## Archived seminars in MathematicsSeminars 1 to 50 | Next 50 seminars |

### Dominic Searles

*Department of Mathematics and Statistics*

Date: Tuesday 29 May 2018

In joint work with Assaf, we consider the application of Kohnert's algorithm to arbitrary box diagrams in the positive quadrant; we call the resulting polynomials Kohnert polynomials. We establish some structural results about Kohnert polynomials, including that their stable limits are quasisymmetric. Certain choices of box diagrams yield bases of the polynomial ring in a natural way; as an application, we use these results to introduce a new basis of polynomials whose stable limit is a new basis of quasisymmetric functions that contains the Schur functions. Some further conjectures regarding Kohnert polynomials will be presented.

### Honours and PGDip students

*Department of Mathematics and Statistics*

Date: Friday 25 May 2018

Qing Ruan : ~~Bootstrap selection in kernel density estimation with edge correction~~

Willie Huang : ~~Autoregressive hidden Markov model - an application to tremor data~~

MATHEMATICS

Tom Blennerhassett : ~~Modelling groundwater flow using Finite Elements in FEniCS~~

Peixiong Kang : ~~Numerical solution of the geodesic equation in cosmological spacetimes with acausal regions~~

Lydia Turley : ~~Modelling character evolution using the Ornstein Uhlenbeck process~~

Ben Wilks : ~~Analytic continuation of the scattering function in water waves~~

Shonaugh Wright : ~~Hilbert spaces and orthogonality~~

Jay Bhana : ~~Visualising black holes using MATLAB~~

### Boris Daszuta

*Department of Mathematics and Statistics*

Date: Tuesday 22 May 2018

In particular, assuming a moment in time symmetry in vacuum reduces the problem of solving the constraints to a restriction of zero scalar curvature associated with the initial data set. A result due to [1] at the analytical level provides a technique for local control on the aforementioned set and may be used to engineer initial data with well-defined asymptotics. In short, one may glue together distinct, known solutions from differing regions in a controlled manner forming new data.

The aim of this talk is to demonstrate how a numerical scheme may be fashioned out of the above and present results pertaining to a numerical gluing construction.

Ref:

[1]: (Corvino, J.) Scalar Curvature Deformation and a Gluing Construction for the Einstein Constraint Equations. ~~Communications in Mathematical Physics~~ 214, 1 (2000), 137-189.

### Markus Antoni

*Department of Mathematics and Statistics*

Date: Tuesday 15 May 2018

### Joshua Ritchie

*Department of Mathematics and Statistics*

Date: Tuesday 8 May 2018

### Lettie Roach

*Victoria University Wellington and NIWA*

Date: Tuesday 1 May 2018

### Valerie Isham, NZMS 2018 Forder Lecturer

*University College London*

Date: Tuesday 24 April 2018

In this talk, I will review some stochastic point process-based models constructed in continuous time and continuous space using spatial-temporal examples from hydrology such as rainfall (where flood control is a particular application) and soil moisture. By working with continuous spaces, consistent properties can be obtained analytically at any spatial and temporal resolutions, as required for fitting and applications. I will start by covering basic model components and properties, and then go on to discuss model construction, fitting and validation, including ways to incorporate nonstationarity and climate change scenarios. I will also describe some thoughts about using similar models for wildfires.

### Valerie Isham, NZMS 2018 Forder Lecturer

*University College London*

Date: Monday 23 April 2018

Epidemic models are developed as a means of gaining understanding about the dynamics of the spread of infection (human and animal pathogens, computer viruses etc.) and of rumours and other information. This understanding can then inform control measures to limit spread, or in some cases enhance it (e.g., viral marketing). In this talk, I will give an introduction to simple generic epidemic models and their properties, the role of stochasticity and the effects of population structure (metapopulations and networks) on transmission dynamics, illustrating some past successes and outlining some future challenges.

