The development of quantum field theory and string theory in the last half-century has taken interactions between mathematics and physics to an unprecedented level, incorporating into this area of physics (often called ""high-energy physics"") such traditionally ""pure"" areas of mathematics as algebraic topology, category theory, differential and ......
The development of quantum field theory and string theory in the last half-century has taken interactions between mathematics and physics to an unprecedented level, incorporating into this area of physics (often called ""high-energy physics"") such traditionally ""pure"" areas of mathematics as algebraic topology, category theory, differential and ......
The purpose of the present monograph is to introduce the reader to a free noncommutative analogue of the celebrated Sz.-Nagy-Foias theory of contractions (on Hilbert spaces) in the closed unit ball of $B(H)^n$, where $B(H)$ is the algebra of bounded linear operators on a Hilbert space $H$. The elements of this noncommutative ball are called row ......
The aim of the book is to present some recent results in the theory of stochastic Ito equations with singular deterministic part (drift) and its applications to second-order elliptic and parabolic equations with singular first-order coefficients. The singularity is characterized by means of Morrey spaces, and this allows for much more singular ......
This volume provides a comprehensive introduction to the mathematical analysis of Coulomb, log, and Riesz gases in arbitrary dimensions. These systems of particles with singular long-range interactions are classical ensembles of statistical mechanics and have strong connections to random matrix theory, approximation theory, statistical sampling, ......
The Floer Jungle traces the development of Floer theory while portraying the life of mathematician Andreas Floer (1956-1991), whose ideas transformed geometry and topology. Blending mathematical exposition with biography, it reconstructs the existing ideas, and introduces the main characters, describing their interactions, their judgements and ......
This book presents a rich, insightful exploration of the interplay between randomness, the Riemann Hypothesis, and analytic number theory. Written for readers with a moderate background in mathematics (preferably having some familiarity with probability theory and complex analysis), it offers a deeper and more comprehensive account of the Riemann ......
A Conference in Honor of E. Artal's 60th and a. Melle's 55th Birthdays
The occasion of Enrique Artal's and Alejandro Melle's birthday celebration, held in Jaca, Spain, on June 16-23, 2023, provided the backdrop for a gathering of world-renowned specialists, young researchers, and graduate students interested in singularity theory from the point of view of its multiple connections with the fields of topology, algebra, ......
This volume is an outgrowth of the Regulators V Conference that was held on June 3-13, 2024, at the University of Pisa, Italy. Gathering contributions by leading experts in the field ranging from original surveys to pure research articles, this volume provides comprehensive coverage of the latest advancements in the field of regulator maps and ......
