A Conference Celebrating the Birthdays of Sasha Beilinson and Victor Ginzburg
Explores the influential
Contains cutting-edge
Presents talks
The chapters in this volume explore the influence of the Russian school on the development of
algebraic geometry and representation theory, particularly the pioneering work of two of its
illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th
birthdays. Based on the work of speakers and invited participants at the conference
gInteractions Between Representation Theory and Algebraic Geometryh, held at the University of
Chicago, August 21-25, 2017, this volume illustrates the impact of their research and how it
has shaped the development of various branches of mathematics through the use of Dmodules,
the affine Grassmannian, symplectic algebraic geometry, and other topics. All authors
have been deeply influenced by their ideas and present here cutting-edge developments on
modern topics. Chapters are organized around three distinct themes: Groups, algebras,
categories, and representation theory D-modules and perverse sheaves Analogous varieties
defined by quivers Representation Theory and Algebraic Geometry will be an ideal resource for
researchers who work in the area, particularly those interested in exploring the impact of the
Russian school.
Due 2021-12-12
1st ed. 2021, IV, 332 p. 73 illus., 3 illus. in color.
Hardcover
ISBN 978-3-030-82006-0
Product category : Contributed volume
Series : Trends in Mathematic
Mathematics : Algebraic Geometry
Includes extensive background information for increased accessibility
Contains discussion of computational and algorithmic aspects of the subject
Features an extensive bibliography
This book collects and explains the many theorems concerning the existence of certificates of
positivity for polynomials that are positive globally or on semialgebraic sets. A certificate of
positivity for a real polynomial is an algebraic identity that gives an immediate proof of a
positivity condition for the polynomial.Certificates of positivity have their roots in fundamental
work of David Hilbert from the late 19thcentury on positive polynomials and sums of squares.
Because of the numerous applications of certificates of positivity in mathematics, applied
mathematics, engineering, and other fields, it is desirable to have methods for finding,
describing, and characterizing them. For many of the topics covered in this book, appropriate
algorithms, computational methods, and applications are discussed. This volume contains a
comprehensive, accessible, up-to-date treatment of certificates of positivity, written by an expert
in the field. It provides an overview of both the theory and computational aspects of the
subject, and includes many of the recent and exciting developments in the area. Background
information is given so that beginning graduate students and researchers who are not
specialists can learn about this fascinating subject. Furthermore, researchers who work on
certificates of positivity or use them in applications will find this a useful reference for their
work.
Due 2021-11-20
1st ed. 2021, XI, 156 p. 14 illus.
Hardcover
ISBN 978-3-030-85546-8
Product category : Monograph
Series : Developments in Mathematics
Mathematics : Algebraic Geometry
Proceedings of the Seminar on the Mathematical Modelling of COVID-19
Allows students of mathematics to see the value of these methodologies
applied to a global real-world problem
Contains detailed explanations of mathematical models and their
assumptions and limitations
Provides a broad array of relevant mathematical models and current, timely research
Curated by the Fields Institute for Research in Mathematical Sciences from their COVID-19
Math Modelling Seminars, this first in a series of volumes on the mathematics of public health
allows readers to access the dominant ideas and techniques being used in this area, while
indicating problems for further research. This work brings together experts in mathematical
modelling from across Canada and the world, presenting the latest modelling methods as they
relate to the COVID-19 pandemic. A primary aim of this book is to make the content accessible
so that researchers share the core methods that may be applied elsewhere. The mathematical
theories and technologies in this book can be used to support decision makers on critical
issues such asprojecting outbreak trajectories, evaluating public health interventions for
infection prevention and control, developing optimal strategies to return to a new normal, and
designing vaccine candidates and informing mass immunization program. Topical coverage
includes: basic susceptible-exposed-infectious-recovered (SEIR) modelling framework modified
and applied to COVID-19 disease transmission dynamics; nearcasting and forecasting for
needs of critical medical resources including personal protective equipment (PPE); predicting
COVID-19 mortality; evaluating effectiveness of convalescent plasma treatment and the logistic
implementation challenges; estimating impact of delays in contact tracing; quantifying
heterogeneity in contact mixing and its evaluation with social distancing; modelling point of
care diagnostics of COVID-19; and understanding non-reporting and underestimation. Further,
readers will have the opportunity to learn about current modelling methodologies and
technologies for emerging infectious disease outbreaks, pandemic mitigation rapid response,
and the mathematics behind them.
Due 2021-12-14
1st ed. 2022, VIII, 292 p. 95 illus., 84 illus. in color.
Hardcover
ISBN 978-3-030-85052-4
Product category : Contributed volume
Series : Fields Institute Communications
Mathematics : Mathematical Modeling and Industrial Mathematics
https://doi.org/10.1142/12293 | August 2021
Pages: 176
ISBN: 978-981-123-742-3 (hardcover)
The textbook is a very good start into the mathematical field of topology.
A variety of topological concepts with some elementary applications are introduced.
It is organized in such a way that the reader gets to significant applications quickly.
This revised version corrects the many discrepancies in the earlier edition.