### Robert Aldred

*Department of Mathematics and Statistics*

Date: Tuesday 17 April 2018

Several attempts at proving the famous 4-colour theorem involved the existence of Hamiltonian cycles in planar graphs related to triangulations of the plane. We will discuss some of these and outline a proof that that the number of Hamiltonian cycles in a 5-connected planar triangulation on $n$ vertices grows exponentially with $n$.

### Mihály Kovács

*Chalmers University of Technology and Gothenburg University*

Date: Tuesday 10 April 2018

### Sergei Fedotov

*The University of Manchester*

Date: Tuesday 27 March 2018

### Yawen Chen

*Department of Computer Science*

Date: Tuesday 20 March 2018

In this talk, I would like to introduce my recent graph-related research problems on Optical Network-on-Chips, which need to be investigated with the knowledge of graph theory and combinatorial optimisation. Feedback and suggestions would be much appreciated from the math department. Below is the background of this research.

Nowadays microprocessor development has moved into a new era of many-core on-chip design, with tens or even hundreds of cores fitting within a single processor chip to speed up computing. However, conventional electrical interconnect for inter-core communication is limited by both bandwidth and power density, which creates a performance bottleneck for microchips in modern computer systems - from smartphones to supercomputers, and to large-scale data centers. Optical Network-on-Chip (ONoC), a silicon-based optical interconnection among cores at the chip level, overcomes the limitations of conventional electrical interconnects by supporting greater bandwidth with less energy consumption, and opens the door to bandwidth- and power-hungry applications. This talk will introduce graph-related research problems on ONoCs from a networking perspective and present our current results and challenging problems for designing efficient multicast routing schemes specific for ONoCs.

### Cornelia Schneider

*University Erlangen-Nuremberg*

Date: Tuesday 13 March 2018

### Bernard Deconinck

*University of Washington*

Date: Tuesday 6 March 2018

I will provide an overview of what is known about the stability of spatially periodic water waves, discussing historically significant results, skipping all mathematical details. Then I will introduce different asymptotic models that are used to describe water waves in different regimes (long waves in shallow water, modulated waves in deep water, etc) and I will discuss how the stability results in this context do or do not make sense compared to those in the context of the full water wave problem.

Time permitting, I will give more detail on recent work to understand the stability of modulated waves in deep water with respect to so-called subharmonic perturbations.

### Sarah Wakes

*Centre for Materials Science and Technology*

Date: Tuesday 27 February 2018

Sarah has a BSc (Jt Hons) in Mathematics and Physics and a PhD in Theoretical Mechanics from the University of Nottingham (UK), a chartered engineer in the UK and a chartered member of Engineering NZ.

### Jonny Williams

*National Institute of Water and Atmospheric Research (NIWA)*

Date: Wednesday 15 November 2017

##A joint seminar with the Department of Physics##

Earth System models are able to produce the most advanced computational representations of our planet that we have. They are able to simulate the properties of the atmosphere, ocean and cryosphere as well as biogeochemical processes in the air and in the water. I will give a tour of Earth System models and will discuss their strengths and weaknesses since all models are wrong but some are useful! These models require a lot of computational power and right now we are in the process of replacing New Zealand's supercomputers so I'll discuss these too.

### Tom ter Elst

*University of Auckland*

Date: Tuesday 31 October 2017

The talk is based on a joint work with W Arendt (Ulm).

### Matthew Parry

*Department of Mathematics and Statistics*

Date: Tuesday 24 October 2017

### Rachel Weir

*Allegheny College, Pennsylvania*

Date: Monday 16 October 2017

A common theme in the United States in recent years has been a call to increase the number of graduates in STEM (science, technology, engineering, and mathematics) fields and to enhance the scientific literacy of students in other disciplines. For example, in the 2012 report Engage to Excel, the Obama administration announced a goal of "producing, over the next decade, 1 million more college graduates in STEM fields than expected under current assumptions." Achieving these types of goals will require us to harness the potential of all students, forcing us to identify and acknowledge the barriers encountered by students from traditionally underrepresented groups. Over the past few years, I have been working to understand these barriers to success, particularly in mathematics. In this talk, I will share what I have learned so far and how it has influenced my teaching.

