2021; 138 pp; Softcover
MSC: Primary 00; 01;
Print ISBN: 978-1-4704-6713-5
The articles in this volume grew out of a 2019 workshop, held at Johns Hopkins University, that was inspired by a belief that when mathematicians take time to reflect on the social forces involved in the production of mathematics, actionable insights result. Topics range from mechanisms that lead to an inclusion-exclusion dichotomy within mathematics to common pitfalls and better alternatives to how mathematicians approach teaching, mentoring and communicating mathematical ideas.
This collection will be of interest to students, faculty and administrators wishing to gain a snapshot of the current state of professional norms within mathematics and possible steps toward improvements.
Undergraduate and graduate students and researchers interested in mathematical culture and society.
Cover 1
Title page 4
Copyright 5
Acknowledgment 6
Contents 8
Preface 10
Introduction (Emily Riehl) 12
The Time for Miracles is Over (William Yslas Velez and Ana Cristina Velez) 22
On toxic mentorship and the academic savior complex (Pamela E. Harris) 32
Todxs cuentan: building community and welcoming humanity from the first day of class. (Federico Ardila?Mantilla) 40
Congressive Question Time (Eugenia Cheng) 52
Mathematics, We Have a Problem (Michelle Manes) 60
Fiber Bundles and Intersectional Feminism (Dagan Karp) 74
On Parameters for Communicating Mathematics (Oliver Knill) 86
Turning Coffee into Unions: Mathematicians and Collective Bargaining (Denis R. Hirschfeldt) 112
Universities in the time of climate change (Izabella ?aba) 138
Back cover 150
Mathematical Surveys and Monographs, Volume: 207
2015; 482 pp; Softcover
MSC: Primary 35; 60;
Print ISBN: 978-1-4704-7009-8
This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter.
The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.
Graduate students and researchers interested in partial differential equations and stochastic processes.
This is a well-written book. The authors are world experts in this area. The book contains many of their own results...This book is a highly valuable contribution to the literature on Fokker-Planck-Kolmogorov equations. It will certainly become a classic reference for researchers working in the field of partial differential equations and diffusion processes.
-- Zhen-Qing Chen, Mathematical Reviews
Cover 1
Title page 4
Contents 6
Preface 10
Chapter 1. Stationary Fokker-Planck-Kolmogorov equations 14
Chapter 2. Existence of solutions 68
Chapter 3. Global properties of densities 94
Chapter 4. Uniqueness problems 144
Chapter 5. Associated semigroups 190
Chapter 6. Parabolic Fokker-Planck-Kolmogorov equations 254
Chapter 7. Global parabolic regularity and upper bounds 300
Chapter 8. Parabolic Harnack inequalities and lower bounds 328
Chapter 9. Uniquess of solutions to Fokker-Planck-Kolmogorov equations 350
Chapter 10. The infinite-dimensional case 416
Bibliography 450
Subject index 490
Other titles in this series 494
Back Cover 495
Index
Contemporary Mathematics, Volume: 777
2022; 225 pp; Softcover
MSC: Primary 53; 58;
Print ISBN: 978-1-4704-6015-0
This volume contains the proceedings of the AMS Special Session on Differential Geometry and Global Analysis, Honoring the Memory of Tadashi Nagano (1930?2017), held January 16, 2020, in Denver, Colorado.
Tadashi Nagano was one of the great Japanese differential geometers, whose fundamental and seminal work still attracts much interest today. This volume is inspired by his work and his legacy and, while recalling historical results, presents recent developments in the geometry of symmetric spaces as well as generalizations of symmetric spaces; minimal surfaces and minimal submanifolds; totally geodesic submanifolds and their classification; Riemannian, affine, projective, and conformal connections; the (M+,M?)
method and its applications; and maximal antipodal subsets. Additionally, the volume features recent achievements related to biharmonic and biconservative hypersurfaces in space forms, the geometry of Laplace operator on Riemannian manifolds, and Chen-Ricci inequalities for Riemannian maps, among other topics that could attract the interest of any scholar working in differential geometry and global analysis on manifolds.
Graduate students and research mathematicians interested in differential geometry and global analysis on manifolds.
A co-publication of the AMS and the London Mathematical Society
John von Neumann was perhaps the most influential mathematician of the twentieth century. Not only did he contribute to almost all branches of mathematics, he created new fields and was a pioneering influence in the development of computer science.
During and after World War II, he was a much sought-after technical advisor. He served as a member of the Scientific Advisory Committee at the Ballistic Research Laboratories, the Navy Bureau of Ordinance, and the Armed Forces Special Weapons Project. He was a consultant to the Los Alamos Scientific Laboratory and was appointed by U.S. President Dwight D. Eisenhower to the Atomic Energy Commission. He received the Albert Einstein Commemorative Award, the Enrico Fermi Award, and the Medal of Freedom.
This collection of about 150 of von Neumann's letters to colleagues, friends, government officials, and others illustrates both his brilliance and his strong sense of responsibility. It is the first substantial collection of his letters, giving a rare inside glimpse of his thinking on mathematics, physics, computer science, science management, education, consulting, politics, and war. With an introductory chapter describing the many aspects of von Neumann's scientific, political, and social activities, this book makes great reading. Readers of quite diverse backgrounds will be fascinated by this first-hand look at one of the towering figures of twentieth century science.
