## Australian Mathematical Society Lift-Off Fellows

The *Australian Mathematical Society Lift-off Fellowships* are designed to help recent PhD graduates in Mathematics and Statistics jump-start their career by giving them financial support during the period between the submission of their PhD thesis and their first postdoctoral position. The Lift-off Fellowships are awarded on the basis
of academic merit.

The rules and application forms for the Lift-Off Fellowships can be found on the Lift-Off Fellowship information page.

**The Australian Mathematics Society Lift-Off Fellows to date are**:

- 2015 – Dr Koenraad van den Dungen
Dr van den Dungen's research is in the field of noncommutative geometry applied to gauge theory and relativity.
He has developed two definitions for Lorentzian spectral triples,
shown that they both preserve the link with analytic
*K*-homology, and identified the conditions under which Lorentzian or pseudo-Riemannian manifolds satisfy these definitions. He has also defined Krein spectral triples, proposed a Lorentzian alternative for the fermionic action, and shown that this action recovers exactly the correct physcial Lagrangian. Dr van den Dungen will use his Lift-Off Fellowship to conduct research with Associate Professor Adam Rennie at the University of Wollongong. He intends to develop a symmetric version of a theorem of Kaad and Lesch, in the context of indefinite Kasparov modules, and also to analyse the properties of the Dirac operator on the standard example of Schwarzschild spacetime. - 2015 – Dr Caley Finn
Dr Finn's research area is statistical mechanics, with a focus on the asymmetric exclusion process (ASEP), a one-dimensional
stochastic model. He has calculated the relaxation rate in the reverse bias regime, by numerically solving the Bethe ansatz equations.
He has studied the Prioritising Exclusion Process, a queueing model with high and low priority customer;
he found the exact stationary state in some phases, and calculated approximate average waiting times when the queue length is finite.
He has also found an integral form for some components of the solution of a
*q*-deformed Knizhnik–Zamolodchikov (qKZ) equation with mixed boundaries, along with developing a combinatorial algorithm that determines a factorised expression for a generalised sum rule. Dr Finn will use his fellowship to attend the three-week workshop “Statistical Mechanics, Integrability and Combinatorics”, at the Galileo Galilei Institute in Florence, Italy. He will also visit his future collaborator, Professor Eric Ragoucy, for research discussions at the Laboratoire d'Annecy-le-Vieux de Physique Théorique (LAPTh) in Annecy, France, where he will take up a post-doctoral position in October 2015. - 2015 – Dr Kristen Harley Dr Harley's research focuses on advection–reaction–diffusion equations and travelling wave solutions arising in models from mathematical biology, and uses methods from dynamical systems theory such as geometric singular perturbation theory and canard solutions. She has proved the existence of travelling-wave solutions for a malignant tumour model with small diffusion, and the existence of a shock-fronted travelling wave solution for a wound-healing model. Dr Harley will use her Lift-Off Fellowship to participate in the 2015 SIAM Conference on Applications of Dynamical Systems (DS15) in Utah, USA, and for research collaboration at the University of Oxford with Dr Frits Veerman. She will also continue collaborations on models of solid tumour growth, on the stability of travelling waves, and on periodic solutions to a three-component FitzHugh–Nagumo model, with collaborators including Dr Petrus van Heijster of the Queensland University of Technology, Associate Professor Sanjeeva Balasuriya of the University of Adelaide, Ms Lotte Sewalt of the University of Leiden, and Dr Robert Marangell and Professor Martin Wechselberger of the University of Sydney.
- 2015 – Dr Andrew Holder Dr Holder's research area is the mathematical modelling of tumour invasion, using differential equations, dynamical systems, spatio-temporal modelling, asymptotic analysis and numerical programming. He has introduced an algorithm for reduction of a dynamic system to a set of algebraic equations, from which parameter estimates can be deduced. He has applied this algorithm to three areas within mathematical biology. Dr Holder will use his Fellowship to participate in the 2015 ANZIAM Conference on the Gold Coast, and to write up a paper drawing on research from his thesis on a system of reaction–diffusion equations used for modelling the acid-mediation hypothesis with chemotherapy intervention. He also intends to develop a new model that examines the interaction between a tumour, its metabolism and the host immune response.
