ISBN: 978-1-4704-3783-1
Series, Volume: Contemporary Mathematics, Volume 734
Published: 18 August 2019; Copyright Year: 2019;
Pages: 310; Softcover
Itemcode: CONM/734
Differential Equations
Graduate students and research mathematicians interested in partial differential
equations, fluid dynamics, mathematical physics, biological applications, and the history of
mathematics.
This is the second of two volumes dedicated to the centennial of the distinguished
mathematician Selim Grigorievich Krein. The companion volume is Contemporary
Mathematics, Volume 733.
Krein was a major contributor to functional analysis, operator theory, partial differential equations,
fluid dynamics, and other areas, and the author of several influential monographs in
these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran,
for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced
mathematical life in the former Soviet Union.
The articles contained in this volume are written by prominent mathematicians, former students
and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter
Schools. They are devoted to a variety of contemporary problems in ordinary and partial differential
equations, fluid dynamics, and various applications.
ISBN: 978-1-4704-5271-1
Series, Volume: University Lecture Series, Volume 72
Published: 12 September 2019; Copyright Year: 2019; Pages:
192; Softcover;
Itemcode: ULECT/72
Mathematical Physics
Supplementary Text
Graduate students and researchers interested in mathematical aspects of quantum
field theory.
This book originated from lecture notes for the course given by the author at the
University of Notre Dame in the fall of 2016. The aim of the book is to give an introduction
to the perturbative path integral for gauge theories (in particular, topological field theories) in
Batalin?Vilkovisky formalism and to some of its applications. The book is oriented toward a
graduate mathematical audience and does not require any prior physics background. To elucidate
the picture, the exposition is mostly focused on finite-dimensional models for gauge
systems and path integrals, while giving comments on what has to be amended in the infinitedimensional
case relevant to local field theory. Motivating examples discussed in the book
include Alexandrov?Kontsevich?Schwarz?Zaboronsky sigma models, the perturbative expansion
for Chern-Simons invariants of 3-manifolds given in terms of integrals over configurations
of points on the manifold, the BF (background field) theory on cellular decompositions
of manifolds, and Kontsevichfs deformation quantization formula.
A publication of the Societe Mathematique de France.
ISBN: 978-2-85629-900-5
Series, Volume: Asterisque, Number 408
Published: 15 April 2019; Copyright Year:2019;
Pages: 212; Softcover;
Itemcode: AST/408
Algebra and Algebraic Geometry
Readership: Graduate students and research mathematicians.
In this paper, the authors study the classical and quantum equivariant cohomology
of Nakajima quiver varieties for a general quiver Q . Using a geometric R -matrix formalism,
they construct a Hopf algebra YQ , the Yangian of Q , acting on the cohomology of these varieties,
and show several results about their basic structure theory. The authors prove a formula for
quantum multiplication by divisors in terms of this Yangian action. The quantum connection
can be identified with the trigonometric Casimir connection for YQ ; equivalently, the divisor
operators correspond to certain elements of Baxter subalgebras of YQ . A key role is played by
geometric shift operators which can be identified with the quantum KZ difference connection.
In the second part, the authors give an extended example of the general theory for moduli
spaces of sheaves on C2 , framed at infinity. Here, the Yangian action is analyzed explicitly in
terms of a free field realization; the corresponding R -matrix is closely related to the reflection
operator in Liouville field theory. The authors show that divisor operators generate the quantum
ring, which is identified with the full Baxter subalgebras. As a corollary of our construction,
the authors obtain an action of the W-algebra W (gl(r )) on the equivariant cohomology
of rank r moduli spaces, which implies certain conjectures of Alday, Gaiotto, and Tachikawa.
Information for our distributors: A publication of the Societe Mathematique 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. AMS individual members receive a 10% discount and
members of the SMF receive a 30% discount from list. No other discounts apply.
A publication of Mathematical Society of Japan.
ISBN: 978-4-86497-079-2
Series, Volume: Advanced Studies in Pure Mathematics, Volume 80
Published: 15 May 2019; Copyright Year: 2019;
Pages: 218; Hardcover;
Itemcode: ASPM/80
Analysis
Graduate students and researchers.
This volume contains the proccedings of an international conference on Operator
Algebras and Mathematical Physics, held at Tohoku University in August 2016. This meeting
was the 9th MSJ-Seasonal Institute of the Mathematical Society of Japan. Twenty-eight researchers
gave lectures on a wide range of topics on operator algebras and their applications to mathematical
physics. This volume contains one survey article and 11 research articles based on the
lectures given.
Information for our distributors: Published for the Mathematical Society of Japan by
Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. All commercial
channel discounts apply.
ISBN: 978-1-4704-5272-8
Series, Volume: Student Mathematical Library, Volume 89
Published: 25 September 2019; Copyright Year:
2019; Pages: approximately 195; Softcover;
Itemcode: STML/89
Logic and Foundations
Supplementary Text
Undergraduate and graduate students and researchers interested in learning basics of
mathematical logic.
The aim of this book is to present mathematical logic to students who are interested
in what this field is but have no intention of specializing in it. The point of view is to
treat logic on an equal footing to any other topic in the mathematical curriculum. The book
starts with a presentation of naive set theory, the theory of sets that mathematicians use on
a daily basis. Each subsequent chapter presents one of the main areas of mathematical logic:
first order logic and formal proofs, model theory, recursion theory, Godelfs incompleteness
theorem, and, finally, the axiomatic set theory. Each chapter includes several interesting highlights?
outside of logic when possible?either in the main text, or as exercises or appendices.
Exercises are an essential component of the book, and a good number of them are designed to
provide an opening to additional topics of interest.
A co-publication of the AMS and CBMS.
ISBN: 978-1-4704-5206-3
Series, Volume: CBMS Regional Conference Series in Mathematics,
Number 133
Published: 5 September 2019; Copyright Year: 2019;
Pages: 186; Softcover;
Itemcode: CBMS/133
Geometry and Topology
Mathematical Physics
Applied Mathematics
Graduate students and researchers interested in the interation between geometry,
topology (homotopy theory), and theoretical physics (quantum field theory and condensed
matter theory).
Description: These lectures recount an application of stable homotopy theory to a concrete problem
in low energy physics: the classification of special phases of matter. While the joint work
of the author and Michael Hopkins is a focal point, a general geometric frame of reference on
quantum field theory is emphasized.
Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael
Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry
point for mathematicians to delve into quantum field theory. Classification theorems in low
dimensions are proved to illustrate the framework. The later lectures turn to more specialized
topics in field theory, including the relationship between invertible field theories and stable
homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The
accompanying mathematical explanations touch upon (higher) category theory, duals to the
sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators.
The outcome of computations made using the Adams spectral sequence is presented and
compared to results in the condensed matter literature obtained by very different means. The
general perspectives and specific applications fuse into a compelling story at the interface of
contemporary mathematics and theoretical physics.