Pointwise Convergence of Fourier Series: Past, Present and Future
We recall Lennart Carleson's Theorem asserting the pointwise convergence of partial summation of Fourier series of square integrable functions. We explain what the Theorem says, and why it is worthy of citation by the Abel Prize committee: It is a "multi-scale" theorem. The talk finishes with related results that suggest possibilities for 'non-commutative' variants of Carleson's Theorem.
Joint work with E. Sawyer, C.-Y. Shen and I. Uriarte-Tuero.
Professor Lacey finished his PhD degree in 1989, in probability theory. In 1996, he and Christoph Thiele received the Salem Prize for Analysis, for their work on the bilinear Hilbert transform. Prof Lacey gave an invited lecture at the 1998 International Congress of Mathematicians. His work has been recognized by awards from the Guggenheim Foundation and the Simons Foundation. Besides research grants, he has held 10 years of grants supporting training of students and postdocs.
Integer Programming with The Lot: Recent Advances in Methods and Theory for Two Objectives and Augmented Lagrangian Duality
This two-part talk describes very recent work on extending the state-of-the-art in integer programming in two quite different directions. In the first part, efficient techniques for finding all Pareto-optimal solutions to integer programs with two objectives are described. The techniques seek to exploit the power of current integer programming solver technology as a black box, using new features of such solvers to accelerate the process. Computational experiments show the effectiveness of alternative algorithm variants in both generating the efficient frontier, and in reducing the area of uncertainty about the location of the frontier. In the second part, the augmented Lagrangian dual, which is well known in convex optimization is considered for integer programming – a highly nonconvex problem. We discuss a new primal characterization of this dual that provides some insights about its behaviour, and from which it can be proved that the dual has zero gap, i.e. the value of the dual is precisely the value of the original integer program. Results on a small example illustrate how practically efficient approaches to the augmented Lagrangian relaxation can yield better bounds than the standard Lagrangian relaxation.
Professor Boland has held the position of Professor of Applied Mathematics at the University of Newcastle, Australia, since 2008, a role she took up after completing her PhD at the University of Western Australia in 1992, followed by two years of postdoctoral research at the University of Waterloo, Canada, and the Georgia Institute of Technology, respectively, and 13 years with the University of Melbourne. She is an expert in the field of integer programming, and a leading exponent of its application to address complex problems in industry. Her contributions to the field have spanned theory, algorithms, modelling and applications, across methodologies such as column generation and Lagrangian relaxation, polyhedral analysis and branch-and-cut methods, and meta-heuristics, in domains as diverse as mining, telecommunications and cancer radiotherapy treatment. She is a founding co-director of the University of Newcastle’s newly established Centre for Optimal Planning and Operations.
Geometry and asymptotics
Whether we are looking at waves on a beach, the dispersal of herds of animals in a landscape, or the interaction of black holes, their patterns of movement rely on rules expressed by non-linear mathematical models. In this talk, I will focus on new techniques to describe solutions of nonlinear equations that arise as as universal limits in many applications.
Prof Nalini Joshi's research focuses on longstanding problems concerning the asymptotic and analytic structure of solutions to nonlinear integrable equations. She has solved open problems for the classical Painlevé equations (differential equations that are archetypical nonlinear models of modern physics) and discrete systems.
Nalini is the Chair of Applied Mathematics at The University of Sydney and was the President of the Australian Mathematical Society during 2008-2010. She was elected a Fellow of the Australian Academy of Science in 2008, became the Chair of the National Committee of Mathematical Sciences in 2011, and was elected to the Council of the Australian Academy of Science in 2012. Nalini was awarded the 2012 Georgina Sweet Australian Laureate Fellowship. A. This fellowship recognises her leading research role in science and technology and provides her with additional funding to help her to mentor women in science.
Optimal Control Policies in a Dynamic Model of Economic Growth and Climate Change
We consider a dynamical model of economic growth and climate change consisting of three ordinary differential equations (ODEs). Two ODEs model the rate of change of the average temperature and CO_2 concentration caused by emissions due to economic activities. This physical model is combined with a standard ODE modeling capital and economic growth. There are two time-dependent control (influence) variables in the model: consumption C and abatement A . The goal is to determine control functions C(t) and A(t) that maximize a given utility functional over a finite or infinite time horizon.
Optimal controls (policies) are determined in various scenarios, where either temperature constraints are prescribed (Copenhagen agreement) or constraints on the CO_2 concentration have to be fulfilled (Kyoto protocol). We study the impact of such state constraints on optimal consumption and abatement policies which are considered as guidance to practical policy options. The numerical solutions are obtained by solving large-scale optimization problems. This is joint work with Johann Jakob Preuss (Muenster) and Willi Semmler (The New School for Social Research, New York).
