Contemporary Mathematics, Volume: 646
2015; 186 pp; softcover
ISBN-13: 978-1-4704-1556-3
Expected publication date is September 24, 2015.
The papers in this volume are mainly from the 2013 Midwest Geometry Conference, held October 19, 2013, at Oklahoma State University, Stillwater, OK, and partly from the 2012 Midwest Geometry Conference, held May 12-13, 2012, at the University of Oklahoma, Norman, OK.
The papers cover recent results on geometry and topology of submanifolds. On the topology side, topics include Plateau problems, Voevodsky's motivic cohomology, Reidemeister zeta function and systolic inequality, and freedom in 2- and 3-dimensional manifolds. On the geometry side, the authors discuss classifying isoparametric hypersurfaces and review Hartogs triangle, finite volume flows, nonexistence of stable p-currents, and a generalized Bernstein type problem. The authors also show that the interaction between topology and geometry is a key to deeply understanding topological invariants and the geometric problems.
Graduate students and research mathematicians interested in geometry and topology.
R. M. Hardt -- Plateau problems in metric spaces and related homology and cohomology theories
P. F. dos Santos, P. Lima-Filho, and R. M. Hardt -- Relating equivariant and motivic cohomology via analytic currents
W. Li -- Braids and symplectic Reidemeister zeta functions
L. Chen and W. Li -- Systoles of surfaces and 3-manifolds
Q.-S. Chi -- Ideal theory and classification of isoparametric hypersurfaces
M.-C. Shaw -- The Hartogs triangle in complex analysis
W. Hu -- Finite volume flows and Witten's deformation
R. Howard and W. Wei -- On the existence and nonexistence of stable submanifolds and currents in positively curved manifolds and the topology of submanifolds in Euclidean spaces
S. W. Wei, L. Wu, and Y. Zhang -- Remarks on stable minimal hypersurfaces in Riemannian manifolds and generalized Bernstein problems
Contemporary Mathematics, Volume: 647
2015; 137 pp; softcover
ISBN-13: 978-1-4704-0990-6
Expected publication date is September 24, 2015.
H
This volume contains the proceedings of a conference on Hodge Theory and Classical Algebraic Geometry, held May 13-15, 2013, at The Ohio State University, Columbus, OH.
Hodge theory is a powerful tool for the study and classification of algebraic varieties. This volume surveys recent progress in Hodge theory, its generalizations, and applications. The topics range from more classical aspects of Hodge theory to modern developments in compactifications of period domains, applications of Saito's theory of mixed Hodge modules, and connections with derived category theory and non-commutative motives.
Graduate students and research mathematicians interested in algebraic geometry, representation theory, and derived categories.
A. Bertram, S. Marcus, and J. Wang -- The stability manifolds of P1 and local P1
M. Green and P. Griffiths -- Reduced limit period mappings and orbits in Mumford-Tate varieties
E. Izadi and J. Wang -- The primitive cohomology of theta divisors
J. Kollar -- Neighborhoods of subvarieties in homogeneous spaces
M. Marcolli and G. Tabuada -- Unconditional noncommutative motivic Galois groups
Z. Ran -- Differential equations in Hilbert-Mumford calculus
C. Schnell -- Weak positivity via mixed Hodge modules
2015; 146 pp; softcover
ISBN-13: 978-1-4704-2552-4
Expected publication date is October 19, 2015.
This third edition is a lively and provocative tract on how to teach mathematics in today's new world of online learning tools and innovative teaching devices. The author guides the reader through the joys and pitfalls of interacting with modern undergraduates--telling you very explicitly what to do and what not to do. This third edition has been streamlined from the second edition, but still includes the nuts and bolts of good teaching, discussing material related to new developments in teaching methodology and technique, as well as adding an entire new chapter on online teaching methods.
Graduate students and researchers interested in improving their teaching of college mathematics.