- 2015 – Dr Naghmana Tehseen Dr Tehseen's research areas are partial differential equations, differential geometry and mathematical physics. She has developed a new approach to constructing solutions of differential equations, which is complementary to the symmetry reduction methods initiated by Sophus Lie. She has used her approach to construct solutions to the Boyer–Finley and heavenly equations from general relativity. She has also analysed the monotonicity of the Shannon entropy on solution surfaces of the second-order evolution equation. Dr Tehseen will use her fellowship to collaborate with Professor Peter Vassiliou of the University of Canberra, and Associate Professor Jose de Dona of the University of Newcastle. She plans to use the geometry of differential systems on manifolds to attack the geometric control theory problem of finding computable necessary and sufficient conditions under which a control system is flat. Further, she will investigate higher-order solvable structures, in particular the properties of solutions found by her methods for partial differential equations, in more than two variables, that have infinite-dimensional symmetry algebras. Also, with Professor Geoff Prince of the Australian Mathematical Sciences Institute, she will apply geometric techniques to analyse the monotonic entropy behaviour of fourth-order evolution equations on solution surfaces.
- 2015 – Dr Ying Wan Yap Dr Yap's research area is the kinetic theory of rarefied gases. She has developed high accuracy numerical solutions for rarefied oscillatory nanoscale gas flows, specifically the Boltzmann–BGK equation for unidirectional steady and unsteady Couette flow. She has also found solutions to the 3D flow generated by an oscillating sphere, and has contributed to understanding the validity of the lattice Boltzmann method for non-continuum flows. Dr Yap's Fellowship will enable her to participate in the 2015 ANZIAM Conference. In addition, she intends to prepare further manuscripts stemming from her thesis work, in collaboration with Professor John Sader of the University of Melbourne and Dr Jason Nassios of Victoria University, and to initiate a study of heat transfer using the lattice Boltzmann method.
- 2014 – Dr Yi Huang
Dr Huang’s research focuses on genus
*g*hyperbolic surfaces with*n*cusps and their Teichmüller and moduli spaces. He has generalised known coordinate systems on the moduli space of hyperbolic surfaces with cusps or geodesic boundaries or a combination of both. He has also produced various new McShane identities on hyperbolic surfaces which generalise known identities. He has generated a simple length spectrum of a projective plane with three punctures to prove various results, including calculating the maximum systole on the moduli space of hyperbolic projective planes with three cusps. Dr Huang will use his fellowship to visit A/Prof Hideki Miyachi at Osaka University to develop a quasiconformal maps-based approach to the Teichmüller theory of crowned hyperbolic surfaces. He will also visit Dr Hengnan Hu and Prof Ser Peow Tan at National University of Singapore to determine a geometric interpretation of Hu and Tan’s recently derived new McShane identity. - 2014 – Dr Stephen Maher Dr Maher’s research area is mathematical optimisation with a focus on airline applications. He has investigated such problems using column-and-row generation and found that the implementation of this approach to solve an airline recovery problem required further development to reduce solution runtimes. To address this issue, Dr Maher will use his fellowship to visit Francois Vanderbeck at the University of Bordeaux to establish collaboration in order to improve the column-and-row generation solution approach to significantly improve the solution runtimes of large scale optimisation problems. The fellowship will assist Dr Maher to develop improved row generation strategies, analysing the formulations of problems successfully solved by column-and-row generation and improving the integration of column-and-row generation with branch-and-price.
- 2014 – Dr Hui Li
Dr Li’s research area is operator algebra. He has developed a structure theory for the associated Cuntz–Pimnser algebra and used his theory to show that a result in the literature is an example of a twisted topological graph C*-algebra. Dr Li will use his fellowship to visit Universidade Federal de Santa Catarina (UFSC), Florianópolis, Brazil, in order to collaborate with Professor Daniel Gonçalves and Professor Danilo Royer. At UFSC, Dr Li plans to study a representation of each
*k*-graph algebra on the Hilbert space*L*_{2}(**R**^{k}), where*k*is the dimension of the*k*-graph. For both directed graphs and higher-rank graphs, he intends to find conditions such that these representations are irreducible; conditions which are important in the representation theory of Lie groups and harmonic analysis. - 2013 – Dr Brian Corr Dr Corr is a computational group theorist with a particular interest in matrix groups and so-called black box algorithms for recognising groups. His thesis contains a generalisation of the famous Kung–Stong Cycle Index Theorem as well as developing several new algoithms for matrix group recognition. He will use his Lift-Off fellowship to visit researchers in Germany, the USA and New Zealand.
- 2013 – Dr Natalie Aisbett Dr Aisbett is a combinatorial topologist with particular interest in simplicial spheres. She has made significant contributions towards solving some of the major conjectures in this field. In particular, Dr Aisbett has proved the Nevo-Petersen conjecture for the class of simplicial spheres that are obtained from the boundary of a cross-polytope by an arbitrary sequence of edge subdivisions. She will use her Lift-Off Fellowship to continue her work on simplicial spheres and to study combinatorial complexes for complex reflection groups.