Professor Helmut Maurer is with the Institute of Numerical and Applied Mathematics at the University of Muenster. He has conducted research in various countries, including Austria, France, Poland, Australia, and the United States. His field of research is optimal control, in particular control and state constraints, numerical methods, second-order sufficient conditions, sensitivity analysis, real-time control techniques, and various applications in mechanics, mechatronics, physics, biomedical and chemical engineering, and economics.
The boundaries between algebra, analysis and geometry
Much of my work has involved using geometry to provide insight into algebraic and analytic problems. I will describe some examples that illustrate the types of insight gained using geometric considerations.
Jacqui Ramagge was born in London. She did her PhD in Kac-Moody Groups at Warwick University under the supervision of Roger Carter.
After winning the BH Neumann Prize at the AustMS conference in Perth in 1991, Jacqui accepted a Lectureship at the University of Newcastle (Australia) just before she graduated. She has since worked on operator algebras arising from group actions on buildings, Hecke algebras, and topological groups. In 2007 she moved to the University of Wollongong, where she is currently serving as Head of School.
Her work has helped to solve a number of conjectures, including some cases of the Baum-Connes conjecture. She has held numerous ARC grants and served on the ARC College 2010-2012. In 2012 she was on the Advisory Board for the Senior Mathematics Curriculum for ACARA. She serves on the Educational Advisory Board for the Australian Mathematical Sciences and is on the Australian Academy of Sciences' National Committee for the Mathematical Sciences.
Solving Multi-Armed Bandit Problems Using Row Operations
A novel approach for computing indices of multi-armed bandit problems through the use of elementary row operations is developed. The method will also be used to derive the optimal utility of a priority policy, to prove the optimality of priority policies, to compute optimal priority policies, and to solve constrained problems. The development applies to problems with linear and with exponential utility functions.
This talk is based on a joint paper with Eric V. Denardo and Uriel G. Rothblum and it is dedicated to the memory of Uriel G. Rothblum.
Professor Eugene A. Feinberg received Ph.D. in Probability and Statistics from Vilnius University, Lithuania, in 1979. Between 1976 and 1988 he held research and faculty positions in the Department of Applied Mathematics at Moscow University of Transportation. After holding a one-year visiting faculty position at Yale University in 1988-89, he joined Stony Brook University, a research university, which is a part of the State University of New York system. Dr. Feinberg is currently Distinguished Professor of Operations Research at the Department of Applied Mathematics and Statistics.
His research interests include stochastic models of operations research, Markov Decision Processes, and industrial applications of Operations Research and Statistics. Since 1999, he has been working on electric energy applications. He has published more that 130 papers and edited the Handbook on Markov Decision Processes. His research is partially supported by the National Science Foundation, Department of Energy, Office of Naval Research, New York Office of Science, Technology and Academic Research, and industry. He is a member of several editorial boards including Mathematics of Operations Research, Operations Research Letters, and Applied Mathematics Letters.
He has been awarded Honorary Doctorate from the Institute of Applied System Analysis, National Technical University of Ukraine. Dr Feinberg is a Fellow of INFORMS (The Institute for Operations Research and Management Sciences) and he is a recipient of 2012 IEEE Charles Hirsh Award, 'For developing and implementing on Long Island, electric load forecasting methods and smart grid technologies'.
Fifty years of permutation groups: questions and answers for group theory number theory, combinatorics and finite geometry
Helmut Wielandt published his influential book "Finite Permutation Groups" 50 years ago. It was the fundamental tool-kit on which was built the present comprehensive and powerful theory of group actions underpinning both applications and algorithms, and utilising the full force of the finite simple group classification.
Cheryl Praeger is a Professor of Mathematics at the University of Western Australia, ARC Federation Fellow since 2007. She is best known for her works in group theory, algebraic graph theory and combinatorial designs. She received BSc and MSc degrees from the University of Queensland, and doctorate from the University of Oxford in 1973 under direction of Peter M. Neumann.
Cheryl Praeger is a Fellow of the Australian Academy of Science, member of the executive committee of the International Mathematical Union from (2007 – 2014), and the former president of the Australian Mathematical Society (1992-1994). She is a member of the Order of Australia (since 1999) for her service to Mathematics in Australia. She was named WA Scientist of the Year in 2009.
