A fascinating discussion of the quest to resolve one of the great unanswered problems of modern physics - how can general relativity and quantum mechanics be compatible
Presents the concept of Loop Quantum Gravity, showing how this explanation could be preferable to the much better-known String Theory
One of the first explanations of Loop Quantum Gravity for general readers
Draws on the pioneering work of Lee Smolin and Carlo Rovelli
Written by Jim Baggott, author of the highly successful Higgs (2013) and The Quantum Story (2013)
Today we are blessed with two extraordinarily successful theories of physics. The first is Albert Einstein's general theory of relativity, which describes the large-scale behaviour of matter in a curved spacetime. This theory is the basis for the standard model of big bang cosmology. The discovery of gravitational waves at the LIGO observatory in the US (and then Virgo, in Italy) is only the most recent of this theory's many triumphs.
First academic work of its kind that focuses on Charles L. Dogson's mathematical work, and incorporates contemporary research on his wide-ranging mathematical achievements
Contains a comprehensive bibliography of Dodgson's mathematical works
Includes a number of historial illustrations, some never before seen in print
Charles Lutwidge Dodgson is best known for his 'Alice' books, Alice's Adventures in Wonderland and Through the Looking-Glass, written under his pen name of Lewis Carroll. Yet, whilst lauded for his work in children's fiction and his pioneering work in the world of Victorian photography, his everyday job was a lecturer in Mathematics at Christ Church, Oxford University.
1: A Mathematical Life
2: Geometry
3: Algebra
4: Logic
5: Voting
6: Recreational Mathematics
7: Mathematical Legacy
8: Mathematical Bibliography
Annals of Mathematics Studies, vol.198
Hardcover 2019
ISBN 9780691181370
Paperback 2019
ISBN9780691181387
280 pp. 6 1/8 x 9 1/4 103 b/w illus.
forthcoming February 2019
Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. The Plaid Model, which is a self-contained sequel to Richard Schwartz’s Outer Billiards on Kites, provides a combinatorial model for orbits of outer billiards on kites.
Schwartz relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called “the plaid model,” has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics.
The book includes an extensive computer program that allows readers to explore the materials interactively and each theorem is accompanied by a computer demonstration.
Richard Evan Schwartz is the Chancellor’s Professor of Mathematics at Brown University. He is the author of Spherical CR Geometry and Dehn Surgery and Outer Billiards on Kites (both Princeton).
Annals of Mathematics Studies
Hardcover 2019
ISBN 9780691181820
Paperback 2019
ISBN 9780691191041
272 pp. 6 1/8 x 9 1/4 2 b/w illus.
forthcoming June 2019
This book presents the complete proof of the Bloch-Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of etale cohomology and its relation to motivic cohomology and Chow groups.
Although the proof relies on the work of several people, it is credited primarily to Vladimir Voevodsky. The authors draw on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky’s proof and introduce the key figures behind its development. They go on to describe the highly innovative geometric constructions of Markus Rost, including the construction of norm varieties, which play a crucial role in the proof. The book then addresses symmetric powers of motives and motivic cohomology operations.
Comprehensive and self-contained, The Norm Residue Theorem in Motivic Cohomology unites various components of the proof that until now were scattered across many sources of varying accessibility, often with differing hypotheses, definitions, and language.
Christian Haesemeyer is professor in the School of Mathematics and Statistics at the University of Melbourne. Charles A. Weibel is Distinguished Professor of Mathematics at Rutgers University. He is the author of An Introduction to Homological Algebra and The K-Book: An Introduction to Algebraic K-Theory and the coauthor of Lecture Notes on Motivic Cohomology.
Annals of Mathematics Studies, vol.201
Hardcover 2019
ISBN 9780691190709
ISBN
9780691190716
192 pp. 0 x 0
forthcoming August 2019
Paperback 2019 0
This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While originating in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity.
Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players, as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit.
This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.
Pierre Cardaliaguet is professor of mathematics at Paris Dauphine University. Francois Delarue is professor of mathematics at the University of Nice Sophia Antipolis. Jean-Michel Lasry is associate researcher of mathematics at Paris Dauphine University. Pierre-Louis Lions is professor of partial differential equations and their applications at the College de France.