The emphasis is on the geometric understanding and the use of new concepts,
indicating that topology is really the language of modern mathematics.
Preface
Sets and Numbers
Metric and Topological Spaces
From Old to New Spaces
Very Special Spaces
Function Spaces
Topological Groups
Special Groups
Normality and Paracompactness
The Fundamental Group
Appendix A: Some Inequalities
Appendix B: Binomial Equalities
List of Symbols
Index
Advanced undergraduates and graduates in differential geometry and topology.
https://doi.org/10.1142/12086 | November 2021
Pages: 500
ISBN: 978-981-122-982-4 (hardcover)
ISBN: 978-981-123-141-4 (softcover)
The series is edited by the head coaches of China's IMO National Team.
Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team.
The Chinese edition has won the award of Top 50 most influential educational brand in China.
The series is in line with the mathematics cognition and intellectual development level of the students in the corresponding grade.
The volume lines up the topics in each chapter and introduces a variety of concepts and methods to provide with the knowledge,
then gradually transitions to the competition level. The content covers all the hot topics of the competition.
In each chapter, there are packed with many problems including some real competition questions which students can use to verify their abilities.
Selected detailed answers are provided. Some of the solutions are from national training team and national team members,
their wonderful solutions being the feature of this series.
Quadratic Equations
The Equations That can be Transformed Into the Quadratic Equations
The Discriminant of a Quadratic Equation
The Relationship Between Roots and Coefficients and Its Application
Simultaneous Quadratic Equations with Two Unknowns
Integer Roots of a Quadratic Equation
Perfect Square Numbers
Quadratic Functions
Quadratic Inequalities
The Distribution of Roots of a Quadratic Equation
Maximum and Minimum Values of Quadratic Functions
Maximum and Minimum Values of Simple Fractional Functions
Trigonometric Functions of an Acute Angle
Solve Right Triangles
Rotations
The Basic Properties of Circles
Positional Relation Between a Line and a Circle
Positional Relation of Two Circles
Power of a Point Theorem
Four Concyclic Points
Problems of Geometric Fixed Value
Five Centers of a Triangle
Geometric Inequality
Indefinite Equation
Reductio Ad Absurdum
Extreme Principle
Coloring Problems
Probability
Secondary school students engaged in mathematical competition, coaches in mathematics teaching, and teachers setting up math elective courses.
https://doi.org/10.1142/q0308 | September 2021
Pages: 616
ISBN: 978-1-80061-045-3 (hardcover)
The development of inexpensive and fast computers, coupled with the discovery of efficient algorithms for dealing with polynomial equations, has enabled exciting new applications of algebraic geometry and commutative algebra. Algebraic Geometry for Robotics and Control Theory shows how tools borrowed from these two fields can be efficiently employed to solve relevant problem arising in robotics and control theory.
After a brief introduction to various algebraic objects and techniques, the book first covers a wide variety of topics concerning control theory, robotics, and their applications. Specifically this book shows how these computational and theoretical methods can be coupled with classical control techniques to: solve the inverse kinematics of robotic arms; design observers for nonlinear systems; solve systems of polynomial equalities and inequalities; plan the motion of mobile robots; analyze Boolean networks; solve (possibly, multi-objective) optimization problems; characterize the robustness of linear; time-invariant plants; and certify positivity of polynomials.
Preface
About the Authors
List of Figures
List of Tables
List of Symbols
Algebraic Geometry Notions
Implementations in Macaulay2
The Inverse Kinematics of Robot Arms
Observer Design
Immersions of Polynomial Systems into Linear Ones Up to an Output Injection
Solving Systems of Equations and Inequalities
Motion Planning for Mobile Robots
Computation of the Largest ?-Invariant Set Contained in an Affine Variety
Boolean Networks
Multi-objective Optimization
Distance to Internal Instability of Linear Time-Invariant Systems Under Structured Perturbations
Decomposition in Sum of Squares
Bibliography
Index
Readers and practitioners in the fields of algebraic geometry, control theory, and robotics.
https://doi.org/10.1142/12338 | December 2021
Pages: 460
ISBN: 978-981-123-979-3 (hardcover)
ISBN: 978-981-123-908-3 (softcover)
This is the revised and expanded edition of the problem book Linear Algebra:
Challenging Problems for Students, now entitled Problems in Linear Algebra and Matrix Theory.
This new edition contains about fifty-five examples and many new problems,
based on the author's lecture notes of Advanced Linear Algebra classes at Nova Southeastern University (NSU-Florida)
and short lectures Matrix Gems at Shanghai University and Beijing Normal University.
The book is intended for upper division undergraduate and beginning graduate students,
and it can be used as text or supplement for a second course in linear algebra.
Each chapter starts with Definitions, Facts, and Examples, followed by problems.
Hints and solutions to all problems are also provided.
Vector Spaces
Determinants, Inverses, Rank, and Systems of Linear Equations
Similarity, Eigenvalues, Matrix Decompositions, and Linear Transformations
Special Matrices
Inner Product Spaces
Miscellaneous Problems
Solutions to all Problems
College/university students and instructors in mathematics, physics, statistics, computer science, etc. Upper division/beginning graduate level.