- 2013 – Dr Nahid Banihashemi Dr Banihashemi uses numerical methods to solve optimal control problems with an emphasis on real world applications. She has developed novel algorithms for solving a general class of box-constrained optimal control problems building on inexact restoration methods and Euler discretization. Dr Banihashemi will use her Lift-Off Fellowship to develop a computational model of the co-metabolism of carbon and nitrogen in collaboration with Professor John Crawford at the Charles Perkins Obesity Centre at the University of Sydney.
- 2012 – Dr Nicholas Beaton Dr Beaton works on solvable lattice models, polymer absorption and self-avoiding walks. With coauthors he has given precise estimates for the surface fugacity of random walks on several planar lattices. He will use his fellowship to study self-avoiding walks on a rotated honeycomb lattice and prudent walks on lattices.
- 2012 – Dr James Caffrey Dr Caffrey is a mathematical biologist who has developed models of interacting populations to understand experimental observation using a mixture of analytical tools and simulations. He will use his Lift-Off Fellowship to continue his work and to attend the 12th International Symposium on Mathematical and Computational Biology in Arizona.
- 2012 – Dr Bao Ho Dr Ho is a combinatorial game theorist with expertise in analyzing the game of NIM and its many variations, some of which he introduced. He will use his Lift-off Fellowship to investigate periodicity in subtraction games and, more generally, in octal games.
- 2012 – Dr Anthony Mays Dr Mays works in mathematical physics and random matrix theory, having particular expertise in studying the distributions of the eigenvalues of random matrices. Dr Mays will use his Lift-Off Fellowship to attend the “Random matrices” workshop at the University of Bonn in May 2012 and to visit Professor Akemann at the University of Bielefeld, one of the leaders in his field.
- 2011 – Dr Tyson Ritter Dr Ritter is a complex geometer with particular expertise in elliptic manifolds and Oka theory. He has shown that every Riemann surface with abelian fundamental group can be acyclically embedded into a two dimensional elliptic Stein manifold. Using very different techniques, he constructed some interesting new examples of elliptic manifolds which he then used to prove similar results for open Riemann surfaces. He will use his Lift-Off Fellowships to study related questions in Oka theory.
- 2011 – Dr Joanne Hall Dr Hall works on the interface between coding theory, combinatorics and geometry. She gave the first explicit construction of mutually orthogonal Latin squares from mutually unbiased bases. Her lift-off fellowship will allow her to continue her work relating these structures and Hjelmslev geometries. In addition, it will partially support her collaboration with Metod Saniga at the Slovak Academy of Sciences.
- 2011 – Dr Wendy Baratta Dr Baratta’s research is concerned with the non-symmetric Macdonald polynomials. She will use her Lift-off fellowship to continue working with Forrester at the University of Melbourne and to finishing writing up her work and making it readily available to other mathematicians via Mathematica.
- 2011 – Dr Michael Pauley Dr Pauley works on generalisations of cubic polynomials to Riemannian manifolds and Lie group. He will use his lift-off fellowship to investigate higher order variational problems with Prof Óscar Garay and his colleagues at the University of the Basque Country, Spain, and to visit Imperial College.
- 2010 – Dr Neil Saunders Dr Saunders' has obtained substantial new results about the minimal embeddings of finite groups inside symmetric groups. He will use his Lift-Off fellowship to continue his study of the minimal embedding problem for Coxeter groups and complex reflection groups and to help foster collaborations with groups in Cornell and Melbourne.
- 2010 – Dr Philip Brooker Dr Brooker has obtained significant results in the theory of operator ideals and Banach spaces where he has used Szlenk indices to define a class of operators ideals which, by his work, have very favourable algebraic and geometric properties. Philip will use his Lift-Off Fellowship to compute the Szlenk indices of the Banach spaces of continuous scalar valued functions on a compact space.
- 2010 – Dr Judith Egan Dr Egan has obtained significant results in the area of orthogonal partitions of latin squares. With her Lift-Off Felllowship Judith will continue her collaboration with Ian Wanless (Monash) and Brendan McKay (ANU).
- 2010 – Dr Michael Haythorpe Dr Haythorpe works in numerical optimisation and computational mathematics with particular expertise in numerical algorithms. He was awarded the TM Cherry Prize Winner for Best Student Presentation at the ANZIAM conference in 2008 and he was runner up in 2009 and 2010. Using his Lift-Off Fellowship Michael initiated a collaboration with Walter Murray at Stanford University.
- 2010 – Dr Roslyn Hickson
Dr Hickson is an applied mathematician with particular expertise in
modelling and industrial applications. She has wide ranging interests from
diffusion and heat transfer to disease modelling. Roslyn used her Lift-Off Fellowship to
participate in a course on
*Mathematical Modelling of Infectious Diseases*at the University of Utrecht.