Colloquia Abstracts
Date: 21 July 2016 Name: Andrew C. Fowler, University of Oxford and University of Limerick Title: Predicting the unpredictable: drumlins, exploding rocks, worms, landslidesAbstract. Most physical applied mathematicians use deterministic models to provide unique solutions to well-specified physical problems. But there are many instances where the observed data fills a distribution, and the question then arises for the modeller, how do I use my deterministic model to address such observations? In this talk I will explore four examples where such data exists, and how in three of them the data can be explained by combining the elements of a deterministic model in the framework of a stochastic process.
Date: 11 August 2016 Name: Dimitrios Mitsotakis, Victoria University of Wellington Title: Nonlinear and dispersive wave equations with applications
Abstract. The equations describing water waves in ideal fluids, known as the Euler equations, appear to be exceedingly complex. Certain assumptions on the waves amplitude and wavelength lead to mathematical models that simplify considerably the equations involved. In this talk we consider a class of such models known as Boussinesq systems. Boussinesq systems are comprised of partial differential equations with nonlinear and dispersive terms. We review some theoretical properties of these models such as the existence and uniqueness of smooth solutions. We also present and analyse Galerkin / Finite element methods for their numerical solution. Galerkin methods appear to be very efficient for the approximation of smooth solutions of Boussinesq models in plane domains with complicated boundaries. Applications to the propagation of solitary waves and the generation and propagation of tsunamis are discussed.
Date: 18 August 2016 Name: George Barmpalias, Victoria University of Wellington Title: Minority population in the one-dimensional Schelling model of segregation
Abstract. The Schelling model of segregation looks to explain the way in which a population of agents or particles of two types may come to organize itself into large homogeneous clusters, and can be seen as a variant of the Ising model in which the system is subjected to rapid cooling. While the model has been very extensively studied, the unperturbed (noiseless) version has largely resisted rigorous analysis. Most of the relevant results in the literature pertain to versions of the model in which noise is introduced into the dynamics so as to make it amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory. We rigorously analyze the one-dimensional version of the model in which one of the two types is in the minority, and establish various forms of threshold behavior. Our results are in sharp contrast with the case when the distribution of the two types is uniform (i.e. each agent has equal chance of being of each type in the initial configuration).
Date: 15 September 2016 Name: Peter Smith, Victoria University of Wellington Title: Random Electromagnetic Rays: Models, Design and Analysis
Abstract. New ideas for increasing the data rates available at your mobile phone include so-called millimeter wave (mmWave) systems. In contrast to today’s microwave systems, which behave as if you are surrounded by a sea of electromagnetic (EM) radiation, mmWave signals propagate through the atmosphere like individual rays. Since the environment around us is complex and cluttered, these EM rays depart from the transmitter and arrive at the receiver at random angles. In this talk I will give an overview of three ongoing research projects at VUW which are driven by these random EM rays.
Models: How can we model correlation between the rays departing from different antennas at the transmitter? Design: How can we design effective ray directions at the transmitter? Analysis: What is the statistical distribution of the interference caused by two rays? This is joint work with: Pawel Dmochowski, Harsh Tataria, Calum Neil, Shuang Li (ECS, VUW), Mansoor Shafi (Spark), Yawei Yu, Jianhua Zhang (Beijing University of Posts and Telecommunications).Date: 29 September 2016 Name: Lisa Clark, University of Otago Title: Two abstract supermodels: groupoids and Steinberg algebras
Abstract. A groupoid is a generalisation of group in which composition is only partially defined. In first half of this talk, I will give an overview of groupoid theory and show how groupoids provide a unifying framework for a number of seemingly unrelated mathematical structures. In the second half of the talk, I will introduce Steinberg algebras. A Steinberg algebra is constructed from an `ample' topological groupoid. These algebras can also be used to model a number of seemingly unrelated algebraic constructions. I will describe some recent results in an attempt to convince you that these algebras are indeed supermodels.
Date: 13 October 2016 Name: David Balduzzi, Victoria University of Wellington Title: Strongly-Typed Games
Abstract. Game theory was developed to model interactions between humans. However, it may be more directly applicable as a toolbox for analysing interactions between learning algorithms -- which are rational by construction. Unfortunately, finding equilibria in games is a computationally hard problem that has only been effectively solved in very special cases such as two-player games and potential games.
In this talk, I will introduce a class of games where equilibria can be computed using gradient descent. The analysis draws on unexpected connections with abelian representations of Lie algebras and tensor factorisation.