### Gemma Mason

*University of Auckland*

Date: Tuesday 10 October 2017

### Honours and PGDip students

*Department of Mathematics and Statistics*

Date: Friday 6 October 2017

Jodie Buckby : ~~Model checking for hidden Markov models~~

Jie Kang : ~~Model averaging for renewal process~~

Yu Yang : ~~Robustness of temperature reconstruction for the past 500 years~~

MATHEMATICS

Sam Bremer : ~~An effective model for particle distribution in waterways~~

Joshua Mills : ~~Hyperbolic equations and finite difference schemes~~

### Ken Ono

*Emory University; 2017 NZMS/AMS Maclaurin Lecturer*

Date: Thursday 5 October 2017

Ramanujan’s work has had a truly transformative effect on modern mathematics, and continues to do so as we understand further lines from his letters and notebooks. In this lecture, some of the studies of Ramanujan that are most accessible to the general public will be presented and how Ramanujan’s findings fundamentally changed modern mathematics, and also influenced the lecturer’s work, will be discussed. The speaker is an Associate Producer of the film ~~The Man Who Knew Infinity~~ (starring Dev Patel and Jeremy Irons) about Ramanujan. He will share several clips from the film in the lecture.

Biography: Ken Ono is the Asa Griggs Candler Professor of Mathematics at Emory University. He is considered to be an expert in the theory of integer partitions and modular forms. He has been invited to speak to audiences all over North America, Asia and Europe. His contributions include several monographs and over 150 research and popular articles in number theory, combinatorics and algebra. He received his Ph.D. from UCLA and has received many awards for his research in number theory, including a Guggenheim Fellowship, a Packard Fellowship and a Sloan Fellowship. He was awarded a Presidential Early Career Award for Science and Engineering (PECASE) by Bill Clinton in 2000 and he was named the National Science Foundation’s Distinguished Teaching Scholar in 2005. In addition to being a thesis advisor and postdoctoral mentor, he has also mentored dozens of undergraduates and high school students. He serves as Editor-in-Chief for several journals and is an editor of The Ramanujan Journal. He is also a member of the US National Committee for Mathematics at the National Academy of Science.

### Ken Ono

*Emory University; 2017 NZMS/AMS Maclaurin Lecturer*

Date: Thursday 5 October 2017

In 1927 Pólya proved that the Riemann Hypotheses is equivalent to the hyperbolicity of Jensen polynomials for Riemann’s Xi-function. This hyperbolicity has been proved for degrees $d\leq 3$. We obtain an arbitrary precision asymptotic formula for the derivatives $\Xi^{(2n)}(0)$ which allows us to prove the hyperbolicity of 100% of the Jensen polynomials of each degree. We obtain a general theorem which models such polynomials by Hermite polynomials. This theorem also allows us to prove a conjecture of Chen, Jia, and Wang on the partition function.

This is joint work with Michael Griffin, Larry Rolen and Don Zagier.

### Jörg Frauendiener

*Department of Mathematics and Statistics*

Date: Tuesday 26 September 2017

In this talk the origin of the Penrose inequality and some attempts and special cases of its proof will be discussed in more detail.

### Philippe LeFloch

*Université Pierre et Marie Curie*

Date: Tuesday 19 September 2017

This lecture will present recent work on a class of partial differential equations arising in mathematical physics in the context of Einstein's theory of gravity. Specifically, I will consider the question of the nonlinear stability of Minkowski spacetime and I will review the global evolution problem for self-gravitating massive matter. The presentation will kept at an introductory level, accessible to students and non-experts.