Guiding principles
Practical matters
Spiritual matters
The electronic world
Difficult matters
A new beginning
Bibliography
Index
Student Mathematical Library, Volume: 77
2015; approx. 412 pp; softcover
ISBN-13: 978-1-4704-2320-9
Expected publication date is October 15, 2015.
This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra. This new edition provides many advancements, including more figures and exercises, and--as a new feature--a good number of solutions to selected exercises.
Undergraduate and graduate students interested in differential geometry.
Notations and prerequisites from analysis
Curves in Rn
The local theory of surfaces
The intrinsic geometry of surfaces
Riemannian manifolds
The curvature tensor
Spaces of constant curvature
Einstein spaces
Solutions to selected exercises
Bibliography
List of notation
Index
CBMS Regional Conference Series in Mathematics, Number: 123
2015; 82 pp; softcover
ISBN-13: 978-0-8218-4156-3
Expected publication date is October 12, 2015.
In every sufficiently large structure which has been partitioned there will always be some well-behaved structure in one of the parts. This takes many forms. For example, colorings of the integers by finitely many colors must have long monochromatic arithmetic progressions (van der Waerden's theorem); and colorings of the edges of large graphs must have monochromatic subgraphs of a specified type (Ramsey's theorem). This book explores many of the basic results and variations of this theory.
Since the first edition of this book there have been many advances in this field. In the second edition the authors update the exposition to reflect the current state of the art. They also include many pointers to modern results.
Graduate students and researchers interested in combinatorics, in particular, Ramsey theory.
Introduction
Three views of Ramsey theory
Ramsey's theorem
van der Waerden's theorem
The Hales-Jewett theorem
Szemeredi's theorem
Graph Ramsey theory
Euclidean Ramsey theory
A general Ramsey product theorem
The theorems of Schur, Folkman, and Hindman
Rado's theorem
Current trends
Bibliography
Mathematical Surveys and Monographs, Volume: 206
2015; 374 pp; hardcover
ISBN-13: 978-0-8218-4991-0
October 15, 2015.
Ricci flow is a powerful technique using a heat-type equation to deform Riemannian metrics on manifolds to better metrics in the search for geometric decompositions. With the fourth part of their volume on techniques and applications of the theory, the authors discuss long-time solutions of the Ricci flow and related topics.
In dimension 3, Perelman completed Hamilton's program to prove Thurston's geometrization conjecture. In higher dimensions the Ricci flow has remarkable properties, which indicates its usefulness to understand relations between the geometry and topology of manifolds. This book discusses recent developments on gradient Ricci solitons, which model the singularities developing under the Ricci flow. In the shrinking case there is a surprising rigidity which suggests the likelihood of a well-developed structure theory. A broader class of solutions is ancient solutions; the authors discuss the beautiful classification in dimension 2. In higher dimensions they consider both ancient and singular Type I solutions, which must have shrinking gradient Ricci soliton models. Next, Hamilton's theory of 3-dimensional nonsingular solutions is presented, following his original work. Historically, this theory initially connected the Ricci flow to the geometrization conjecture. From a dynamical point of view, one is interested in the stability of the Ricci flow. The authors discuss what is known about this basic problem. Finally, they consider the degenerate neckpinch singularity from both the numerical and theoretical perspectives.
This book makes advanced material accessible to researchers and graduate students who are interested in the Ricci flow and geometric evolution equations and who have a knowledge of the fundamentals of the Ricci flow.
Graduate students and researchers interested in geometric evolution equations.
Noncompact gradient Ricci solitons
Special ancient solutions
Compact 2-dimensional ancient solutions
Type I singularities and ancient solutions
Hyperbolic geometry and 3-manifolds
Nonsingular solutions on closed 3-manifolds
Noncompact hyperbolic limits
Constant mean curvature surfaces and harmonic maps by IFT
Stability of Ricci flow
Type II singularities and degenerate neckpinches
Implicit function theorem
Bibliography
Index