Dynamics of Nanomechanical Devices in Fluid Environment
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. Particularly, the fluid-structure interaction of resonating microcantilevers in fluid has been widely studied and is a cornerstone in nanomechanical sensor development. In this talk, I will give an overview of work being undertaken in our group dedicated to exploring the underlying physical processes in these and related systems. This will include exploration of recent developments that focus on cantilever sensors with embedded microfluidic fluid channels and examination of the effects of surface stress on the resonant properties of cantilever sensors.
 M. J. Lachut and J. E. Sader, "Effect of surface stress on the stiffness of cantilever plates", Physical Review Letters, 99, 206102 (2007).
 M. J. Lachut and J. E. Sader, "Effect of surface stress on the stiffness of cantilever plates: Influence of cantilever geometry", Applied Physics Letters, 95, 193505 (2009).
 T. P. Burg, J. E. Sader and S. R. Manalis, "Nonmonotonic energy dissipation in microfluidic resonators", Physical Review Letters, 102, 228103 (2009).
 J. E. Sader, T. P. Burg and S. R. Manalis, "Energy dissipation in microfluidic beam resonators", Journal of Fluid Mechanics, 650, 215-250 (2010).
John E. Sader is a Professor in the Department of Mathematics and Statistics, University of Melbourne, Australia. He leads an interdisciplinary theoretical group studying a range of topics including the dynamic response of nanoparticles under femtosecond laser excitation, mechanics of nanoelectromechanical devices, high Reynolds number flow of thin films and rarefied gas dynamics in nanoscale systems. http://www.ampc.ms.unimelb.edu.au/srg/
Mathematical Aspects of Public Transport
My cooperation with providers of public transport started about 20 years ago. I will report about real success stories, such as designing and implementing algorithms that help reduce the number of vehicles and/or drivers needed for a public transport system without changing the service level, or the very recent support for the design of a new public transport network in a German city. There were, however, a number of cases where our approach was not too successful. In this lecture I will mention also several such "failure cases" that my research group encountered and will analyze the reasons for that. The obstacles to a successful implementation of optimization and operations research techniques are often "missing data" or "unclear specifications" and "moving goals", but may also be due to psychological reasons and basic misunderstandings of the roles the people involved play. There are also various fears and "business and power games" that one has to understand, something that mathematicians have not learned and have difficulties to cope with.
Professor Martin Grötschel Biography (Word Document 37 KB)
Removing unwanted variation from microarray data
Principal components have been used a lot with microarray data to exhibit unwanted variation, and to some extent to remove such variation. Such efforts are also called normalization. In this talk I will review some of these methods, and related work, and propose a simple but apparently novel variant which works a lot of the time, though not always. Part of my story will be a discussion of how one tells whether one is helping or hurting the analysis by adjusting.
Professor Terry Speed Biography (PDF 104 KB)
Index theory in Mathematics and Physics
This lecture is a personal (and partly historical) overview in non-technical terms of the topic described in the title, from first year linear algebra to von Neumann algebras.
Alan Carey studied at the Universities of Sydney and Oxford, then took up research fellowships at the University of Adelaide and the ANU. He held a continuing position at the University of Adelaide from 1985 to 2002, with brief appointments to Flinders University and to ANU during that time. Since 2002 he has been the Director of the Mathematical Sciences Institute at ANU. He has been a Clay Mathematics Institute Scholar on three occasions, in 2000 and again in 2001 at Harvard, and in 2006 at the Erwin Schrödinger Institute in Vienna. He was President of the AustMS from 2000 to 2002. He received the Moyal Medal in 2008 and a senior fellowship from the Erwin Schrödinger Institute in 2009.
Entropy and Projection Methods for Inverse Problems
I shall discuss in "tutorial mode" the formalization of inverse problems such as signal recovery and option pricing; first as (convex and non-convex) optimization problems and second as feasibility problems --- over the infinite dimensional space of signals. I shall touch on the following topics (more is an unrealistic task):
||The impact of the choice of "entropy" (e.g., Boltzmann-Shannon, Burg entropy, Fisher information) on the well-posedness of the problem and the form of the solution.
||Convex programming duality: what it is and what it buys you.
||Non-convex extensions: life is hard. But sometimes more works than should.
Jonathan Michael Borwein is currently Laureate Professor in the School of Mathematical and Physical Sciences at the University of Newcastle (NSW) with adjunct appointments at Dalhousie and at Simon Fraser. He directs the University's Priority Research Centre in Computer Assisted Research Mathematics and its Applications (CARMA).
Dr. Borwein was Shrum Professor of Science (1993-2003) and a Canada Research Chair in Information Technology (2001-08) at Simon Fraser University, and was founding Director of the Centre for Experimental and Constructive Mathematics. From 2004 to 2009 he worked in the Faculty of Computer Science at Dalhousie as a Canada Research Chair in Distributed and Collaborative Research, cross-appointed in Mathematics.