### Philippe LeFloch

*Université Pierre et Marie Curie, visiting William Evans fellow*

Date: Wednesday 13 September 2017

Waves surround us, and many technological advances were made possible only because engineers, physicists, and applied mathematicians worked together in order to understand these phenomena. Understanding shock waves was essential to design the modern airliners, which we use to travel. Understanding electro-magnetic waves propagating in space (and time!) was essential to design the GPS global navigation system and allow us to use cell phones. In this lecture, from the perspective of an applied mathematician, I will illustrate with examples the role of mathematics in overcoming practical problems using pioneering works by Leonhard Euler, James Maxwell, and Albert Einstein. Blog: https://philippelefloch.org/

### Melissa Tacy

*Department of Mathematics and Statistics*

Date: Tuesday 12 September 2017

### Richard Norton

*Department of Mathematics and Statistics*

Date: Tuesday 5 September 2017

Markov chain Monte Carlo (MCMC) methods compute a sequence of correlated samples of the random variable, and estimate the expectation by an average over the samples. The error of computing finitely many samples is estimated by computing estimates of the integrated autocorrelation time and variance. Generally, to be accurate, MCMC requires cheap evaluations of the density function.

When the density function is costly (in CPU time) to evaluate then we can try replacing it with a 'proxy' that is cheap to evaluate and perform MCMC on the proxy. But what error does this introduce?

I will present a computable upper bound for this error and apply it to a couple of simple examples.

### Alice Harang

*Department of Marine Science*

Date: Tuesday 22 August 2017

### Markus Antoni

*Department of Mathematics and Statistics*

Date: Tuesday 15 August 2017

\begin{equation*}

d X(t) + A X(t) d t = F(t,X(t)) d t + B(t,X(t)) d β(t)

\end{equation*}

for random fields $X \colon \Omega \times [0,T] \times U \to \mathbb{R}$, where $[0,T]$ is a time interval, $(\Omega,\mathcal{F},\mathbb{P})$ a measure space representing the randomness of the system, and $U$ is typically a domain in $\mathbb{R}^d$ (or again a measure space). We reduce the existence and uniqueness of solutions to a fixed point equation in certain fixed point spaces. To be more precise, we look for mild solutions so that $X(\omega,\cdot,\cdot)$ has values in $L^p(U;L^q[0,T])$ for almost all $\omega \in \Omega$ under appropriate Lipschitz and linear growth conditions on the nonlinearities $F$ and $B$. In contrast to the classical semigroup approach, which gives $X(\omega,\cdot,\cdot) \in L^q([0,T];L^p(U))$, the order of integration is reversed. In combination with concrete examples of stochastic partial differential equations we show that this new approach leads to strong regularity results in particular for the time variable of the random field $X(\omega,t,u)$, e.g.

*pointwise*Hölder estimates for the paths $t \mapsto X(\omega,t,u), \mathbb{P}$-almost surely.

### Johannes Mosig

*Department of Mathematics and Statistics*

Date: Tuesday 8 August 2017

I will present my Mathematica package which makes it easy to work with gPC methods on any physical model, and demonstrate a few applications in the area of ocean wave/sea ice interactions.

### Boris Baeumer

*Department of Mathematics and Statistics*

Date: Tuesday 1 August 2017

### Florian Beyer

*Department of Mathematics and Statistics*

Date: Tuesday 23 May 2017

### Chris Horvat

*Harvard University*

Date: Tuesday 2 May 2017

I'll discuss how melt ponding on sea ice floes has dramatically shifted the ecological status quo in the Arctic. Using a combination of simple modeling techniques, observations, and reanalysis products I'll demonstrate that the thinning of sea ice in the past several decades allows for extensive and frequent under-ice phytoplankton blooms, which can have a significant effect on the ecological and carbon cycle in the high latitudes.

I'll also discuss how the thermodynamic evolution of sea ice is determined through the interaction of sea ice floes and ocean eddies, and how these are determined by the floe size distribution. I'll then present a predictive model for the joint statistical distribution of floe sizes and thicknesses (FSTD) which is tested under different forcing scenarios to establish its conservation properties and demonstrate its usability in future climate studies.

