I state a conjecture describing the set of toric specializations of a Fano variety with klt singularities. The conjecture asserts that for all generic Fano varieties X with klt singularities, there exists a polarized cluster variety U and a surjection from the set of torus charts on U to the set of toric specializations of X.

I outline the first steps of a theory of the cluster varieties that I use. In dimension 2, I sketch a proof of the conjecture after Kasprzyk–Nill–Prince, Lutz, and Hacking by way of work of Lai–Zhou. This reveals a surprising structure to the classification of log del Pezzo surfaces that was first conjectured in [1]. In higher dimensions, I survey the evidence from the Fanosearch program, cluster structures for Grassmannians and flag varieties, and moduli spaces of conformal blocks.

Before Enid Blyton's stories about picturesque girls’ residential schools entered the Indian literary market, colonial boarding schools, with their distinctive architectural form and curriculum, held a unique place in the educational landscape. We can discern three kinds of boarding schools during this period, identifiable by the geographies in which they were located and the social character of their pupils, but essentially, as Satadru Sen notes, ‘paralysed by an articulation of difference that implied that native children were essentially small, perverse adults’. As with early European military-style institutions, the boarding schools established by Catholic and Protestant missionary societies and the British colonial administration had strict timetables, corporal punishment, and physical and intellectual training aligned with specified educational goals regarding children's capacities and futures.

First, the boarding schools established during the 1870s mainly catered to children of royal parentage in many parts of India, aimed at training them (mainly boys) in habits and codes of behaviour befitting their status. Located in remote locations, these schools were immersed in a curriculum aligned with those similar to British public schools, which included horse riding, classical languages, and military training, among other subjects. In this way, imperial administrators considered young sons of princely rulers, enveloped in colonial discourses of effeminacy, to be removed from their immediate surroundings to soften any propensity to rebel against their imperial masters. The second type of boarding school, known as Lawrence Military Asylums and based in the cooler climes of hill stations, was designed to educate and train mainly children of British soldiers serving in the subcontinent and reluctantly admitted a handful of children of mixed-race descent. In the tropical heat, these schools served as enclaves amid constant anxieties about racial miscegenation. This chapter analyses the third type, the oldest, most modestly resourced charity boarding schools run by Christian missionary organizations that offered education to orphaned, destitute, famine-stricken, runaway, and poor Indian children in villages and towns since the 1830s. Often, orphans presented ‘a problem of governance’, resulting in sharp disagreements over financial management and the kind and duration of instruction these pupils should receive.

• ◦ The case study of the liquid crystal display (LCD) cartel underscores the strong incentives that arise in an oligopoly to limit competition but also the practical difficulties in doing so when there are many products and varieties involved.

• ◦ The breadth of the cartel is impressive in that it encompassed all uses of LCD panels and did so for at least a decade. It is partly that breadth that posed a challenge for there were hundreds of different products and a dozen manufacturers. Rather than trying to coordinate the prices of the entire product line, the cartel focused only on the highest selling products, and at a degree of aggregation which did not fully take account of quality differences.

• ◦ The lack of collusion over all products’ prices could result in less effective collusion which the case study finds as the estimated overcharge is no higher than 2 percent. But even a 2 percent overcharge would have resulted in incremental revenues to the conspirators exceeding $3 billion. The takeaway is that even a highly imprecise collusive arrangement can be profitable to firms and harmful to buyers.

Chapter 1 will examine the ontological and epistemological questions surrounding music in the knowledge system of the medieval Islamic world by exploring the philosophical system of Ibn Sina and his later followers, all of whose works laid the foundations for scholars of music in the centuries to come. In particular, I will address how mathematics was conceptualized vis-à-vis the cosmology of the falsafa tradition as the discipline that examined the existents whose existence was dependent on physical matter but could be conceptualized without the said matter. Through this conceptualization of music and mathematics, scholars of music were able to broaden their subject matter to cover topics from the melodic modes in vogue in their time to the poetics of music. At the same time, since everything in the universe was connected to one another, music was linked with many other scientific disciplines such as astronomy and medicine.

Diamonds and jewels – their brilliant refractions providing prototypes for intellectual elasticity and insight into connections between things and gender, colonialism, marriage for hire, and ecosystems – spring forth in Belinda and Les bijoux indiscrets to teach characters to become better interpreters. This chapter argues that in these novels gems become “mouths” that kinesthetically narrate and enact material histories: the labor and commerce that produced them, the deleterious enmeshment of women and objects, and women’s right to be human – that is, honest, rational, fragmented, stained, and radiant. Belinda’s allusion to the historic 48-carat Pigot links domestic larceny in matchmaking to colonial theft in India and Ireland. Markets collide as Belinda demonstrates how the lexicon of purity and perfection dominates the commercialization of courtship and of advisory treatises instructing the public how to buy authentic diamonds. In conclusion, the chapter analyzes how a diamond leads to Lady Delacour’s restoration by teaching her how to belong with the human–nonhuman network.

Avowing that love awakens one’s attention to the material world and to one another, Corinne provides a theory for establishing human–nonhuman connection, the energizing and curative praxis of belonging with. The heroine’s thing therapy positively associates women with materiality and, while exercising her right to connect with things, she sustains her élan vital. This chapter argues that she harnesses her feminist thing theory to teach her lover to respect the female body’s integrity and rights and to challenge his repressive politics: If Oswald could belong with materiality by sensuously responding to things, he could remedy his commitment to abstraction and his nationalistic gender proscriptions. Diagnosing Oswald’s melancholy as also emerging from his identification with “modern” (post Renaissance) art, associated with Napoleon’s tyranny and a self-absorptive grief that paralyzes creative potential, Corinne offers a remedy: companionship with classical art. Her thing theory has political ramifications, for it provides a workshop for practicing an embodied cosmopolitanism that itself ameliorates nationalism’s intolerances.

