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This book introduces a simple dynamical model
for a planar heat map that is invariant under projective
transformations. The map is defined by iterating a polygon map, where
one starts with a finite planar \(N\)-gon and produces a new
\(N\)-gon by a prescribed geometric construction. One of the
appeals of the topic of this book is the simplicity of the
construction that yet leads to deep and far reaching mathematics. To
construct the projective heat map, the author modifies the classical
affine invariant midpoint map, which takes a polygon to a new polygon
whose vertices are the midpoints of the original.
The author provides useful background which makes this book
accessible to a beginning graduate student or advanced undergraduate
as well as researchers approaching this subject from other fields of
specialty. The book includes many illustrations, and there is also a
companion computer program.
Undergraduate and graduate students and researchers interested in analysis, geometry, and topology.
The Grothendieck–Teichmüller group was
defined by Drinfeld in quantum group theory with insights coming from
the Grothendieck program in Galois theory. The ultimate goal of this
book is to explain that this group has a topological interpretation as
a group of homotopy automorphisms associated to the operad of little
2-discs, which is an object used to model commutative homotopy
structures in topology.
This volume gives a comprehensive survey on the algebraic aspects
of this subject. The book explains the definition of an operad in a
general context, reviews the definition of the little discs operads,
and explains the definition of the Grothendieck–Teichmüller
group from the viewpoint of the theory of operads. In the course of
this study, the relationship between the little discs operads and the
definition of universal operations associated to braided monoidal
category structures is explained. Also provided is a comprehensive and
self-contained survey of the applications of Hopf algebras to the
definition of a rationalization process, the Malcev completion, for
groups and groupoids.
Most definitions are carefully reviewed in the book; it requires
minimal prerequisites to be accessible to a broad readership of
graduate students and researchers interested in the applications of
operads.
Graduate students and researchers interested in algebraic topology and algebraic geometry.
This book combines the spirit of a textbook with that of a
monograph on the topic of semigroups and their applications. It is
expected to have potential readers across a broad spectrum that includes
operator theory, partial differential equations, harmonic analysis,
probability and statistics, and classical and quantum mechanics.
A reasonable amount of familiarity with real
analysis, including the Lebesgue-integration theory, basic functional
analysis, and bounded linear operators is assumed. However, any discourse on a
theory of semigroups needs an introduction to unbounded linear
operators, some elements of which have been included in the Appendix,
along with the basic ideas of the Fourier transform and of Sobolev
spaces. Chapters 4–6 contain advanced material not often found
in textbooks but which have many interesting applications, such as the
Feynman–Kac formula, the central limit theorem, and the
construction of Markov semigroups. The exercises are given in the
text as the topics are developed so that interested readers can solve
these while learning that topic.
A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.
Graduate students and research mathematicians interested in semigroups.
This volume contains the proceedings of the
Logic at Harvard conference in honor of W. Hugh Woodin's 60th
birthday, held March 27–29, 2015, at Harvard University. It
presents a collection of papers related to the work of Woodin, who has
been one of the leading figures in set theory since the early 1980s.
The topics cover many of the areas central to Woodin's work,
including large cardinals, determinacy, descriptive set theory and the
continuum problem, as well as connections between set theory and
Banach spaces, recursion theory, and philosophy, each reflecting a
period of Woodin's career. Other topics covered are forcing axioms,
inner model theory, the partition calculus, and the theory of
ultrafilters.
This volume should make a suitable introduction to Woodin's work
and the concerns which motivate it. The papers should be of interest
to graduate students and researchers in both mathematics and
philosophy of mathematics, particularly in set theory, foundations and
related areas.
Graduate students and research mathematicians interested in set theory, foundations, and related areas.
This volume contains the proceedings of the
AMS Special Session on Algebraic and Combinatorial Structures in Knot
Theory and the AMS Special Session on Spatial Graphs, both held from
October 24–25, 2015, at California State University, Fullerton,
CA.
Included in this volume are articles that draw on techniques from
geometry and algebra to address topological problems about knot theory
and spatial graph theory, and their combinatorial generalizations to
equivalence classes of diagrams that are preserved under a set of
Reidemeister-type moves.
The interconnections of these areas and their connections within
the broader field of topology are illustrated by articles about knots
and links in spatial graphs and symmetries of spatial graphs in
\(S^3\) and other 3-manifolds.
Graduate students and research mathematicians interested in knot theory.
William Browder served as President of the
American Mathematical Society during 1990–1991. This DVD
contains his Retiring Presidential Address—which combined short
remarks about his presidency with a mathematical lecture—preceded
by an informal interview in which he discusses a range of topics,
including public awareness of mathematics and his interest in
music.
