The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book, reissued with a new Foreword, presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic.

After an informal preparatory chapter, the book follows an historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves.

Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text.

My ongoing engagements with international and national debates on climate justice are a result of an intellectual journey over the past two decades that has brought me time and again to the complex intersections of environmental protection and social justice. Market-based solutions became the backbone of ostensible global responses to climate change at the United Nations Climate Change Conference held in Bali in December 2007. The sense of excitement among environmental economists then is difficult to describe from where we are today. However, to those of us who had spent time in the field, this euphoria was evidently and grossly misplaced. The journey that marketbased solutions would have to take, from Bali to places like Bastar in Chhattisgarh, where they would be eventually implemented, is not paved with the freedom of choice that pro-market advocates like to celebrate.

Markets are designed to facilitate the accumulation of surplus in the hands of those who can channel it higher up in the ‘food chain’. In most cases, the market ecosystem is essentially a centralizing force and does not work for the poor and marginalized. Unfortunately, this argument often falls through the cracks due to the lack of interdisciplinary work that is needed to produce knowledge that may help inform public debates on these complex questions. The market-based solutions institutionalized at the Bali climate conference, especially carbon offsets and carbon emissions trading, have proven to be colossal failures.

Perhaps even more embarrassingly, the advocates of market-based climate solutions lost the battle of ideologies to right-wing reactionary forces. Even in the supposedly knowledge-driven market economies of the Global North, ultra-conservatives have been successful in labelling neoliberal policies, such as offsets and cap-and-trade policies, as part of ‘the radical Left's progressive wish list’. This is not surprising to many on the left but this also offers much food for thought for students of policy analysis, who focus rather narrowly on coming up with ‘efficient solutions’. While smart analyses can be helpful, the belief that such analyses are sufficient to drive policy change has proven to be a chimera. This is why it is necessary to cultivate a strong awareness of the extent to which the beneficiaries of the status quo use their political and economic power to thwart sensible debates on the unprecedented environmental and social crises.

This case study examines the dispute between Micron Technology, United Microelectronics Corporation (UMC), and Fujian Jinhua Integrated Circuit Co. Ltd. over the alleged theft of Micron’s trade secrets in integrated circuits (ICs), specifically dynamic random-access memory chips. This dispute offers a lens through which to analyze China’s strategic efforts to strengthen its semiconductor industry by overseas investment. It begins by introducing China’s ambitious policy framework aimed at achieving self-reliance in the semiconductor industry, set against the backdrop of geopolitical tensions and the COVID-19 pandemic’s impact on global IC supply chains. It then turns to the case adjudicated by Taiwanese courts in 2020, where UMC and Jinhua faced allegations of trade secret misappropriation from Micron. Finally, this study compares the different legal and regulatory approaches of Taiwan and the United States in addressing such disputes, highlighting the challenges in regulating global supply chains amidst evolving geopolitical and economic landscapes.

Chapter 8 discusses MiCA’s rules on crypto custody. After examining international developments (Section 8.2), we discuss the scope of MiCA’s custody rules (Section 8.3) prior to analysing the impact of MiCA’s general requirements for CASPs (e.g., fiduciary duties and safekeeping rules) (Section 8.4) and discussing Article 75 MiCA on crypto custody in-depth (Section 8.5). We go on by exploring how crypto custodians regulated by MiCA interact with other regulated intermediaries that safekeep assets either as their main business or as side services to supplement their brokerage or asset management services (Section 8.6), and then, we conclude (Section 8.7).

Chapter 6 examines the legacy of architectural terracottas during the period of the Augustan Principate and the rise of the so-called “Campana” reliefs. While architectural terracottas had long been used to define and assert specific local identities, they were now employed to express an idealized Augustan vision of a unified, pious Italic past.

