Softcover ISBN: 978-1-4704-7117-0
Product Code: PSPUM/108
Expected availability date: August 21, 2024
Proceedings of Symposia in Pure Mathematics Volume: 108; 2024; 523 pp
MSC: Primary 17; 18; 20
This book is the third Proceedings of the Southeastern Lie Theory Workshop Series covering years 2015?21.
During this time five workshops on different aspects of Lie theory were held at North Carolina State University in
October 2015; University of Virginia in May 2016; University of Georgia in June 2018; Louisiana State University
in May 2019; and College of Charleston in October 2021.
Some of the articles by experts in the field describe recent developments while others include new results in
categorical, combinatorial, and geometric representation theory of algebraic groups, Lie (super) algebras,
and quantum groups, as well as on some related topics.
The survey articles will be beneficial to junior researchers. This book will be useful to any researcher working i
n Lie theory and related areas.
Graduate students and researchers interested in algebraic groups, Lie (super)algebras, quantum groups, and related areas.
Jonathan D. Axtell and Kyu-Hwan Lee ? Quantum generalized Kac?Moody algebras via Hall algebras of complexes
Christopher P. Bendel ? Cohomology of algebraic groups, Lie algebras, and finite groups of Lie type
Jon F. Carlson ? Idempotent modules, locus of compactness and local supports
Tsao-Hsien Chen and David Nadler ? Real and symmetric quasi-maps
Christopher M. Drupieski and Jonathan R. Kujawa ? Support varieties for Lie superalgebras in characteristic 2
Jie Du, Haixia Gu and Zhongguo Zhou ? Canonical bases for the modified quantum glm|n
Jie Du, Brian Parshall and Leonard Scott ? An exact category approach to Hecke endomorphism algebras
Vyacheslav Futorny, Dimitar Grantcharov, Luis Enrique Ramirez and Pablo Zadunaisky ? On two constructions
of Gelfand-Tsetlin modules with arbitrary characters
Jiuzu Hong and Shrawan Kumar ? Lie algebra cohomology of the positive part of twisted affine Lie algebras
Zongzhu Lin and Daniel K. Nakano ? Realizing rings of regular functions via the cohomology of quantum groups
Ming Lu and Weiqiang Wang ? ?
Hall algebras and ?
quantum groups
G. Lusztig ? Unipotent blocks and weighted affine Weyl groups
George Lusztig and Zhiwei Yun ? From conjugacy classes in the Weyl group to representations
Toshiki Nakashima ? Geometric crystal on unipotent variety
Daniel Orr and Mark Shimozono ? Difference operators for wreath Macdonald polynomials
Felipe Albino dos Santos, Vyacheslav Futorny and Kaiming Zhao ? Universal central extensions of
Krichever-Novikov algebras and orthogonal polynomials
Peter Tingley ? Notes on Fock space
Softcover ISBN: 978-1-4704-7142-2
Product Code: CONM/802
Expected availability date: August 14, 2024
Contemporary Mathematics, Volume: 802; 2024; 323 pp
MSC: Primary 18; 55; 81; Secondary 16; 32; 57
This volume contains the proceedings of the AMS Special Session on Higher Structures in Topology,
Geometry, and Physics, held virtually on March 26?27, 2022.
The articles give a snapshot survey of the current topics surrounding the mathematical formulation of field theories.
There is an intricate interplay between geometry, topology, and algebra which captures these theories.
The hallmark are higher structures, which one can consider as the secondary algebraic or geometric background
on which the theories are formulated. The higher structures considered in the volume are generalizations of operads,
models for conformal field theories, string topology, open/closed field theories, BF/BV formalism, actions on
Hochschild complexes and related complexes, and their geometric and topological aspects.
Graduate students and research mathematicians interested in algebraic and topological aspects of quantum field theory.
Boris Tsygan ? On noncommutative differential forms
Manuel Rivera ? An algebraic model for the free loop space
Yang Mo ? The structure of simply colored coalgebras
Ivan Contreras, Adele Long, Sophia Marx and Rajan Amit Mehta ? On examples and classification of Frobenius objects in Rel
Benjamin C. Ward ? Stirling decomposition of graph homology in genus 1
Ralph M. Kaufmann and Javier Zuniga ? A combinatorial model for the moduli of bordered Riemann surfaces and a compactification
Michael Monaco ? Calculations for plus constructions
Philip Hackney ? Segal conditions for generalized operads
Daniel A. Ramras ? The topological Atiyah?Segal map
Arun Debray ? Bordism for the 2-group symmetries of the heterotic and CHL strings
Emil Hossjer, Philippe Mathieu and Frank Thuillier ? Generalized Abelian Turaev?Viro and U(1)
BF theories
Softcover ISBN: 978-1-4704-7296-2
Product Code: CONM/803
Expected availability date: August 14, 2024
Contemporary Mathematics, Volume: 803; 2024
MSC: Primary 14; 53; 58
This volume contains the proceedings of the VBAC 2022 Conference on Moduli Spaces and Vector
Bundles?New Trends, held in honor of Peter Newstead's 80th birthday, from July 25?29, 2022, at
the University of Warwick, Coventry, United Kingdom.
The papers focus on the theory of stability conditions in derived categories, non-reductive geometric invariant theory,
Brill-Noether theory, and Higgs bundles and character varieties. The volume includes both survey and original research
articles. Most articles contain substantial background and will be helpful to both novices and experts.
Graduate students and research mathematicians interested in Moduli Spaces in algebraic geometry and other areas
of mathematics.
Usha N. Bhosle ? Poincare and Picard bundles on the moduli spaces of bundles on curves
Indranil Biswas, Carlos Florentino, and Azizeh Nozad ? Topology of the moduli spaces of Higgs bundles over abelian varieties
Steven Bradlow ? Global properties of Higgs bundle moduli spaces
L. Brambila-Paz and R. Rios-Sierra ? Moduli of unstable bundles of HN-length two with fixed algebra of endomorphisms
Izzet Coskun, Jack Huizenga, and Howard Nuer ? The Brill-Noether theory of the moduli spaces of sheaves on surfaces
Simona DfEvangelista and Margherita Lelli-Chiesa ? Double covers of curves on Nikulin surfaces
Emilio Franco ? OfGrady spaces and symplectic resolution of moduli spaces of Higgs bundles
Oscar Garcia-Prada ? Vinberg pairs and Higgs bundles
Tomas L. Gomez, Andres Fernandez Herrero, and Alfonso Zamora ? A guide to moduli theory beyond GIT
Angel Gonzalez-Prieto, Marina Logares, Javier Martinez, and Vicente Munoz ? Stratification of SU(r
)-character varieties of twisted Hopf links
George H. Hitching ? Secant loci of scrolls over curves
Victoria Hoskins ? Moduli spaces and geometric invariant theory: Old and new perspectives
Softcover ISBN: 978-1-4704-7490-4
Expected availability date: September 08, 2024
2024; 126 pp
The Whatfs Happening in the Mathematical Sciences series presents a selection of recent discoveries and exciting
fields of research in mathematics, explained in depth but in a slow-paced, reader-friendly way.
In the first few months of 2023, artificial gbrainsh like ChatGPT and GPT-4 were constantly in the news, and they
have already turned into big business. One chapter in this book, gDeep Learning: Part Math, Part Alchemyh,
explains how math disentangles hype from reality and explains some of the remarkable advances of machine learning.
Meanwhile, gOrganizing the Chaos Inside the Brainh explores animal brains, and describes how biologists can apply
chaos theory to simulate the wanderings of a fly from firing data on neurons within its brain.
This issue of What's Happening also includes many treats for readers who like pure math?especially those who are
interested in geometry. In recent months and years, there have been unexpected discoveries in tiling
(gOne Stone to Rule Them Allh), sphere-packing in more than three dimensions (gA Fascination of Spheresh) and
the reconstruction of three-dimensional scenes from two-dimensional images (gMulti-View Geometry: E Pluribus Unumh).
The chapter gHow to Draw an Alternate Universeh will, as promised, open a door to a completely different, non-Euclidean
universe?or several of them. Shakespearefs words, gsomething rich and strangeh, only begin to describe them.
In gHow Mathematicians Unearthed the Stubborn Secrets of Fano Varietiesh, readers will learn about one of the building
blocks of algebraic geometry, the branch of geometry that deals with surfaces defined by polynomial equations.
The chapter gMissing One Digith addresses a seemingly elementary problem in number theory: how many prime numbers
do not have a g7h in them? The answer is easy to guess?but hard to prove. gFluid Flow: Two Paths to a Singularityh
discusses another guess that is hard to prove: can fluids in an enclosed region develop gsingularitiesh akin to a breaking
wave? Computer evidence is mounting that they can?including some evidence from machine learning algorithms.
(Which brings us full circle back to the gDeep Learningh chapter.)
Dana Mackenzie has written for the What's Happening series since Volume 6, published in 2006. In this volume
he is joined by Leila Sloman, whose name will be familiar to many readers from her work for Quanta Magazine.
Anyone interested in cutting-edge advancements in mathematics.
Hardcover ISBN: 978-1-4704-7557-4
Expected availability date: September 22, 2024
Graduate Studies in Mathematics, Volume: 243; 2024; 204 pp
MSC: Primary 81; 68; 94; 20
This book presents the basics of quantum computing and quantum information theory. It emphasizes the mathematical
aspects and the historical continuity of both algorithms and information theory when passing from classical to quantum
settings.
The book begins with several classical algorithms relevant for quantum computing and of interest in their own right.
The postulates of quantum mechanics are then presented as a generalization of classical probability. Complete,
rigorous, and self-contained treatments of the algorithms of Shor, Simon, and Grover are given.
Passing to quantum information theory, the author presents it as a straightforward adaptation of Shannon's
foundations to information theory. Both Shannon's theory and its adaptation to the quantum setting are explained
in detail. The book concludes with a chapter on the use of representation theory in quantum information theory.
It shows how all known entropy inequalities, including the celebrated strong subadditivity of von Neumann entropy,
may be obtained from a representation theory perspective.
With many exercises in each chapter, the book is designed to be used as a textbook for a course in quantum
computing and quantum information theory. Prerequisites are elementary undergraduate probability and undergraduate
algebra, both linear and abstract. No prior knowledge of quantum mechanics or information theory is required.
Graduate students and research mathematicians interested in the mathematical aspects of quantum computing.
Classical and probabilistic computation
Quantum mechanics for quantum computation
Algorithms
Classical information theory
Language and background material for quantum information theory
Quantum information
Representation theory and quantum information
Algebra and linear algebra
Probability
Hints and answers to selected exercises
Bibliography
Index
Handbook of Nulmerical Analysis Volume 25 -
July 19, 2024
Hardback ISBN: 9780443239847
Numerical Analysis Meets Machine Learning series, highlights new advances in the field, with this new volume
presenting interesting chapters. Each chapter is written by an international board of authors.
Optimal Introduction
Methods and feedback
Techniques
Practical approach and laws