This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

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The Scientific Image

https://place.asburyseminary.edu/cgi/viewcontent.cgi?article=1803&context=faithandphilosophy

The Conscious Mind: In Search of a Fundamental Theory

The Unreality of Time

Philosophy and scientific realism

A 'duality' is a formal mapping between the spaces of solutions of two empirically equivalent theories. In recent times, dualities have been found to be pervasive in string theory and quantum field theory. Naively interpreted, duality-related theories appear to make very different ontological claims about the world---differing in e.g. spacetime structure, fundamental ontology, and mereological structure. In light of this, duality-related theories raise questions familiar from discussions of underdetermination in the philosophy of science: in the presence of dual theories, what is one to say about the ontology of the world? In this paper, we undertake a comprehensive and non-technical survey of the landscape of possible ontological interpretations of duality-related theories. We provide a significantly enriched and clarified taxonomy of options---several of which are novel to the literature.

Duality and ontology

I will defend two claims. First, Schaffer’s priority monism is in tension with many research programs in quantum gravity. Second, priority monism can be modified into a view more amenable to this physics. The first claim is grounded in the fact that promising approaches to quantum gravity such as loop quantum gravity or string theory deny the fundamental reality of spacetime. Since fundamental spacetime plays an important role in Schaffer’s priority monism by being identified with the fundamental structure, namely the cosmos, the disappearance of spacetime in these views might undermine classical priority monism. My second claim is that priority monism can avoid this issue with two moves: first, in dropping one of its core assumption, namely that the fundamental structure is spatio-temporal, second, by identifying the connection between the non-spatio-temporal structure and the derivative spatio-temporal structure with mereological composition.

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Priority Monism Beyond Spacetime

Important features of space and time are taken to be missing in quantum gravity, allegedly requiring an explanation of the emergence of spacetime from non-spatio-temporal theories. In this paper, we argue that the explanatory gap between general relativity and non-spatio-temporal quantum gravity theories might significantly be reduced with two moves. First, we point out that spacetime is already partially missing in the context of general relativity when understood from a dynamical perspective. Second, we argue that most approaches to quantum gravity already start with an in-built distinction between structures to which the asymmetry between space and time can be traced back.

/pdf/have-we-lost-spacetime-on-the-way-narrowing-the-gap-between-vfgi4jkcic.pdf

Have we lost spacetime on the way? Narrowing the gap between general relativity and quantum gravity

‘Space does not exist fundamentally: it emerges from a more fundamental non-spatial structure.’ This intriguing claim appears in various research programs in contemporary physics. Philosophers of physics tend to believe that this claim entails either that spacetime does not exist, or that it is derivatively real. In this article, I introduce and defend a third metaphysical interpretation of the claim: reductionism about space. I argue that, as a result, there is no need to subscribe to fundamentality, layers of reality and emergence in order to analyse the constitution of space by non-spatial entities. It follows that space constitution, if borne out, does not provide empirical evidence in favour of a stratified, Aristotelian in spirit, metaphysics. The view will be described in relation to two particular research programs in contemporary physics: wave function realism and loop quantum gravity.

/pdf/space-emergence-in-contemporary-physics-why-we-do-not-need-5aiqyk6r6l.pdf

Space Emergence in Contemporary Physics: Why We Do Not Need Fundamentality, Layers of Reality and Emergence

Resistors based on silicon nanowires (SiNWs) are developed for the direct detection of Escherichia coli bacteria The devices are manufactured using conventional silicon technology The SiNWs are synthesized by the vapor liquid solid process (VLS) using gold as the catalyst The electrodes of the device consist of highly in situ doped polycrystalline silicon The results show that the corresponding resistances can be potentially used for the detection of bacteria by electrical measurements, using SiNWs as sensitive units The bacteria are preferentially hooked in the SiNWs network, which causes a drastic reduction in the electrical resistance of the component Such resistor manufactured in a simple and low-cost CMOS (Complementary Metal Oxide Semiconductor) technology acts as proof of concept This device offers promising potentialities taking advantages of integration into CMOS platform for alternative direct electrical detection of bacteria to monitor the contamination in environment for hygiene applications

/pdf/bacteria-electrical-detection-using-3d-silicon-nanowires-4zuc9vre5s.pdf

Baptiste Le Bihan

Papers

Duality and ontology

Priority Monism Beyond Spacetime

Have we lost spacetime on the way? Narrowing the gap between general relativity and quantum gravity

Space Emergence in Contemporary Physics: Why We Do Not Need Fundamentality, Layers of Reality and Emergence

Bacteria electrical detection using 3D silicon nanowires based resistor