This biography explores the life and career of the Italian physicist Enrico Fermi, which is also the story of thirty years that transformed physics and forever changed our understanding of matter and the universe: nuclear physics and elementary particle physics were born, nuclear fission was discovered, the Manhattan Project was developed, the atomic bombs were dropped, and the era of "big science" began.It would be impossible to capture the full essence of this revolutionary period without first understanding Fermi, without whom it would not have been possible. Enrico Fermi: The Obedient Genius attempts to shed light on all aspects of Fermi's life - his work, motivation, influences, achievements, and personal thoughts - beginning with the publication of his first paper in 1921 through his death in 1954. During this time, Fermi demonstrated that he was indeed following in the footsteps of Galileo, excelling in his work both theoretically and experimentally by deepening our understanding of the Pauli exclusion principle, winning the Nobel Prize for his discovery of the fundamental properties of slow neutrons, developing the theory of beta decay, building the first nuclear reactor, and playing a central role in the development of the atomic bomb. Interwoven with this fascinating story, the book details the major developments in physics and provides the necessary background material to fully appreciate the dramatic changes that were taking place. Also included are appendices that provide a timeline of Fermi's life, several primary source documents from the period, and an extensive bibliography. This book will enlighten anyone interested in Fermi's work or the scientific events that led to the physics revolution of the first half of the twentieth century.

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry, category theory, gauge theory, and string theory has been closely related to generalizations of integral transforms of a more geometric character.

"Fourier Mukai and Nahm Transforms in Geometry and Mathematical Physics" examines the algebro-geometric approach (Fourier Mukai functors) as well as the differential-geometric constructions (Nahm). Also included is a considerable amount of material from existing literature which has not been systematically organized into a monograph.

Key features: Basic constructions and definitions are presented in preliminary background chapters - Presentation explores applications and suggests several open questions - Extensive bibliography and index.

This self-contained monograph provides an introduction to current research in geometry and mathematical physics and is intended for graduate students and researchers just entering this field."

This biography explores the life and career of the Italian physicist Enrico Fermi, which is also the story of thirty years that transformed physics and forever changed our understanding of matter and the universe: nuclear physics and elementary particle physics were born, nuclear fission was discovered, the Manhattan Project was developed, the atomic bombs were dropped, and the era of "big science" began.It would be impossible to capture the full essence of this revolutionary period without first understanding Fermi, without whom it would not have been possible. Enrico Fermi: The Obedient Genius attempts to shed light on all aspects of Fermi's life - his work, motivation, influences, achievements, and personal thoughts - beginning with the publication of his first paper in 1921 through his death in 1954. During this time, Fermi demonstrated that he was indeed following in the footsteps of Galileo, excelling in his work both theoretically and experimentally by deepening our understanding of the Pauli exclusion principle, winning the Nobel Prize for his discovery of the fundamental properties of slow neutrons, developing the theory of beta decay, building the first nuclear reactor, and playing a central role in the development of the atomic bomb. Interwoven with this fascinating story, the book details the major developments in physics and provides the necessary background material to fully appreciate the dramatic changes that were taking place. Also included are appendices that provide a timeline of Fermi's life, several primary source documents from the period, and an extensive bibliography. This book will enlighten anyone interested in Fermi's work or the scientific events that led to the physics revolution of the first half of the twentieth century.

Geometry, if understood properly, is still the closest link between mathematics and theoretical physics, even for quantum concepts. In this collection of outstanding survey articles the concept of non-commutation geometry and the idea of quantum groups are discussed from various points of view. Furthermore the reader will find contributions to conformal field theory and to superalgebras and supermanifolds. The book addresses both physicists and mathematicians.

The aim of the book is to present a precise and comprehensive introduction to the basic theory of derived functors, with an emphasis on sheaf cohomology and spectral sequences. It keeps the treatment as simple as possible, aiming at the same time to provide a number of examples, mainly from sheaf theory, and also from algebra.The first part of the book provides the foundational material: Chapter 1 deals with category theory and homological algebra. Chapter 2 is devoted to the development of the theory of derived functors, based on the notion of injective object. In particular, the universal properties of derived functors are stressed, with a view to make the proofs in the following chapters as simple and natural as possible. Chapter 3 provides a rather thorough introduction to sheaves, in a general topological setting. Chapter 4 introduces sheaf cohomology as a derived functor, and, after also defining Cech cohomology, develops a careful comparison between the two cohomologies which is a detailed analysis not easily available in the literature. This comparison is made using general, universal properties of derived functors. This chapter also establishes the relations with the de Rham and Dolbeault cohomologies. Chapter 5 offers a friendly approach to the rather intricate theory of spectral sequences by means of the theory of derived triangles, which is precise and relatively easy to grasp. It also includes several examples of specific spectral sequences. Readers will find exercises throughout the text, with additional exercises included at the end of each chapter.

This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the use of powerful tools from algebraic geometry, and with strong inputs from physics. The notes are based on lectures delivered at the CIME school "Geometric Representation Theory and Gauge Theory" held in Cetraro, Italy, in June 2018. They comprise three contributions, due to Alexander Braverman and Michael Finkelberg, Andrei Negut, and Alexei Oblomkov, respectively. Braverman and Finkelberg's notes review the mathematical theory of the Coulomb branch of 3D N=4 quantum gauge theories. The purpose of Negut's notes is to study moduli spaces of sheaves on a surface, as well as Hecke correspondences between them. Oblomkov's notes concern matrix factorizations and knot homology. This book will appeal to both mathematicians and theoretical physicists and will be a source of inspiration for PhD students and researchers.