Suggested reading:

Horvat, Rees Jones, Iams, Schroeder, Flocco, & Feltham (2017). The frequency and extent of sub-ice phytoplankton blooms in the Arctic Ocean.

*Science Advances*.

Horvat, Tziperman, & Campin (2016) Interaction of sea ice floe size, ocean eddies, and sea ice melting.

*Geophys. Res. Lett.*

### Jörg Hennig

*Department of Mathematics and Statistics*

Date: Tuesday 11 April 2017

### John Clark

*Department of Mathematics and Statisitcs*

Date: Tuesday 4 April 2017

$$r(sm) = (rs)m, \; (r+s)m = rm + sm,\; \text{ and }\; r(m+n) = rm + rn.$$

Note that this definition generalises that of a vector space $M$ over a field $R$.

In the special vector space setting, linear algebra introduces the important concepts of linearly (in)dependent subsets and generating subsets of a vector space $M$. The same definitions carry over to modules. A pivotal result in linear algebra says that every vector space $M$ has a ${\bf basis}$, i.e., $M$ has a linearly independent subset $B$ which also generates $M$. Moreover any two bases of $M$ have the same size. This unique size, say $n$, is called the ${\bf dimension}$ of $M$ and we write $\dim(M) = n$.

In this talk we’ll look at how the transfer of these and some related results fail for some rings.

### Maciej Floryan

*University of Western Ontario*

Date: Thursday 30 March 2017

**Note venue for this seminar**

A joint seminar by the Departments of Mathematics and Statistics, and Physics

A joint seminar by the Departments of Mathematics and Statistics, and Physics

It has been recognized since the pioneering experiments of Reynolds in 1883 that surface roughness plays a significant role in the dynamics of shear layers. This is a classical problem in fluid dynamics but, nevertheless, its resolution is still lacking. Most of the efforts have been focused on experimental approaches that have resulted in a number of correlations but have failed to uncover the mechanisms responsible for the flow response. Theoretical analyses have also failed to provide a consistent explanation of the flow dynamics. As there are an uncountable number of possible geometrical roughness forms, the problem formulation represents a logical contradiction as it might not be possible to find a general answer to a problem that has an uncountable number of variations. The recent progress towards the theoretical resolution of this apparent contradiction will be discussed and recent results dealing with the problem of distributed surface roughness will be presented. The progress has hinged on the development of the immersed boundary conditions method and the reduced geometry concept. It will be shown that it is possible to propose a rational definition of a hydraulically smooth surface by invoking flow bifurcations associated with the presence of roughness. Successful resolution of roughness problems gives access to the design of surface roughness for passive flow control where drag reduction can be achieved either directly, through re-arrangement of the form of the flow that results in the reduction of the shear stress, or indirectly, through delay of the laminar-turbulent transition.

### David Bryant

*Department of Mathematics and Statisitcs*

Date: Tuesday 21 March 2017

### Vee-Liem Saw

*Department of Mathematics and Statisitcs*

Date: Tuesday 28 February 2017

### Rajeev Rajaram

*Kent State University, Ohio*

Date: Tuesday 7 February 2017

**NOTE venue is not our usual**

In this talk, I will develop an entropy-based measure called case-based entropy which can be used to compare the diversity of distributions. The measure is based on computing the support of a

*Shannon-equivalent equi-probable*distribution. It also has the capacity to compare whole or parts of distribution in a scale-free manner. I will develop the main idea from scratch and will keep the talk accessible to graduate students and researchers alike. The utility of the measure is still being explored, but one of the latest uses that I found is its use in economics as a better method to compare income or wealth inequality than the Gini index, for example. I have also used the measure to compare the diversity of complexity in a variety of distributions from the velocities of galaxies to the energy distribution of Maxwell Boltzmann, Bose-Einstein and Fermi-Dirac distributions.