The lecture discusses the action of finite groups on manifolds, exploring
the question of how large a finite group can effectively act on a
given manifold (here, “effectively” means that there is
no subgroup that fixes everything). A related question is, what kind
of spaces have the given manifold as a covering space? Beginning with
the historical roots of these questions, Browder concentrates on
familiar examples such as the sphere, the \(n\)-sphere, or a
product of spheres of different dimensions.
The lecture is accessible to mathematics majors with background in
algebraic topology. The interview segment provides a fine complement
to the lecture.
The reviewer recommends enthusiastically this … to the mathematical community, in particular those interested in algebraic topology and its applications to transformation groups.
-- Zentralblatt MATH<
The aim of this book is to introduce and develop an arithmetic
analogue of classical differential geometry. In this new geometry the
ring of integers plays the role of a ring of functions on an infinite
dimensional manifold. The role of coordinate functions on this
manifold is played by the prime numbers. The role of partial
derivatives of functions with respect to the coordinates is played by
the Fermat quotients of integers with respect to the primes. The role
of metrics is played by symmetric matrices with integer
coefficients. The role of connections (respectively curvature)
attached to metrics is played by certain adelic (respectively global)
objects attached to the corresponding matrices.
One of the main conclusions of the theory is that the spectrum of
the integers is “intrinsically curved”; the study of this
curvature is then the main task of the theory. The book follows, and
builds upon, a series of recent research papers. A significant part of
the material has never been published before.
Graduate students and researchers interested in algebraic geometry, number theory, and algebraic groups.
In the past 50 years, quantum physicists have discovered, and
experimentally demonstrated, a phenomenon which they termed
superoscillations. Aharonov and his collaborators showed that
superoscillations naturally arise when dealing with weak values, a
notion that provides a fundamentally different way to regard
measurements in quantum physics. From a mathematical point of view,
superoscillating functions are a superposition of small Fourier
components with a bounded Fourier spectrum, which result, when
appropriately summed, in a shift that can be arbitrarily large, and
well outside the spectrum.
The purpose of this work is twofold: on one hand the authors
provide a self-contained survey of the existing literature, in order
to offer a systematic mathematical approach to superoscillations; on
the other hand, they obtain some new and unexpected results, by
showing that superoscillating sequences can be seen of as solutions to
a large class of convolution equations and can therefore be treated
within the theory of analytically uniform spaces. In particular, the
authors will also discuss the persistence of the superoscillatory
behavior when superoscillating sequences are taken as initial values
of the Schrödinger equation and other equations.
The authors describe the (equivariant) intersection cohomology of certain moduli spaces (“framed Uhlenbeck spaces”) together with some structures on them (e.g.,the Poincaré pairing) in terms of representation theory of some vertex operator algebras (\(\mathcal{W}\)-algebras").
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.
Pushing Limits: From West Point to
Berkeley and Beyond challenges the myth that mathematicians lead
dull and ascetic lives. It recounts the unique odyssey of a noted
mathematician who overcame military hurdles at West Point, Army Ranger
School and the Vietnam War, and survived many civilian
escapades—hitchhiking in third-world hotspots, fending off
sharks in Bahamian reefs, and camping deep behind the forbidding Iron
Curtain. From ultra-conservative West Point in the ’60s to
ultra-radical Berkeley in the ’70s, and ultimately to genteel
Georgia Tech in the ’80s, this is the tale of an academic career
as noteworthy for its offbeat adventures as for its teaching and
research accomplishments. It brings to life the struggles and risks
underlying mathematical research, the unparalleled thrill of making
scientific breakthroughs, and the joy of sharing those discoveries
around the world. Hill's book is packed with energy, humor, and
suspense, both physical and intellectual. Anyone who is curious about
how one maverick mathematician thinks, who wants to relive the zanier
side of the ’60s and ’70s, who wants an armchair journey
into the third world, or who
seeks an unconventional view of several of society's iconic
institutions, will be drawn to this book.
Click here to Listen to
an interview with author Ted Hill.
General readers interested in mathematics careers and education, adventure travel, military life, the 1960s-70s, and how all this combines together; mathematics educators, students, and graduates, especially those of West Point, Stanford, and Berkeley.
... captivating memoir reveals an intriguing character who is part Renaissance Man, part Huckleberry Finn. Fast-paced and often hilarious ... provides some penetrating and impious insights into some of our more revered institutions.
-- Rick Atkinson, three-time Pulitzer Prize winner, author of The Long Gray Line
Ted Hill is unique in having both a very exciting internal mathematical life ... and an action-filled, adventurous, external life. ... his natural gift, very rare for mathematicians, of story-telling, [makes this] a page-turner.
