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The 21st century may come to be known as the Age of Photonics, as we exploit our ability to make and manipulate light as an amazing carrier of energy and information. From quantum computing and entanglement to eye surgery and solar energy, humans are already reaping the benefits of our own endeavours to understand and control light.

In her public lecture webcast at Perimeter on March 6, Cather Simpson from the University of Auckland will highlight her research in exploring how recent advances in the physics of light are transforming our ability to feed the planet safely and sustainably.

Simpson moved from Case Western Reserve University in the USA to the University of Auckland’s Physics and Chemistry Departments in 2007. There, she started the Photon Factory, a laser centre whose mission is to exploit exotic, ultrashort pulsed lasers to enable cross-disciplinary research from the very fundamental to the applied and entrepreneurial.

Simpson’s research explores the interaction of light with matter, particularly how materials can convert light into more useful forms of energy. A relatively recent area of focus is in agriculture, where her work has led to two international award-winning spinout companies. Her many recent accolades include a National Tertiary Teaching Excellence Award, the 2016 Silicon Valley Forum 1st-place AgTech medal, and election as a Fellow of the Royal Society of New Zealand Te Apārangi.

The Leggett-Garg (LG) inequalities were introduced, as a temporal parallel of the Bell inequalities, to test macroscopic realism -- the view that a macroscopic system evolving in time possesses definite properties which can be determined without disturbing the future or past state. The talk will begin with a review of the LG framework. Unlike the Bell inequalities, the original LG inequalities are only a necessary condition for macrorealism, and are therefore not a decisive test. I argue, for the case of measurements of a single dichotomic variable Q, that when the original four three-time LG inequalities are augmented with a set of twelve two-time inequalities also of the LG form, Fine's theorem applies and these augmented conditions are then both necessary and sufficient [1]. A comparison is carried out with the alternative necessary and sufficient conditions for macrorealism  based on no-signaling in time conditions which ensure that all probabilities for Q at one and two times are independent of whether earlier or intermediate measurements are made. I argue that the two tests differ in their implementation of the key requirement of non-invasive measurability so are testing different notions of macrorealism, and these notions are elucidated.  I also describe some alternative protocols which achieve non-invasiveness, one involving continuous measurement of the velocity conjugate to Q [2], which was recently implemented in an experiment at IQC, the other involving a modification of the standard ideal negative measurement protocol [3].

[1] J.J.Halliwell, Phys Rev A96, 012121 (2017); A93, 022123 (2016); arxiv:1811.10408.

[2]  J.J.Halliwell, Phys. Rev. A94, 052114 (2016).

[3] J.J.Halliwell, Phys. Rev. A99, 022119 (2019).

Many of the rich interactions between mathematics and physics arise using general mathematical frameworks that describe a host of physical phenomena: from differential equations, to algebra, to topology and geometry. On the other hand, mathematics also possesses many examples of "exceptional objects": they constitute the finite set of leftovers that appear in numerous classification problems. For example, groups of symmetries in three dimensions appear in two infinite families (cyclic groups and dihedral groups of n-sided polygons) and the symmetry groups of the five Platonic solids--- the 'exceptional' structures. 

The mathematical subject of moonshine refers to surprising relationships between other kinds of special/exceptional objects that arise from the theory of finite groups and from number theory. Increasingly, string theory has been a source of insights in and explanations for moonshine. It is even the source of new examples of moonshine that further implicate special objects in geometry. We will review moonshine, survey these developments, and highlight some of the (many!) exciting mysteries that remain.

It is known that there is a relationship between conformal Carroll transformations and BMS symmetry. In this talk I will explore the geometry of generic Carroll structures which may be thought of as the basic underlying geometric structure on null hypersurfaces. A Carroll structure can be thought of as a fibre bundle with Ehresmann connection, and one finds that (generalized) BMS symmetry emerges as the conformal symmetry of this bundle and connection. I’ll briefly also describe how this story fits into the physics of ’soft modes.’

Mirror sectors -- hidden sectors that are approximate copies of the Standard Model -- are a generic prediction of many models, notably the Mirror Twin Higgs model. Such models can have a rich cosmology and many interesting detection signatures beyond the realm of colliders. In this talk, I will focus on the possibility that mirror matter can form stars which undergo mirror nuclear fusion in their cores. I will discuss the mechanisms by which these objects can emit Standard Model light and estimate their luminosity and prospects for their detection.