### Olaf Knapp

*University of Education Weingarten, Germany*

Date: Wednesday 25 January 2017

**Note day, time and venue of this special seminar**

3D-dynamic geometry systems (3D-DGS) with graphical user interfaces can open up a wide range of creative activities for mathematics education. Examples will be given from a research project into their use for didactic presentations, visualization, synthetic geometry, 3D modelling, morphing and mapping, design, and analogization. They allow interactive exploration of mathematical concepts. I will show their potential to become an integral part of mathematics education and to modify the curriculum. There is also the opportunity for hands-on experience with a 3D-DGS.

### Scotland Leman

*Virginia Tech, USA*

Date: Tuesday 8 November 2016

**NOTE day and time of this seminar**

In this talk I will primarily discuss the Multiset Sampler (MSS): a general ensemble based Markov Chain Monte Carlo (MCMC) method for sampling from complicated stochastic models. After which, I will briefly introduce the audience to my interactive visual analytics based research.

Proposal distributions for complex structures are essential for virtually all MCMC sampling methods. However, such proposal distributions are difficult to construct so that their probability distribution match that of the true target distribution, in turn hampering the efficiency of the overall MCMC scheme. The MSS entails sampling from an augmented distribution that has more desirable mixing properties than the original target model, while utilizing a simple independent proposal distributions that are easily tuned. I will discuss applications of the MSS for sampling from tree based models (e.g. Bayesian CART; phylogenetic models), and for general model selection, model averaging and predictive sampling.

In the final 10 minutes of the presentation I will discuss my research interests in interactive visual analytics and the Visual To Parametric Interaction (V2PI) paradigm. I'll discuss the general concepts in V2PI with an application of Multidimensional Scaling, its technical merits, and the integration of such concepts into core statistics undergraduate and graduate programs.

### Ivor Cribben

*University of Alberta*

Date: Wednesday 19 October 2016

**NOTE day and time of this seminar**

Spectral clustering is a computationally feasible and model-free method widely used in the identification of communities in networks. We introduce a data-driven method, namely Network Change Points Detection (NCPD), which detects change points in the network structure of a multivariate time series, with each component of the time series represented by a node in the network. Spectral clustering allows us to consider high dimensional time series where the number of time series is greater than the number of time points. NCPD allows for estimation of both the time of change in the network structure and the graph between each pair of change points, without prior knowledge of the number or location of the change points. Permutation and bootstrapping methods are used to perform inference on the change points. NCPD is applied to various simulated high dimensional data sets as well as to a resting state functional magnetic resonance imaging (fMRI) data set. The new methodology also allows us to identify common functional states across subjects and groups. Extensions of the method are also discussed. Finally, the method promises to offer a deep insight into the large-scale characterisations and dynamics of the brain.

### Richard Norton

*Department of Mathematics and Statistics*

Date: Tuesday 18 October 2016

I analyse the efficiency of Metropolis-Hastings algorithms with stochastic autoregressive proposals. These include many existing methods, such as the Metropolis-Adjusted Langevin Algorithm (MALA), the preconditioned Crank-Nicolson algorithm (pCN) and the Hybrid Monte Carlo algorithm (HMC). Previously, each of these algorithms required their own separate analyses. Using my analysis I can extend what is known about these algorithms as well as analysing new algorithms.

### John Tipton

*Colorado State University*

Date: Tuesday 18 October 2016

**NOTE day and time of this seminar**

Many scientific disciplines have strong traditions of developing models to approximate nature. Traditionally, statistical models have not included scientific models and have instead focused on regression methods that exploit correlation structures in data. The development of Bayesian methods has generated many examples of forward models that bridge the gap between scientific and statistical disciplines. The ability to fit forward models using Bayesian methods has generated interest in paleoclimate reconstructions, but there are many challenges in model construction and estimation that remain.

