Hardcover ISBN: 978-606-8443-13-3
Product Code: THETA/27
Theta Foundation International Book Series of Mathematical Texts Volume: 27;
2024; 168 pp
The volume contains the proceedings of the twenty-eighth International Conference on Operator Theory, held in Timi?oara between June 27? July 1, 2022. It consists of a careful selection of expository papers on topics of contemporary research authored by the invited speakers. The subjects covered include:
pseudodifferential operators
bounded representations of groups and semigroups
paired operators on Lebesgue spaces
decomposition of unitary operators
Stein's theorem in harmonic analysis
the finite Hilbert transform in various spaces of functions
characterizations of central positive definite elements in C?
-algebras
A publication of the Theta Foundation. Distributed worldwide, except in Romania, by the AMS.
Graduate students and research mathematicians.
Softcover ISBN: 978-1-4704-6106-5
Product Code: HMATH/46
History of Mathematics Volume: 46;
2024; Estimated: 290 pp
Max Dehn (1878?1952) is known to mathematicians today for his seminal contributions to geometry and topology?Dehn surgery, Dehn twists, the Dehn invariant, etc. He is also remembered as the first mathematician to solve one of Hilbert’s famous problems. However, Dehn's influence as a scholar and teacher extended far beyond his mathematics. Dehn also lived a remarkable life, described in this book in three phases. The first phase focuses on his early career as one of David Hilbert’s most gifted students. The second, after World War I, treats his time in Frankfurt where he led an intimate community of mathematicians in explorations of historical texts. The final phase, after 1938, concerns his flight from Nazi Germany to Scandinavia and eventually to the United States where, after various teaching experiences, the Dehns settled at iconic Black Mountain College.
This book is a collection of essays written by mathematicians and historians of art and science. It treats Dehn’s mathematics and its influence, his journeys, and his remarkable engagement in history and the arts. A great deal of the information found in this book has never before been published.
Undergraduate and graduate students and researchers interested in the history of mathematics.
Brenda Danilowitz and Philip Ording ? Max Dehn’s family: A brief history
David E. Rowe ? Max Dehn as Hilbert’s first star pupil
Jeremy J. Gray and John McCleary ? Dehn’s early mathematics
Cameron McA. Gordon and David E. Rowe ? Dehn’s early work in topology
David E. Rowe ? Golden years in Frankfurt
John Stillwell ? Three students of Max Dehn
James W. Cannon ? Max Dehn and the Word Problem
Stefan Muller-Stach ? Max Dehn, Axel Thue, and the undecidable
David E. Rowe ? Mathematics under the sign of the Swastika
Marjorie Senechal ? Max Dehn’s long journey
Marjorie Senechal ? Max Dehn’s American students
Brenda Danilowitz and Philip Ording ? Toward a happy life: Max Dehn at Black Mountain College
Hardcover ISBN: 978-1-4704-7666-3
Colloquium Publications Volume: 67;
2024; 927 pp
This book provides a detailed treatment of the various facets of modern Sturm?Liouville theory, including such topics as Weyl?Titchmarsh theory, classical, renormalized, and perturbative oscillation theory, boundary data maps, traces and determinants for Sturm?Liouville operators, strongly singular Sturm?Liouville differential operators, generalized boundary values, and Sturm?Liouville operators with distributional coefficients. To illustrate the theory, the book develops an array of examples from Floquet theory to short-range scattering theory, higher-order KdV trace relations, elliptic and algebro-geometric finite gap potentials, reflectionless potentials and the Sodin?Yuditskii class, as well as a detailed collection of singular examples, such as the Bessel, generalized Bessel, and Jacobi operators. A set of appendices contains background on the basics of linear operators and spectral theory in Hilbert spaces, Schatten?von Neumann classes of compact operators, self-adjoint extensions of symmetric operators, including the Friedrichs and Krein?von Neumann extensions, boundary triplets for ODEs, Krein-type resolvent formulas, sesquilinear forms, Nevanlinna?Herglotz functions, and Bessel functions.
Graduate students and researchers interested in ordinary differential operators
Introduction
A bit of physical motivation
Preliminaries on ODEs
The regular problem on a compact interval [a,b]⊂R
The singular problem on (a,b)⊆R
The spectral function for a problem with a regular endpoint
The 2 x 2 spectral matrix function in the presence of two singular interval endpoints for the problem on (a,b)⊆R
Classical oscillation theory, principal solutions, and nonprinicpal solutions
Renormalized oscillation theory
Perturbative oscillation criteria and perturbative Hardy-type inequalities
Boundary data maps
Spectral zeta functions and computing traces and determinants for Sturm-Liouville operators
The singular problem on (a,b)⊆R
revisited
Four-coefficient Sturm-Liouville operators and distributional potential coefficients
Epilogue: Applications to some partial differnetial equations of mathematical physics
Basic facts on linear operators
Basics of spectral theory
Classes of bounded linear operators
Extensions of symmetric operators
Elements of sesquilinear forms
Basics of Nevanlinna-Herglotz functions
Bessel functions in a nutshell
Bibliography
Author index
List of symbols
Subject index
Softcover ISBN: 978-1-4704-7333-4
Proceedings of Symposia in Pure Mathematics Volume: 110;
2024; 371 pp
In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume.
