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.

Over the last 18 years, there have been many advances in the field of intraoperative monitoring. This new edition of Neurophysiology in Neurosurgery: A Modern Approach provides updates on the original techniques, as well as other more recent methodologies that may either prove beneficial or are commonly used in neuromonitoring. The purpose of this book is to describe the integration of neuromonitoring with surgical procedures. Each methodology is discussed in detail as well as chapters describing how those methodologies are applied to multiple surgical procedures and the evidence used to support those uses. The second edition features a surgical procedure section, which focuses on specific surgical procedures and the type of monitoring used during these procedures. The original chapters have been updated, expanded, and the structure modified to ensure the book is beneficial to both physiologists and surgeons. This book is written for neurosurgeons, neurophysiologists, neurologists, anesthesiologists, interventional neuroradiologists, orthopedic surgeons, and plastic surgeons.