I will present two statistical reconstructions of climate variables using paleoclimate proxy data. The first example is a joint reconstruction of temperature and precipitation from tree rings using a mechanistic process model. The second reconstruction uses microbial species assemblage data to predict peat bog water table depth. I validate predictive skill using proper scoring rules in simulation experiments, providing justification for the empirical reconstruction. Results show forward models that leverage scientific knowledge can improve paleoclimate reconstruction skill and increase understanding of the latent natural processes.

### Benjamin Fitzpatrick

*Queensland University of Technology*

Date: Monday 17 October 2016

**NOTE day and time of this seminar**

When making inferences concerning the environment, ground truthed data will frequently be available as point referenced (geostatistical) observations accompanied by a rich ensemble of potentially relevant remotely sensed and in-situ observations.

Modern soil mapping is one such example characterised by the need to interpolate geostatistical observations from soil cores and the availability of data on large numbers of environmental characteristics for consideration as covariates to aid this interpolation.

In this talk I will outline my application of Least Absolute Shrinkage Selection Opperator (LASSO) regularized multiple linear regression (MLR) to build models for predicting full cover maps of soil carbon when the number of potential covariates greatly exceeds the number of observations available (the p > n or ultrahigh dimensional scenario). I will outline how I have applied LASSO regularized MLR models to data from multiple (geographic) sites and discuss investigations into treatments of site membership in models and the geographic transferability of models developed. I will also present novel visualisations of the results of ultrahigh dimensional variable selection and briefly outline some related work in ground cover classification from remotely sensed imagery.

Key references:

Fitzpatrick, B. R., Lamb, D. W., & Mengersen, K. (2016). Ultrahigh Dimensional Variable Selection for Interpolation of Point Referenced Spatial Data: A Digital Soil Mapping Case Study.

*PLoS ONE*, 11(9): e0162489.

Fitzpatrick, B. R., Lamb, D. W., & Mengersen, K. (2016). Assessing Site Effects and Geographic Transferability when Interpolating Point Referenced Spatial Data: A Digital Soil Mapping Case Study. https://arxiv.org/abs/1608.00086

### Chris Linsell

*College of Education*

Date: Tuesday 6 September 2016

### Miguel Moyers-Gonzalez

*University of Canterbury*

Date: Tuesday 23 August 2016

### Melissa Tacy

*Australian National University*

Date: Tuesday 23 August 2016

**Note day, time and venue of this special seminar**

Semiclassical analysis arose as a set of techniques for studying the high energy (or semiclassical) limit of quantum mechanics. These techniques have the advantage that intuition derived from the quantum-classical correspondence principle can guide our technical development. In this talk I will introduce some of the key techniques and discuss results such as the $L^{p}$ growth for products of Laplacian eigenfunctions and high energy phase space concentration estimates.

### Fabien Montiel

*Department of Mathematics and Statistics*

Date: Monday 22 August 2016

**Note day and time of this special seminar**

In a one-dimensional homogeneous medium, linear wave scattering by an array of inclusions, e.g. beads on a string, can be reduced to a multiple reflection/transmission problem, in which the reflected and transmitted waves by an inclusion become incident waves on the adjacent inclusions. Under time-harmonic conditions, fast iterative methods can be used to obtain the solution of this class of scattering problems. In a two-dimensional medium, however, such methods cannot be directly extended as there is no natural way of uniquely ordering a finite number of arbitrarily positioned inclusions, e.g. circles, in the plane. A semi-analytical method was devised to solve deterministically the scattering of time-harmonic waves by a large finite array of inclusions in two dimensions. The method consists of clustering the inclusions into adjacent parallel slabs. The solution is obtained by combining plane wave expansions of the scattered field by each slab and a fast iterative technique for slab-slab interactions similar to the one-dimensional method mentioned above.

In this talk, I will describe this so-called

*slab-clustering method*(SCM) and demonstrate how it provides a convenient framework to analyse the evolution of a multi-directional wave field through a large random array of inclusions. I will consider several applications of the methods in acoustics and water waves science. In particular, I will discuss some model predictions based on the SCM that generated key insights into the directional properties of water wave fields propagating in ice-covered oceans.