The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.
Graduate students and research mathematicians interested in algebraic combinatorics and related areas.
Francois Bergeron ? (GLk× Sn)
-modules of multivariate diagonal harmonics
Francesco Brenti ? Some open problems on Coxeter groups and unimodality
R. Kenyon ? Some combinatorial problems arising in the dimer model
Per Alexandersson and Valentin Feray ? A positivity conjecture on the structure constants of shifted Jack functions
Greta Panova ? Complexity and asymptotics of structure constants
Jonathan Novak and Brendon Rhoades ? Increasing subsequences and Kronecker coefficients
Nathan Williams ? Combinatorics and braid varieties
Isabella Novik and Hailun Zheng ? Neighborly spheres and transversal numbers
Hugh Thomas ? Realizing simplicial complexes as the boundary of the totally non-negative part of a variety
Sam Hopkins ? Order polynomial product formulas and poset dynamics
Thomas Lam ? An invitation to positive geometries
Satoshi Murai ? An upper bound problem for triangulations of manifolds
Igor Pak ? What is a combinatorial interpretation?
James Propp ? Trimer covers in the triangular grid: Twenty mostly open problems
Laura Colmenarejo, Rosa Orellana, Franco Saliola, Anne Schilling and Mike Zabrocki ? The mystery of plethysm coefficients
Tri Lai ? Problems in the enumeration of tilings
Zhao Gao, Claudiu Raicu and Keller VandeBogert ? Some questions arising from the study of cohomology on flag varieties
Alexander Yong ? Castelnuovo-Mumford regularity and Schubert geometry
Ralf Schiffler ? Perfect matching problems in cluster algebras and number theory
Softcover ISBN: 978-1-4704-7356-3
Contemporary Mathematics Volume: 805;
2024; 250 pp
This volume contains the proceedings of the AMS-EMS-SMF Special Session on Deformations of Artinian Algebras and Jordan Type, held July 18?22, 2022, at the Universite Grenoble Alpes, Grenoble, France.
Articles included are a survey and open problems on deformations and relation to the Hilbert scheme; a survey of commuting nilpotent matrices and their Jordan type; and a survey of Specht ideals and their perfection in the two-rowed case.
Other articles treat topics such as the Jordan type of local Artinian algebras, Waring decompositions of ternary forms, questions about Hessians, a geometric approach to Lefschetz properties, deformations of codimension two local Artin rings using Hilbert-Burch matrices, and parametrization of local Artinian algebras in codimension three. Each of the articles brings new results on the boundary of commutative algebra and algebraic geometry.
Graduate students and research mathematicians interested in local Artinian algebras and deformations, as well as their connections with algebraic geometry, singularity theory, and combinatorics.
Surveys
Joachim Jelisiejew ? Open problems in deformations of Artinian algebras, Hilbert schemes and around
Leila Khatami ? Commuting Jordan types: A survey
Chris McDaniel ? A brief survey of Specht ideals and their perfection in the two-rowed case
Articles
Nancy Abdallah ? A note on Artin Gorenstein algebras with Hilbert function (1,4,k,k,4,1)
Nasrin Altafi ? A note on Jordan types and Jordan degree types
Elena Angelini, Luca Chiantini and Alessandro Oneto ? Waring decompositions of special ternary forms with different Hilbert functions
Vincenzo Antonelli and Gianfranco Casnati ? Some remarks on varieties whose twisted normal bundle is an instanton
Edoardo Ballico and Emanuele Ventura ? On the Koiran-Skomra’s question about Hessians
Davide Bricalli and Filippo Francesco Favale ? Standard Artinian algebras and Lefschetz properties: A geometric approach
Luca Chiantini and Fulvio Gesmundo ? Decompositions and Terracini loci of cubic forms of low rank
Joan Elias and Maria Evelina Rossi ? Almost finitely generated inverse systems and reduced k
-algebras
Roser Homs and Anna-Lena Winz ? Deformations of local Artin rings via Hilbert-Burch matrices
Shreedevi K. Masuti ? The Hilbert function of local Artinian level algebras of codimension 3
and type 2
Bernard Mourrain ? Isolated singularities, inverse systems and the punctual Hilbert scheme
Liana M. ?ega and Deepak Sireeshan ? Dg module structures and minimal free resolutions modulo an exact zero divisor
Hardcover ISBN: 978-1-4704-7767-7
Graduate Studies in Mathematics Volume: 245;
2024; 750 pp
Differential geometry is a subject related to many fields in mathematics and the sciences. The authors of this book provide a vertically integrated introduction to differential geometry and geometric analysis. The material is presented in three distinct parts: an introduction to geometry via submanifolds of Euclidean space, a first course in Riemannian geometry, and a graduate special topics course in geometric analysis, and it contains more than enough content to serve as a good textbook for a course in any of these three topics.
