in proving this result there are several non-trivial challenges related to establishing uniform integrabillity conditions. The talk aims to focus on these aspects.
Joint work with Ahmad Al-Hanbali, Michel Mandjes and Ward Whitt.

Techniques of Constraint Integer Programming

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Speaker: Timo Berthold, Zuse Institute Berlin (ZIB) and MATHEON (Berlin)
Institution:
Date: Fri 29 Jan 2010
Time: 3:15 pm
Location: Theatre 2, ICT Bldg (ground floor, 111 Barry Street)

Abstract: Abstract: Mixed-integer programming (MIP) and constraint programming CP) proved to be a powerful tools to model and solve large-scale optimization problems. Constraint integer programming (CIP) is a novel generalization of MIP that supports the notion of arbitrary constraints as in CP. We introduce the basic notion and algorithmic ideas of CIP. Further, we present the software SCIP which is a solver and framework for constraint integer programming that also features SAT solving techniques.

Chaos expansion of Poisson functionals

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Speaker: Prof. Guenter Last
Institution: Karlsruhe Universitaet (TH)
Date: Fri 4 Sep 2009
Time: 3:15 pm
Location: Theatre 1, ICT Bldg (ground floor, 111 Barry Street, Carlton)

Abstract: In the first part of the talk we recall the definition of a Poisson process on a general state space and discuss some basic properties of this process (random measure). Then we proceed with deriving an explicit Fock space representation for Poisson processes in terms of iterated difference operators. Finally we apply this result to get an explicit version of the Wiener-Ito chaos expansion and variance inequalities.

The talk is based on joint work with Mathew Penrose (Bath).

Littlewood's Conjecture

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Speaker: Professor Andrew Pollington
Director for the Algebra, Number Theory and Combinatorics panel
Institution: National Science Foundation, Division of Mathematical Sciences
Date: Thu 3 Sep 2009
Time: 12:00 pm
Location: Prince Philip Theatre, Architecture and Planning Building (Ground Floor), The University of Melbourne

Abstract:

Experimental Mathematics Meets Mathematical Physics

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Speaker: David H Bailey
Institution: Lawrence Berkeley Laboratory, USA
Date: Thu 20 Aug 2009
Time: 3:15 pm
Location: Old Geology Theatre 1, The University of Melbourne

Abstract: 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.

Wild emergence of complex organisation in a simple cellular automata

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Speaker: Tony Smith
Institution: Complex Systems Analyst, Meme Media
Date: Fri 1 May 2009
Time: 3:15 pm
Location: Theatre 1, ICT Building (Ground Floor, 111 Barry Street, Carlton)

Abstract: 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/

Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions

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Speaker: Kostya Borovkov
Institution: The University of Melbourne
Date: Fri 13 Mar 2009
Time: 3:15 pm
Location: Theatre 1, ICT Bldg (Ground Floor, 111 Barry Street, Carlton)

Abstract: 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.