What's Happening in the Mathematical Sciences, Volume: 12
2022; 126 pp; Softcover
Print ISBN: 978-1-4704-6498-1
As always, What's Happening in the Mathematical Sciences presents a selection of topics in mathematics that have attracted particular attention in recent years. This volume is dominated by an event that shook the world in 2020 and 2021, the coronavirus (or COVID-19) pandemic. While the world turned to politicians and physicians for guidance, mathematicians played a key role in the background, forecasting the epidemic and providing rational frameworks for making decisions. The first three chapters of this book highlight several of their contributions, ranging from advising governors and city councils to predicting the effect of vaccines to identifying possibly dangerous ?gescape variants?h that could re-infect people who already had the disease.
In recent years, scientists have sounded louder and louder alarms about another global threat: climate change. Climatologists predict that the frequency of hurricanes and waves of extreme heat will change. But to even define an ?gextreme?h or a ?gchange,?h let alone to predict the direction of change, is not a climate problem: it's a math problem. Mathematicians have been developing new techniques, and reviving old ones, to help climate modelers make such assessments.
In a more light-hearted vein, ?gDescartes' Homework?h describes how a famous mathematician's blunder led to the discovery of new properties of foam-like structures called Apollonian packings. ?gSquare Pegs and Squiggly Holes?h shows that square pegs fit virtually any kind of hole, not just circular ones. ?gMuch Ado About Zero?h explains how difficult problems about eigenvalues of matrices can sometimes be answered by playing a simple game that involves coloring dots on a grid or a graph.
Finally, ?gDancing on the Edge of the Impossible?h provides a progress report on one of the oldest and still most important challenges in number theory: to devise an effective algorithm for finding all of the rational-number points on an algebraic curve. In the great majority of cases, number theorists know that the number of solutions is finite, yet they cannot tell when they have found the last one. However, two recently proposed methods show potential for breaking the impasse.
Undergraduate and graduate students interested in expository accounts of recent developments in mathematics.
Contemporary Mathematics
Volume: 778; 2022; Softcover
MSC: Primary 11; 14; 32; 82;
Print ISBN: 978-1-4704-6779-1
This volume contains the proceedings of the 2019 Lluis A. Santalo Summer School on p-Adic Analysis, Arithmetic and Singularities, which was held from June 24?28, 2019, at the Universidad Internacional Menendez Pelayo, Santander, Spain.
The main purpose of the book is to present and analyze different incarnations of the local zeta functions and their multiple connections in mathematics and theoretical physics. Local zeta functions are ubiquitous objects in mathematics and theoretical physics. At the mathematical level, local zeta functions contain geometry and arithmetic information about the set of zeros defined by a finite number of polynomials. In terms of applications in theoretical physics, these functions play a central role in the regularization of Feynman amplitudes and Koba-Nielsen-type string amplitudes, among other applications.
This volume provides a gentle introduction to a very active area of research that lies at the intersection of number theory, p-adic analysis, algebraic geometry, singularity theory, and theoretical physics. Specifically, the book introduces p-adic analysis, the theory of zeta functions, Archimedean, p-adic, motivic, singularities of plane curves and their Poincare series, among other similar topics. It also contains original contributions in the aforementioned areas written by renowned specialists.
This book is an important reference for students and experts who want to delve quickly into the area of local zeta functions and their many connections in mathematics and theoretical physics.
Graduate students and research mathematicians interested in local zeta functions and their multiple connections in mathematics and theoretical physics.
Student Mathematical Library
Volume: 96; 2022; 416 pp; Softcover
MSC: Primary 53;
Print ISBN: 978-1-4704-6959-7
This book features plane curves?the simplest objects in differential geometry?to illustrate many deep and inspiring results in the field in an elementary and accessible way.
After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number (with a proof of the fundamental theorem of algebra), rotation index, Jordan curve theorem, isoperimetric inequality, convex curves, curves of constant width, and the four-vertex theorem. The last chapter connects the classical with the modern by giving an introduction to the curve-shortening flow that is based on original articles but requires a minimum of previous knowledge.
Over 200 figures and more than 100 exercises illustrate the beauty of plane curves and test the reader's skills. Prerequisites are courses in standard one variable calculus and analytic geometry on the plane.
Undergraduate and graduate students interested in curves in the Euclidean plane.
MAA Press: An Imprint of the American Mathematical Society
AMS/MAA Textbooks, Volume: 72
2022; Softcover
MSC: Primary 12; 13; 16; 20;
Print ISBN: 978-1-4704-6881-1
A Friendly Introduction to Abstract Algebra offers a new approach to laying a foundation for abstract mathematics. Prior experience with proofs is not assumed, and the book takes time to build proof-writing skills in ways that will serve students through a lifetime of learning and creating mathematics.
The author's pedagogical philosophy is that when students abstract from a wide range of examples, they are better equipped to conjecture, formalize, and prove new ideas in abstract algebra. Thus, students thoroughly explore all concepts through illuminating examples before formal definitions are introduced. The instruction in proof writing is similarly grounded in student exploration and experience. Throughout the book, the author carefully explains where the ideas in a given proof come from, along with hints and tips on how students can derive those proofs on their own.
Readers of this text are not just consumers of mathematical knowledge. Rather, they are learning mathematics by creating mathematics. The author's gentle, helpful writing voice makes this text a particularly appealing choice for instructors and students alike. The book's website has companion materials that support the active-learning approaches in the book, including in-class modules designed to facilitate student exploration.
Undergraduate students interested in learning abstract algebra.