I first met the jhupri labourers behind a row of parked buses. They were sprawled out on the backs of their rickshaw vans after a night of work: some were asleep, some smoking, some playing ludo. Rubel was seated on a van with others huddled around him. He wore a white panjabi (kurta) and a sparse beard, giving the impression he was both pious and not in fact a labourer. Unlike the rest of the group who were lean from carrying heavy sacks of vegetables, he was large, or ‘short and fat’ as others would later describe him. Foreigners were not an unfamiliar sight at the bazaar. Nearby offices and a five-star hotel meant visitors passed by on their way elsewhere. Some took photos of the colours and chaos. Foreign sisters from the Missionaries of Charity occasionally shopped here. An Italian priest had for decades visited weekly to help children with small ailments and injuries. Some of the group later claimed that ‘bad foreigners’ used the cheap hotels to meet sex workers, with Australians for some reason singled out as particularly guilty.

As the first foreigner to speak to the group there, Rubel saw it as an opportunity to preach. He gave a speech about Islam that I barely understood and the group found amusing. He then stated provocatively, ‘We are all BNP here. Do you have a problem with that?’ The claim of affiliation to the opposition BNP was an odd one. The election a few months previously in early 2014 had been highly controversial: the opposition had boycotted, the nation had seen widespread violence, and with the Awami League re-elected, public claims of loyalty to their rivals were risky. Whatever Rubel's motivations, the encounter was precisely the opportunity I had been looking for. For the past couple months I had been walking around the city, getting to know it better, looking for a route in to study local politics, somewhere to embed myself and normalise my presence on the pavements, in the bastis and bazaars of the city. Scattered across Dhaka at the time were shelters run by local NGOs to support people living on the streets.

Introduction

In the Kingdom of Thailand, known as Siam until 1939, the great Sanskrit epic of the Ramayana, or rather the Thai-language Ramakien, composed under King Phra Phutthayotfa Chulalok (King Rama I, 1737–1809, r. 1782–1809), is omnipresent. It is the national epic of the Southeast Asian kingdom, taught not only in schools but encountered also in picture books and manga. The epic is deeply embedded in the kingdom's history and culture of everyday life. King Ramkamhaeng (‘Rama, the Bold’, r. 1279–98) of Sukhothai, named after the epic's hero, is today remembered in official historiography not simply as a great king but also as a founding figure of the Thai nation as a cultural community through his invention of the Thai script. He is depicted on banknotes, and major public works are named after him, such as a university and a major thoroughfare in Bangkok. And according to a late seventeenth-century chronicle, the former capital was founded in 1350 as Phra Nakhon Si Ayutthaya. Its founder took the title Ramathibodi (‘Rama, the Mighty’, 1315–69, r. 1351–69) upon ascending to his throne and founded the Phra Ram temple in the capital in 1369, the year of his death.

Ayutthaya was destroyed in 1767 by an invading army from Burma. After a short intermezzo under the charismatic King Taksin (1734–82, r. 1767–82) ruling from Thonburi, the current capital and dynasty were founded by Taksin's former general, King Phra Phutthayotfa Chulalok. He added Ayutthaya to the city's full name and included Ramathibodi to his full royal title. In addition to having had a new version of the Ramakien written, he also had murals with scenes from the epic added to the Temple of the Emerald Buddha, where the kingdom's palladium of the same name is enshrined. The national dance drama of Khon is also based on the epic and can be found recounted in children's literature today. The epic is furthermore the source of proverbs and placenames far from royal palaces, such as Huai Sukhrip, or Sukhrip's Brook, a stream located near the city of Chonburi, close to Bangkok.

This chapter paints the political and intellectual backdrop of Padua in the 1300s, which sets the stage for Alberti’s education. While Rolandino, Lovato, and Mussato were intellectual giants of a commune, Petrarch, Conversino, and Vergerio were literary giants at a court – that of Francesco Il Vecchio da Carrara, a patron of classical medals, art, and humanist educators and antiquarians. Accordingly, five factors made Padua a center of early humanism: independent university faculty, accession of classical rhetoric, Petrarch and his library, Carrara’s support for educators and antiquarians, and the city’s absorption by Venice, allowing unfettered education to gift Alberti a literary and visual universe.