-- Doron Zeilberger, Rutgers University, winner of MAA Ford Prize, AMS Steele Prize, and ICA Euler Medal
Thoughtful, funny, evocative, Ted Hill takes us through a life well-lived ... an intensely personal story that will appeal to every profession—and to every generation!
-- General Wesley Clark, former NATO Supreme Commander
Ted Hill is an original. Mathematician. Adventurer. Activist. His life has seen both his mind and body tested to extremes ... insightful, entertaining and —in a very good way—unlike any other book you will ever read by a mathematician.
-- Alex Bellos, author of Here's Looking at Euclid and The Grapes of Math
A fascinating journey from pure adventurism...through West Point and the Vietnam War to the highest intellectual accomplishments. At the center is a beautiful portrayal of the tedious, but highly rewarding road from graduate school to becoming a substantial research mathematician. A joy to read.
-- David Gilat, Professor Emeritus, School of Mathematical Sciences, Tel Aviv University
It is well known that math is boring and that mathematicians are dull individuals lacking both social skills and common sense. Wait a minute.Ted Hill might change your mind. His almost mathemagical life experiences are like a platter of petit fours: sample one and you'd want a second, then a third and soon you're addicted.
-- Christian Houdré , Professor of Mathematics, Georgia Institute of Technology
I loved the book. Extraordinary job of making scenes come alive...with great energy and really good dialog.
-- David Ignatius, Columnist and Associate Editor at The Washington Post, author of Body of Lies
Most people think that mathematics has nothing to do with daily life. These folks need to spend a few hours with Ted. He sees life through a mathematical lens and brings excitement and adventure to everything he comes in contact with.
-- Martin Jones, Professor of Mathematics, College of Charleston
Ted Hill's incredible life story shows that a mathematical life can be heroic.
-- Reuben Hersh, coauthor of The Mathematical Experience, winner of a National Book Award in Science
The first adjectives...when thinking about a mathematician...are likely to [be] words such as: eccentric, reclusive, nerd. Ted Hill amply demonstrates that, at least in his case, nothing could be further from the truth, as he offers us a glimpse of the fascinating world of an accomplished mathematician.
-- Mario Livio, author of The Golden Ratio and the upcoming Why?
Ted Hill's fascinating and raucous memoir...is proof that life in the exotic world of theoretical mathematics doesn't preclude and in fact benefits from passionate engagement with the real world.
-- Jack Miller, Physicist, Lawrence Berkeley National Laboratory
Ted Hill is the Indiana Jones of mathematics. A West Point graduate, [he] served in Vietnam, swam with sharks in the Caribbean, and has resolutely defied unreasoned authority. With this same love of adventure, he has confronted the sublime challenges of mathematics. Whether it's discovering intellectual treasures or careening down jungle trails, this real life Dr. Jones has done it all.
-- Michael Monticino, Professor of Mathematics and Special Assistant to the President, U. North Texas
Straddling the military and the mathematical worlds, Ted Hill's life is full of contradictions, daring exploits and accomplishments, and outright fun and adventure. A fascinating read...
-- John Allen Paulos, Professor of Mathematics at Temple University, author of Innumeracy and A Mathematician Reads the Newspaper
This [memoir]...will thrill and perplex the reader, by the seamless mixture of mind-adventure and body adventure, and for the unconventional academic path traveled by its author. Hill perpetually runs into trouble with authorities...[but] befriends mathematicians all over the world... With verve and nerve, Hill writes the story of...a life that touches on the highly exceptional, rich in friendship, thought, and humane warmth.
-- Mircea Pitici, Cornell University, Editor of Best Writing on Mathematics
Ted Hill has led an exciting life, and his vivid stories shed light on some remarkable times and places. Mathematicians will especially appreciate his chapters on graduate school and his early professional life; he brings our shared experiences to life in a way that only an outstanding writer can do.
-- Walter Stromquist, past Editor of Mathematics Magazine
Ted Hill paints vivid pictures of his life in the military and academia. From West Point and Vietnam to Berkeley and Georgia Tech, his trials and hair-raising adventures are highly entertaining and informative.
-- Bill Sudderth, Professor Emeritus of Statistics, U. of Minnesota
Ted Hill took a very unusual route to...mathematics: a military start and a stint in Vietnam, followed by a first-rate degree at one of the top programs in the world (Berkeley) and a highly successful career. This path, in addition to providing him with many adventures, has allowed him to look at thing(s) a little differently than most mathematicians...
-- Stan Wagon, Macalester College, winner of MAA Ford Prize, author of The Banach-Tarski Paradox