He was born in St Andrews in 1951, and received his DPhil from Oxford in 1974, as a Rhodes Scholar. Prior to joining SFU in 1993, he worked at Dalhousie (1974-91), Carnegie-Mellon (1980-82) and Waterloo (1991-93).
Awards and Honours: He has received various awards including the Chauvenet Prize of the MAA (93), Fellowship in the Royal Society of Canada (94), Fellowship in the American Association for the Advancement of Science (02), an honorary degree from Limoges (99), and foreign membership in the Bulgarian Academy of Sciences (03).
Modelling the Variability of Rankings
For better or for worse, rankings of institutions, such as universities, schools and hospitals, play an important role today in conveying information about relative performance. They inform policy decisions and budgets, and are often reported in the media. While overall rankings can vary markedly over relatively short time periods, it is not unusual to find that the ranks of a small number of ``highly performing'' institutions remain fixed, even when the data on which the rankings are based are extensively revised, and even when a large number of new institutions are added to the competition. In this talk we endeavour to model this phenomenon. We interpret as a random variable the value of the attribute on which the ranking should ideally be based, and we interpret data as providing a noisy approximation to this variable. We show that, if the distribution of the true attributes is light-tailed (for example, normal or exponential), then the number of institutions whose ranking is correct, even after recalculation using new data and even after many new institutions are added, is essentially fixed. Cases where the number of reliable rankings increases significantly when new institutions are added are those for which the distribution of the true attributes is relatively heavy-tailed.
Peter Hall was born in Sydney, Australia, and received his BSC degree from the University of Sydney in 1974. His MSc and DPhil degrees are from the Australian National University and the University of Oxford, both in 1976. He taught at the University of Melbourne before taking, in 1978, a position at the Australian National University. In November 2006 he moved back to the University of Melbourne. His research interests range across several topics in probability and statistics.
The Square Root Problem of Kato for Elliptic Operators: Survey, Solution and Sequel
About 1960 Tosio Kato, during his investigation of the evolution of physical systems, was led to pose a key question about the square roots of elliptic partial differential operators. A positive answer to his question implies that the square root is stable under small perturbations, this being useful in solving related hyperbolic equations with time-varying coefficients. The one-dimensional problem was solved by Coifman, McIntosh and Meyer in 1982, while it was only in 2001 that the question was fully answered by Auscher, Hofmann, Lacey, McIntosh and Tchamitchian. The speaker will survey this development, and discuss further progress made with Axelsson and Keith.
An Introduction to Quantum Control
This talk will present an introduction to quantum control, with a particular emphasis on feedback control. Quantum mechanical models are discussed, using the language of quantum probability. In particular, the theory of quantum measurement and filtering is discussed due to its importance in measurement-based feedback control. Some examples from our current work are described.
Quantum Networks: Modelling, Analysis and Design
The focus of this talk is networks consisting of quantum and classical components. Such networks cover a wide range of situations relevant to quantum technologies including feedback systems, quantum information and computing systems, device modelling, etc. We begin by describing how components can be connected using algebraic and graphical tools, analogous to classical circuit theory. We then discuss dissipation in quantum systems in a manner which combines perspectives from physics and engineering using a network framework. We show how Willems' control by interconnection paradigm can be implemented using quantum network models.
Towards a Theory of Information for Control Systems
There has been a long held view that some form of information theory holds the key to a rigorous understanding of control problems which are subject to non-classical information patterns. In this talk we will review this idea and present recent results which connect information theory and stabilization theory. We discuss the so called data-rate theorem for classical stochastic linear systems and then present new results on the 'lowest data-rate' stabilization of interconnected large scale systems.
Hedging Contingent Claims with portfolios submitted to constraints and frictions
A contingent claim is a random financial commitment to be fulfilled at some future time. This entails risk and opportunities. Black-Scholes-Merton approach consists in providing a way to benefit from opportunities without taking risks. It is based on hedging the contingent claim with a portfolio of stocks valued on the market. With some initial investment, it is possible to guarantee a sufficient wealth at the time of commitment to pay the contingent claim in all circumstances. This wealth is provided by an adequate portfolio, which evolves according to market changes. However, the approach is based on many assumptions, which are not in general satisfied. One of them is the absence of constraints on admissible portfolios. A lot of efforts has been devoted to extend the approach to take into account constraints and frictions on admissible portfolios. We will review some of the ideas to treat this question, and emphasize the interest of an approach based on penalty techniques.