# Congratulations to the MSI ARC grant recipients

The MSI wishes to congratulate the recipients of the latest ARC grant round which was announced on Tuesday, 1 November. These grants make up part of the $43 million in funding awarded to the Australian National University which includes 15 Future Fellowships, 26 Discovery Early Career Research Awards (DECRAs), 46 Discovery Projects and four Linkage Infrastructure Equipment and Facilities (LIEF) grants.

**Scheme:** ARC Future Fellowships 2016 round 1**Recipient:** Associate Professor Uri Onn**Grant amount:** $776,000.00**Project:** Representations of arithmetic groups and their associated zeta functions.

This project aims to investigate deep connections between number theory and group theory by studying linear actions of arithmetic groups. Arithmetic groups are used in geometry, dynamics, number theory and other areas of pure mathematics. This project will study their representations from two perspectives. First, it will establish properties of the associated zeta functions to resolve open problems about the asymptotic behaviour of the dimensions of the irreducible representations. Second, it will explore the evolution of representations across families of groups under new induction and restriction functors, in analogy with creation and annihilation operators in physics. The project will enhance Australia's capacity in representation theory and group theory, the mathematics that underline symmetry in nature.

**Scheme: **ARC Future Fellowships 2016 round 1**Recipient:** Dr Timothy Trudgian**Grant amount:** $652,000.00**Project:** Explicit methods in number theory: Computation, theory and application.

This project aims to use explicit estimates to unify three problems in number theory: primitive roots, Diophantine quintuples, and linear independence of zeroes of the Riemann zeta-function. It will use computational and analytic number theory to reduce the quintuples problem to a soluble level. Pursuing relations between the zeta zeroes will overhaul many current results. This project will apply its findings about primitive roots to signal processing, cryptography and cybersecurity.

**Scheme:** Discovery Early Career Research Award 2017 round 1**Recipient:** Dr Zsuzsanna Dancso**Grant amount:** $360,000.00**Project:** Homological methods in combinatorics, algebra and geometry.

This project aims to solve problems in graph theory, lattice theory and geometry using algebraic techniques. The techniques and language provided by this algebraic approach will be used to gain fresh insight into classical problems, prove stronger theorems and uncover connections between different areas. This project intends to integrate Australia’s strength in homological algebra and category theory with applications in various different fields of mathematics. This is expected to provide tools for further investigation of applications in other fields, including computer science and combinatorial optimisation.

**Scheme:** Discovery Projects 2017 round 1**Recipient:** Professor Xu-Jia Wang; Professor Neil Trudinger; Dr Jiakun Liu (University of Wollongong)**Grant amount: **$538,500.00**Project:** Variational theory for fully nonlinear elliptic equations.

This project aims to develop new methods and techniques to solve challenging mathematical problems in fully nonlinear partial differential equations arising in important applications. The project will develop methods and techniques to study these equations’ regularity and variational properties. This project is expected to establish comprehensive theories and enhance and promote Australian participation and leadership in this area of mathematics.

**Scheme:** Discovery Projects 2017 round 1**Recipient:** Professor Murray Batchelor**Grant amount:** $362,000.00**Project:** Mathematical structure of the quantum Rabi model.

This project aims to find the mathematical structure behind the quantum Rabi model, the simplest model describing the interaction between quantum light and matter. The Rabi model is the connecting link in the essential interplay between mathematics, physics, and technological applications. Solving the mathematical structure behind it is expected to form the basis for solving related and equally important models. Such models describe a qubit, the building block of quantum information technologies, and so could realise quantum algorithms and quantum computations.

**Scheme:** Discovery Projects 2017 round 1 (External with the University of New South Wales)**Recipient: **Professor Fedor Sukochev; Dr Denis Potapov; Professor Alan Carey**Grant amount:** $388,000.00**Project:** New methods in spectral geometry.

This project aims to use methods from mathematical scattering theory to resolve problems in the spectral analysis and index theory of differential operators. Both areas underpin the theoretical understanding of physical materials at micro length scales where quantum phenomena dominate. The project will develop new mathematical results in spectral analysis and geometry, and apply its results to theoretical models of quantum phenomena whose spectral properties are at the limit of the range of mathematical techniques. Solving these problems is expected to influence non-commutative analysis.