Translational tilings by a polytope, with multiplicity

We study the problem of covering R^d by overlapping translates of a convex body P, such that almost every point of R^d is covered exactly k times. Such a covering of Euclidean space by translations is called a k-tiling. The investigation of tilings (i.e. 1-tilings in this context) by translations began with the work of Fedorov and Minkowski. Here we extend the investigations of Minkowski to k-tilings by proving that if a convex body k-tiles R^d by translations, then it is centrally symmetric, and its facets are also centrally symmetric. These are the analogues of Minkowski's conditions for 1-tiling polytopes. Conversely, in the case that P is a rational polytope, we also prove that if P is centrally symmetric and has centrally symmetric facets, then P must k-tile R^d for some positive integer k

The Just Transition: Shaping the delivery of the Inevitable Policy Response

At the heart of the 2015 Paris Agreement and Sustainable Development Goals is a theory of change which sees the delivery of critical environmental targets (such as the net-zero economy) as intrinsically connected with wider social objectives such as ending poverty, cutting inequality and achieving decent working conditions across the world. The result needs to be a 'just transition,' one that recognises the fundamental injustices of the current fossil-fuel based energy system, the ways in which climate change exacerbates many inequalities (notably in the developing world) and the opportunity of shaping the drive to net-zero so that it helps to overcome these structural failings. This report updates a 2019 IPR report on the just transition in light of growing policy and market action (notably around COP26), as well as the crisis sparked by the war in Ukraine.The shock of Russia's invasion of Ukraine in February 2022 is deepening existing energy inequalities through the sharp rises in energy and other commodity prices, worsening the livelihoods for large sections of the global population. It could also accelerate the shift to the net-zero economy by once again adding security to decarbonisation as key drivers for accelerated deployment of resource efficiency and renewable energy. This makes the just transition a strategic issue for investors and policymakers in 2022

Financing net-zero: mobilising the money for action on the ground

The net-zero target needs to become core to the purpose of the financial system to deliver an investment-led green recovery, writes Nick Robin

Sustainable central banking: clear green water between the Fed and the ECB?

All major central banks recognise that the climate crisis and nature loss pose material threats for the financial system. But central bank mandates and political environments vary. Action on sustainability is a bipartisan issue in Europe, while in the US parts of the Republican Party are leading an anti-ESG campaign that is out of line with science and at odds with a prudent view on financial management. Nick Robins writes that a second phase of sustainable central banking is needed to minimise the environmental threats to banks’ core mandates, as well as the other goals they are set

India: becoming a sustainable finance maker

In the year of India’s presidency of the G20, Nick Robins shows how key pieces of the country’s sustainable finance framework are falling into place and how an ambitious approach connecting net zero with the human dimension could help to mobilise the trillions the country needs

The $468 trillion climate question: how the financial system is starting to shift

Nick Robins writes from COP27 on the steps being made to transform finance for a net-zero and resilient world

The inverse moment problem for convex polytopes: implementation aspects

We give a detailed technical report on the implementation of the algorithm presented in Gravin et al. (Discrete & Computational Geometry'12) for reconstructing an $N$-vertex convex polytope $P$ in $\mathbb{R}^d$ from the knowledge of $O(Nd)$ of its moments

The Corporation That Changed the World

The English East India Company was the mother of the modern multinational. Its trading empire encircled the globe, importing Asian luxuries such as spices, textiles and teas. But the Company’s takeover of much of India was achieved by force and fraud; in China, the battering ram was opium. The East India Company’s corruption and violence shocked its contemporaries and still reverberates today. The Corporation That Changed the World is the first book to examine the Company’s enduring legacy as a corporation. It uncovers the factors that drove it to excess and eventual collapse. This expanded edition looks at recent activist and cultural responses to the Company in China and India, and the corporate reform agenda in light of the economic crisis. In his account of the Company's story Robins highlights enduring lessons on how to make global business accountable. This will be vital reading for students and academics in economics and history

Nick Robins: “we can’t speed ahead with a technocratic climate focus that leaves people behind”

The race is on to implement a “just transition” to guide climate action. Just transition is a framework to ensure that workers are not left behind when their employers make changes that will help cut emissions and make their businesses more climate-resilient. Nick Robins, Professor in Practice at LSE’s Grantham Research Institute, has spearheaded the creation of the Just Transition Finance Lab, which will be working with business and finance to experiment and propose financial solutions towards a just transition. In this Q&A, he explains to Helena Vieira (LSE Business Review) what the Lab expects to be doing in the next few years