Bøger i IAS/Park City Mathematics Series serien

Presents lectures from the Graduate Summer School 'Quantum Field Theory and Manifold Invariants' held at Park City Mathematics Institute 2019. The lectures span topics in topology, global analysis, and physics, and they range from introductory to cutting edge.

Based on lectures presented at the summer school on Harmonic Analysis, this voluume offers fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere.

Data science is a highly interdisciplinary field, incorporating ideas from applied mathematics, statistics, probability, and computer science, as well as many other areas. This book provides an introduction to the mathematical methods that form the foundations of machine learning and data science.

This book is based on lectures given at the Graduate Summer School of the 2015 Park City Mathematics Institute program, "Geometry of moduli spaces and representation theory", and is devoted to several interrelated topics in algebraic geometry, topology of algebraic varieties, and representation theory.

Examines material behaviour that is rooted in statistical mechanics. While many presentations of mathematical problems in materials science begin with continuum mechanics, this volume takes an alternate approach. Contributions to this volume present unique pedagogical introductions to the rich variety of material behaviour that emerges from the interplay of geometry and statistical mechanics.

Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and this volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory.

Suitable for graduate students and research scientists, this title features chapters that are based on a series of lectures given by a leading researcher and develops methods and theory of mathematical biology from first principles. It also includes exercises for those who wish to delve further into the material.

Based on a series of lectures at the PCMI summer school, this volume gives an introduction to the advanced techniques behind recent developments in algebraic and analytic geometry. The lectures contain many illustrative examples, detailed computations, and new perspectives on the topics presented.

Symplectic geometry has its origins as a geometric language for classical mechanics. But it has exploded into an independent field interconnected with many other areas of mathematics and physics. This book intends to give an intensive introduction to these areas of research.

Explores topics from classical and quantum mechanics and field theory. This book covers Lie groups and symplectic geometry, examining the connection with mechanics and the application to differential equations and the work of the Gromov school. It also describes the application of supersymmetry to prove the Atiyah-Singer index theorem.

Offers a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. This book predates Donaldson's applications of the subject to 4-manifold topology, where the central concern was the geometry of the moduli space.