The reader will learn about the classical theory of submanifolds, smooth manifolds, Riemannian comparison geometry, bundles, connections, and curvature, the Chern?Gauss?Bonnet formula, harmonic functions, eigenfunctions, and eigenvalues on Riemannian manifolds, minimal surfaces, the curve shortening flow, and the Ricci flow on surfaces. This will provide a pathway to further topics in geometric analysis such as Ricci flow, used by Hamilton and Perelman to solve the Poincare and Thurston geometrization conjectures, mean curvature flow, and minimal submanifolds.
The book is primarily aimed at graduate students in geometric analysis, but it will also be of interest to postdoctoral researchers and established mathematicians looking for a refresher or deeper exploration of the topic.
Undergraduate and graduate students and researchers interested in differential geometry and geometric analysis.
Geometry of submanifolds of Euclidean space
Intuitive introduction to submanifolds in Euclidean space
Differential calculus of submanifolds
Linearizing submanifolds: Tangent and tensor bundles
Curvature and the local geometry of submanifolds
Global theorems in the theory of submanifolds
Differential topology and Riemannian geometry
Smooth manifolds
Riemannian manifolds
Differential forms and the method of moving frames on manifolds
The Gauss?Bonnet and Poincare?Hopf theorems
Bundles and the Chern?Gauss?Bonnet formula
Elliptic and parabolic equations in geometric analysis
Linear elliptic and parabolic equations
Elliptic equations and the geometry of minimal surfaces
Geometric flows of curves in the plane
Uniformization of surfaces via heat flow
Bibliography
Index
Lectures on Random Matrices cover
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Random matrices are cool! In this book we give an idea why random matrices are so fascinating and have become a centrepiece of modern mathematics.
This an introduction to random matrix theory, giving an impression of some of the most important aspects of this modern subject. In particular, it covers the basic combinatorial and analytic theory around Wigner’s semicircle law, featuring also concentration phenomena, and the Tracy?Widom distribution of the largest eigenvalue. The circular law and a discussion of Voiculescu’s multivariate extension of the semicircle law, as an appetiser for free probability theory, also make an appearance.
This book is based on a lecture series for graduate and advanced undergraduate students at Saarland University, Germany.
Frontmatter
Download pp. i?iv
Preface
Download pp. v?viii
Contents
Download pp. ix?xi
1 Introduction pp. 1?11
2 Gaussian random matrices: Wick formula and combinatorial proof of Wigner’s semicircle law pp. 13?23
3 Wigner matrices: Combinatorial proof of Wigner’s semicircle law pp. 25?30
4 Analytic tools: Stieltjes transform and convergence of measures pp. 31?40
5 Analytic proof of Wigner’s semicircle law for Gaussian random matrices pp. 41?47
6 Concentration phenomena and stronger forms of convergence for the semicircle law pp. 49?59
7 Analytic description of the eigenvalue distribution of Gaussian random matrices pp. 61?72
8 Determinantal processes and non-crossing paths: Karlin?McGregor and Gessel?Viennot pp. 73?78
9 Statistics of the largest eigenvalue and Tracy?Widom distribution pp. 79?94
10 Statistics of the longest increasing subsequence pp. 95?100
11 The circular law pp. 101?106
12 Several independent GUEs and asymptotic freeness pp. 107?112
References pp. 113?115
Index pp. 117?119
Panoramas et Syntheses | 2024
Annee : 2024
Tome : 61
Format : Electronique, Papier
Langue de l'ouvrage : Anglais
ISBN : 978-2-85629-987-6
This volume includes the lecture notes of the three mini-courses that have been given during the CIRM-SMF week entitled Inhomogeneous Flows: Asymptotic Models and Interfaces Evolution that took place at the CIRM from September 23 to September 27, 2019. The conference followed the themes of the ANR-15-CE40-0011 INFAMIE project and aimed at bringing together experts coming from various branches of mathematical fluid dynamics and interested in inhomogeneous fluids where problems of interfaces occur. Beside the mini-courses, the event comprised 14 plenary talks that were specifically dedicated to inhomogeneous flows.
The mini-courses emphasized on the one hand theoretical approaches that proved to be efficient in the study of evolutionary fluid mechanics (maximal regularity issues in the notes of P. Kunstmann with stress on the L1
-in-time estimates that turn out to be crucial in the study of free boundary problems, and the prospective course by P. Auscher on tent spaces), and on the other hand the modeling aspect with the lectures by S. Gavrilyuk devoted to the derivation of models of bi-fluids by means of Hamiltonian principle.
The originality of these texts is that they have been written conjointly by the speaker and young participants, from the notes that have been taken during the courses.