This book collects together original research and survey articles highlighting the fertile interdisciplinary applications of convex lattice polytopes in modern mathematics. Covering a diverse range of topics, including algebraic geometry, mirror symmetry, symplectic geometry, discrete geometry, and algebraic combinatorics, the common theme is the study of lattice polytopes. These fascinating combinatorial objects are a cornerstone of toric geometry and continue to find rich and unforeseen applications throughout mathematics. The workshop Interactions with Lattice Polytopes assembled many top researchers at the Otto-von-Guericke-Universität Magdeburg in 2017 to discuss the role of lattice polytopes in their work, and many of their presented results are collected in this book. Intended to be accessible, these articles are suitable for researchers and graduate students interested in learning about some of the wide-ranging interactions of lattice polytopes in pure mathematics.

This book examines interactions of polyhedral discrete geometry and algebra. What makes this book unique is the presentation of several central results in all three areas of the exposition - from discrete geometry, to commutative algebra, and K-theory.

This volume contains the proceedings of the conference on Interactions of Classical and Numerical Algebraic Geometry, held May 22-24, 2008, at the University of Notre Dame, in honor of the achievements of Professor Andrew J. Sommese. While classical algebraic geometry has been studied for hundreds of years, numerical algebraic geometry has only recently been developed. Due in large part to the work of Andrew Sommese and his collaborators, the intersection of these two fields is now ripe for rapid advancement. The primary goal of both the conference and this volume is to foster the interaction between researchers interested in classical algebraic geometry and those interested in numerical methods. The topics in this book include (but are not limited to) various new results in complex algebraic geometry, a primer on Seshadri constants, analyses and presentations of existing and novel numerical homotopy methods for solving polynomial systems, a numerical method for computing the dimensions of the cohomology of twists of ideal sheaves, and the application of algebraic methods in kinematics and phylogenetics.

This memorial volume on the work of Wolfgang Kummer brings together articles devoted to the history of high energy physics with detailed coverage on the scientific concepts and scientific institutions, in particular CERN OCo and the underlying physics involved. Covering recent advances and developments as well as giving a reminiscent overview in two rapidly evolving fields of high energy/particle physics, and gravitational physics, the commemorative volume contains more than 20 original invited paper contributions OCo which will appear for the first time in print OCo from eminent and renowned physicists who interacted and collaborated with Wolfgang Kummer, including Physics Nobel Laureate Jack Steinberger. Wolfgang Kummer was president of the CERN council from 1985 to 1987, among his numerous eminent academic and administrative positions which he held during his illustrious career. This volume also aims to demonstrate and highlight Wolfgang Kummer''s significant contribution to the foundational work in gauge field theory, particle physics, and quantum gravity, and the tremendous impact leading to cutting-edge findings and advances at LHC. Sample Chapter(s). Foreword (155 KB). Chapter 1: Noncovariant Gauges at Zero and Nonzero Temperature (215 KB). Contents: Gauge Field Theory and Particle Physics: Noncovariant Gauges at Zero and Nonzero Temperature (P V Landshoff); Non-Relativistic Bound States: The Long Way Back from the BetheOCoSalpeter to the SchrAdinger Equation (A Vairo); Distended/Diminished Topologically Massive Electrodynamics (S Deser); Dynamical Spin (P G O Freund); Quantum Corrections to Solitons and BPS Saturation (A Rebhan et al.); Gauging Noncommutative Theories (H Grosse & M Wohlgenannt); Topological Phases and Contextuality Effects in Neutron Quantum Optics (H Rauch); First Class Constrained Systems and Twisting of Courant Algebroids by a Closed 4-Form (M Hansen & T Strobl); Some Local and Global Aspects of the Gauge Fixing in YangOCoMills-Theories (D N Blaschke et al.); Frozen Ghosts in Thermal Gauge Field Theory (P V Landshoff & A Rebhan); Classical and Quantum Gravity: Wolfgang Kummer and the Vienna School of Dilaton (Super-)Gravity (L Bergamin & R Meyer); Order and Chaos in Two Dimensional Gravity (R B Mann); 2-D Midisuperspace Models for Quantum Black Holes (J Gegenberg & G Kunstatter); Global Solutions in Gravity. Euclidean Signature (M O Katanaev); Thoughts on the Cosmological Principle (D J Schwarz); When Time Emerges (C Faustmann et al.); Towards Noncommutative Gravity (D V Vassilevich); Superembedding Approach to Superstring in AdS 5 X S 5 Superspace (I A Bandos); Heterotic (0,2) Gepner Models and Related Geometries (M Kreuzer); Canonical Analysis of Cosmological Topologically Massive Gravity at the Chiral Point (D Grumiller et al.); Wolfgang Kummer and the Physics Community: Wolfgang Kummer at CERN (H Schopper); Wolfgang Kummer and the Little Lost Lane Boy (K Lane); Mitigation of Fossil Fuel Consumption and Global Warming by Thermal Solar Electric Power Production in the World''s Deserts (J Steinberger); (My) Life with Wolfgang Kummer (M Schweda); Schubert in Stony Brook and Kinks in Vienna (P van Nieuwenhuizen). Readership: Scientists, researchers, graduates and undergraduates interested in high energy, particle or gravitational physics."

This volume consists of research papers and expository survey articles presented by the invited speakers of the Summer Workshop on Lattice Polytopes. Topics include enumerative, algebraic and geometric combinatorics on lattice polytopes, topological combinatorics, commutative algebra and toric varieties.Readers will find that this volume showcases current trends on lattice polytopes and stimulates further developments of many research areas surrounding this field. With the survey articles, research papers and open problems, this volume provides its fundamental materials for graduate students to learn and researchers to find exciting activities and avenues for further exploration on lattice polytopes.

The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the “Némethi60: Geometry and Topology of Singularities” conference held at the Alfréd Rényi Institute of Mathematics in Budapest, from May 27 to 31, 2019. Both the conference and this resulting volume are in honor of Professor András Némethi, on the occasion of his 60th birthday, whose work plays a decisive and influential role in the interactions between the above fields. The book should serve as a valuable resource for graduate students and researchers to deepen the new perspectives, methods, and connections between geometry and topology regarding singularities.

While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory Thorough revisions of all remaining chapters Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software Two indices: An Index of Defined Terms and an Index of Cited Authors Greatly expanded bibliographies

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.

Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs