Contemporary Mathematics, Volume: 652
2015; 242 pp; softcover
ISBN-13: 978-1-4704-1023-0
Expected publication date is December 30, 2015.
This volume contains the proceedings of the Workshop on Lie Algebras, in honor of Helmut Strade's 70th Birthday, held from May 22-24, 2013, at the Universita degli Studi di Milano-Bicocca, Milano, Italy.
Lie algebras are at the core of several areas of mathematics, such as, Lie groups, algebraic groups, quantum groups, representation theory, homogeneous spaces, integrable systems, and algebraic topology.
The first part of this volume combines research papers with survey papers by the invited speakers. The second part consists of several collections of problems on modular Lie algebras, their representations, and the conjugacy of their nilpotent elements as well as the Koszulity of (restricted) Lie algebras and Lie properties of group algebras or restricted universal enveloping algebras.
Graduate students and research mathematicians interested in Lie theory, quantum groups, and representation theory.
M. Avitabile and S. Mattarei -- Grading switching for modular non-associative algebras
Y. Bahturin, M. Kochetov, and J. McGraw -- Gradings by groups on Cartan type Lie algebras
A. Baranov -- Simple locally finite Lie algebras of diagonal type
A. Elduque -- Okubo algebras: Automorphisms, derivations and idempotents
P. Faccin and W. A. de Graaf -- Constructing semisimple subalgebras of real semisimple Lie algebras
L. Hille -- Tilting modules over the path algebra of type A, polytopes, and Catalan numbers
G. T. Lee, S. K. Sehgal, and E. Spinelli -- Lie identities on skew elements in group algebras
A. Premet -- Regular derivations of truncated polynomial rings
S. Siciliano and H. Usefi -- Lie properties of restricted enveloping algebras
S. Skryabin -- Generic semisimplicity of reduced enveloping algebras
Z. Tong, N. Hu, and X. Wang -- Modular quantizations of Lie algebras of Cartan type H via Drinfeld twists
G. Benkart and J. Feldvoss -- Some problems in the representation theory of simple modular Lie algebras
W. A. De Graaf -- Conjugacy of nilpotent elements in characteristic p
G. T. Lee, S. K. Sehgal, and E. Spinelli -- Problems on Lie properties of skew and symmetric elements of group rings
S. Siciliano and H. Usefi -- Some problems in Lie properties of restricted enveloping algebras
S. Skryabin -- Open questions on modular Lie algebras
T. Weigel -- Koszul Lie algebras
2016; 386 pp; hardcover
ISBN-13: 978-1-4704-2535-7
Expected publication date is January 16, 2016.
This book is an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas. Though the book can be read and enjoyed by nonmathematicians, college students, or even eager high school students, it is intended to be used as an undergraduate textbook.
The book is divided into three parts corresponding to the three areas referred to in the title. Part 1 develops techniques that enable two- and three-dimensional creatures to visualize possible shapes for their universe and to use topological and geometric properties to distinguish one such space from another. Part 2 is an introduction to knot theory with an emphasis on invariants. Part 3 presents applications of topology and geometry to molecular symmetries, DNA, and proteins. Each chapter ends with exercises that allow for better understanding of the material.
The style of the book is informal and lively. Though all of the definitions and theorems are explicitly stated, they are given in an intuitive rather than a rigorous form, with several hundreds of figures illustrating the exposition. This allows students to develop intuition about topology and geometry without getting bogged down in technical details.
Undergraduate students and instructors interested in elementary topology.
Universes
An introduction to the shape of the universe
Visualizing four dimensions
Geometry and topology of different universes
Orientability
Flat manifolds
Connected sums of spaces
Products of spaces
Geometries of surfaces
Knots
Introduction to knot theory
Invariants of knots and links
Knot polynomials
Molecules
Mirror image symmetry from different viewpoints
Techniques to prove topological chirality
The topology and geometry of DNA
The topology of proteins
Index
Contemporary Mathematics, Volume: 653
2015; 313 pp; softcover
ISBN-13: 978-1-4704-1653-9
Expected publication date is January 7, 2016.
This volume contains the proceedings of the Sixth International Conference on Complex Analysis and Dynamical Systems, held from May 19-24, 2013, in Nahariya, Israel, in honor of David Shoikhet's sixtieth birthday.
The papers in this volume range over a wide variety of topics in Partial Differential Equations, Differential Geometry, and the Radon Transform. Taken together, the articles collected here provide the reader with a panorama of activity in partial differential equations and general relativity, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis.
The companion volume (Contemporary Mathematics, Volume 667) is devoted to complex analysis, quasiconformal mappings, and complex dynamics.
Graduate students and research mathematicians interested in PDEs, differential geometry, and radon transform.
G. Ambartsoumian and V. P. Krishnan -- Inversion of a class of circular and elliptical radon transforms
J. Bara?ska and Y. Kozitsky -- Free jump dynamics in continuum
J. Ben-Artzi -- Instabilities in kinetic theory and their relationship to the ergodic theorem
N. Bez and M. Sugimoto -- Some recent progress on sharp Kato-type smoothing estimates
C. Cederbaum -- Uniqueness of photon spheres in static vacuum asymptotically flat spacetimes
N. Charalambous and Z. Lu -- The L1 Liouville property on weighted manifolds
M. Cicognani and M. Reissig -- Some remarks on Gevrey well-posedness for degenerate Schrodinger equations
M. D'Abbicco -- Asymptotics for damped evolution operators with mass-like terms
E. Dyachenko and N. Tarkhanov -- Singular perturbations of elliptic operators
A. V. Faminskii -- An initial-boundary value problem in a strip for two-dimensional equations of Zakharov-Kuznetsov type
Y.-L. Fang and D. Vassiliev -- Analysis of first order systems of partial differential equations
P. Harjulehto and R. Hurri-Syrjanen -- An embedding into an Orlicz space for L11-functions from irregular domains
M. K. Mezadek and M. Reissig -- Qualitative properties of solutions to structurally damped ƒÐ-evolution models with time decreasing coefficient in the dissipation
M. Khuri, G. Weinstein, and S. Yamada -- The Riemannian Penrose inequality with charge for multiple black holes
G. Kresin and V, Maz'ya -- Criteria for invariance of convex sets for linear parabolic systems
J. ?awrynowicz, A. Niemczynowicz, M. Nowak-Kepczyk, and L. M. Tovar Sanchez -- On an extension of harmonicity and holomorphy
S. Lucente -- Large data solutions for critical semilinear weakly hyperbolic equations
V. Rabinovich -- The Fredholm property and essential spectra of pseudodifferential operators on non-compact manifolds and limit operators
B. Rubin -- Overdetermined transforms in integral geometry
Part of London Mathematical Society Student Texts
Not yet published - available from April 2016
format: Hardback
isbn: 9781107125407
format: Paperback
isbn: 9781107564800
elestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.
Preface
1. The central force problem
2. Conic sections
3. The Kepler problem
4. The dynamics of the Kepler problem
5. The two-body problem
6. The n-body problem
7. The three-body problem
8. The differential geometry of the Kepler problem
9. Hamiltonian mechanics
10. The topology of the Kepler problem
Bibliography
Index.
Part of London Mathematical Society Student Texts
Not yet published - available from June 2016
format: Hardback
isbn: 9781107136571
format: Paperback
i sbn: 9781316501917
The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through self-study, covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.
Editors' introduction
Part I. Long Paths and Hamiltonicity in Random Graphs:
1. Introduction
2. Tools
3. Long paths in random graphs
4. The appearance of Hamilton cycles in random graphs
References for Part I
Part II. Random Graphs from Restricted Classes:
1. Introduction
2. Random trees
3. Random graphs from block-stable classes
References for Part II
Part III. Lectures on Random Geometric Graphs:
1. Introduction
2. Edge counts
3. Edge counts: normal approximation
4. The maximum degree
5. A sufficient condition for connectivity
6. Connectivity and Hamiltonicity
7. Solutions to exercises
References for Part III
Part IV. On Random Graphs from a Minor-closed Class:
1. Introduction
2. Properties of graph classes
3. Bridge-addability, being connected and the fragment
4 Growth constants
5. Unlabelled graphs
6. Smoothness
7. Concluding remarks
References for Part IV
Index.