Bøger i IAS/Park City Mathematics Series serien

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.

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.

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.

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.