This chapter covers regional loyalties and religious institutions, focusing on the Kulturkampf, the state’s attack on Catholicism.

At the end of my research on the 1946–47 interim government published as India in the Interregnum (2019), I had hoped to produce a second instalment, on its 1947–51 successor, given its relative neglect in published accounts and presence in primary sources, especially the now-accessible post-1947 Jawaharlal Nehru papers. The last years of the 1940s and the first of the 1950s constitute an intermediate period between Partition/Freedom (1947) and Republic/Democracy (1950–52) that is often seen through either or both of these lenses. This was captured in a critical review of India in the Interregnum that considered ‘this continuity … to be the root cause of the ills that plague the post-colonial nation.…’

Approaching its eighth decade, as independent India experiences its eighteenth government, this book seeks to remember its first predecessor, which functioned in a uniquely intermediate period. It is important to do so because, whether in public recall or in academic research, the first Nehru government has had a somewhat shadowy existence, which is compensated by the axiom that it stood for a transitional phase for the country. But, as the late D. L. Sheth wrote, ‘historicization makes historical sense, only when made in terms of contemporary sensibilities….’ This intervention then surveys the 1947–51 government, liminally located between dominion and democracy, and subsumed between Partition and nation-building, in an ‘academic no-man's land’. It attempts an exercise of historical recovery crystallised from the post-1947 prime ministerial papers in the hope that this reconstruction might help in reading post-Partition Indian party politics. The standard conception of that multi-party government is that it is clustered around a duumvirate, but this book tries to bring forth and intertwine its multiple individual traits, identity tensions and institutional trends.

This triangular pyramid was held together by provincial or princely politics, progressive or prejudicial passions and party pronouncements. The all-India whole that was forged in those first years, before being put to a popular test, was pivotal to subsequent state-building, and this book probes the performance of that pre-1952 government, whose political heritage continues to be dissected. As it has been said, ‘nations themselves are narrations …’, so a history of the first independent Indian government is one way to contextualise the contemporary by answering the ‘need for links and connections’.6

The goal of this chapter is to develop a very general method for constructing (functorially) complete cotorsion pairs in exact categories. In essence we develop an algebraic version of Quillen’s small object argument for cotorsion pairs. This naturally leads us to the notion of cofibrantly generated cotorsion pairs and abelian model structures. The approach taken here is inspired by Saorin and Stovicek’s notion of an efficient exact category. We generalize this idea a bit more by considering classes of objects that we say are efficient relative to the exact structure. We show that with mild hypotheses on the exact category, any efficient set (not a proper class) of objects cogenerates a functorially complete cotorsion pair. Along the way we prove results about generators for exact categories, and use them to construct generating monics for cotorsion pairs. We also prove Eklof’s Lemma, and its dual, for exact categories, and give general conditions guaranteeing that the left side of a cotorsion pair is closed under direct limits.

The purpose of this note is to introduce three methods of the Sarkisov program, which aims to factorize birational maps of log Mori fibre spaces.

There are many reasons why the implicit bias construct took root in everyday conversation, but one of them is that millions of people have experienced the most commonly used measure of implicit bias – the Implicit Association Test (IAT; Greenwald, McGhee, & Schwartz, 1998) at the Project Implicit websites. Project Implicit is a non-profit organization and international research collaboration between behavioral scientists interested in implicit social cognition. The organization’s primary public contribution is its education websites (https://implicit.harvard.edu) where more than twenty-eight million IATs have been completed. This chapter provides an overview of Project Implicit and the contributions and challenges of more than twenty years of internet-based data collection on implicit attitudes and stereotypes. The first section describes Project Implicit’s history and organizational structure; next, some of the key insights gleaned from the data collected at the Project Implicit websites are reviewed. These include assessment of the pervasiveness and correlates of implicit bias, comparisons across time and by geographic area, and reactions to learning about one’s own implicit bias. Finally, we reflect on some of the challenges of being uniquely situated between academic researchers and the general public, and describe how changing scientific knowledge has changed scientific communication about implicit bias.

We offer a conceptual framework by which to consider implicit bias. In contrast to a far too common presumption that implicit bias involves unconscious attitudes and stereotypes, i.e., ones for which individuals lack awareness, we emphasize a view of implicit bias as an effect of attitudes of which individuals are unaware. The perspective is grounded in decades of social psychological theory and research concerning the constructive nature of perception and the potential biasing influence of attitudes on perceptions and judgments. Attitudes that are automatically activated from memory can exert such a biasing influence, without individuals’ awareness that they have been affected. We articulate the advantages of such a perspective for both the science and the politics of implicit bias. We also discuss how individuals can overcome the influence of an automatically activated attitude, given appropriate motivation and opportunity to do so, and briefly review evidence concerning the joint influence of these factors on prejudicial judgments and behavior.

This chapter studies the left and right derived functors of an additive functor whose domain is a (closed) abelian model category. The most important scenario is when we have a Quillen adjunction, and we show that its left and right derived functors induce a triangulated adjunction of homotopy categories. We characterize Quillen equivalences, which are the Quillen adjunctions that induce triangle equivalences of homotopy categories. The end of the chapter turns to the basics of abelian monoidal model structures. The main result is that a tensor product on the ground category, which is compatible with the model structure, will descend to a well-behaved tensor product on the homotopy category. We give Hovey’s criteria for abelian monoidal model structures which provides a powerful way to construct tensor triangulated categories.