A mathematical formalization of Chomsky’s theory of Merge in generative linguistics.The Minimalist Program advanced by Noam Chomsky thirty years ago, focusing on the biological nature of human language, has played a central role in our modern understanding of syntax. One key to this program is the notion that the hierarchical structure of human language syntax consists of a single operation Merge. For the first time, Mathematical Structure of Syntactic Merge

Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story.In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lo...

This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. One of the main questions in the field is understanding when the residues of Feynman integrals in perturbative quantum field theory evaluate to periods of mixed Tate motives. The question originates from the occurrence of multiple zeta values i...

Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos.This is a book about art—and a book about mathematics and physics. In Lumen Naturae (the title refers to a purely immanent, non-supernatural form of enlightenment), mathematical physicist Matilde Marcolli explores common themes in modern art and modern science—the concept of space, the notion of randomness, ...

Modified gravity models play an important role in contemporary theoretical cosmology. The present book proposes a novel approach to the topic based on techniques from noncommutative geometry, especially the spectral action functional as a gravity model. The book discusses applications to early universe models and slow-roll inflation models, to the problem of cosmic topology, to non-isotropic cosmologies like mixmaster universes and Bianchi IX gravitational instantons, and to multifractal s...

The US economy today is confronted with the prospect of extended stagnation. This book explores why. Thomas I. Palley argues that the Great Recession and destruction of shared prosperity is due to flawed economic policy over the past thirty years. One flaw was the growth model adopted after 1980 that relied on debt and asset price inflation to fuel growth instead of wages. A second flaw was the model of globalization that created an economic gash. Third, financial deregulation and the hous...

This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure—the Schrödinger-Virasoro algebra. Just as Poincaré invariance or conformal (Virasoro) invariance play a key rôle in understanding, respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study of some models of non-equilibrium statist...

This monograph explains the theory of quantum waveguides, that is, dynamics of quantum particles confined to regions in the form of tubes, layers, networks, etc. The focus is on relations between the confinement geometry on the one hand and the spectral and scattering properties of the corresponding quantum Hamiltonians on the other. Perturbations of such operators, in particular, by external fields are also considered. The volume provides a unique summary of twenty-five years of research ...

The finite element method is a technique for solving problems in applied science and engineering. The essence of this book is the application of the finite element method to the solution of boundary and initial-value problems posed in terms of partial differential equations. The method is developed for the solution of Poisson's equation, in a weighted-residual context, and then proceeds to time-dependent and nonlinear problems. The relationship with the variational approach is also explain...

The theories describing seemingly unrelated areas of physics have surprising analogies that have aroused the curiosity of scientists and motivated efforts to identify reasons for their existence. Comparative study of physical theories has revealed the presence of a common topological and geometric structure. The Mathematical Structure of Classical and Relativistic Physics is the first book to analyze this structure in depth, thereby exposing the relationship between (a) global phy...

Continuum mechanics and thermodynamics are foundational theories of many fields of science and engineering. This book presents a fresh perspective on these fundamental topics, connecting micro- and nanoscopic theories and emphasizing topics relevant to understanding solid-state thermo-mechanical behavior. Providing clear, in-depth coverage, the book gives a self-contained treatment of topics directly related to nonlinear materials modeling. It starts with vectors and tensors, finite deform...

As many readers will know, the 20th century was a time when the fields of mathematics and the sciences were seen as two separate entities. Caused by the rapid growth of the physical sciences and an increasing abstraction in mathematical research, each party, physicists and mathematicians alike, suffered a misconception; not only of the opposition’s theoretical underpinning, but of how the two subjects could be intertwined and effectively utilized. One sub-discipline that played a part in t...