This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.

The Tom & Charlotte Mittler Collection

Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.

Packed with advice, tips, how-tos, and patterns for DIY crafts or crafting with kids, Craft Wisdom & Know-Howis a must-have home reference for both aspiring and experienced crafters alike. Covering dozens of the most popular projects in one complete, all-encompassing guide, this book is organized by type of craft, and also illustrated with line drawings and photos throughout. There is invaluable information about numerous crafting topics, including: Sewing Knitting and Other Needlework Paper Crafts and Bookmaking Glasswork Jewelry Making Pottery and Clay Mosaics Candle-making and Decorating Woodworking and Furniture Making, plus so much more. Each chapter covers a specific craft, with step-by-step directions and projects for crafters of all levels, from beginner to advanced. Hundreds of projects are included, such as Super Sock Monkeys, Crocheted Hats, Etched Glass, One-Afternoon Skirts, and Beading Vintage-Style Jewelry, among so many more. This book is also a part of the Know-How series which includes other titles such as: Country Wisdom & Know-How Woodworking Wisdom & Know-How Garden Wisdom & Know-How Natural Healing Wisdom & Know-How

Apply a variety of techniques to more than 20 mosaic projects.

This beautifully illustrated book represents the first full publication of the most elaborate metal vessel from the ancient world yet discovered. Found in an undisturbed Macedonian tomb of the late 4th century B.C., the volute krater is a tour de force of highly sophisticated methods of bronze working. An unusual program of iconography informs every area of the vessel. Snakes with copper and silver inlaid stripes frame the rising handles, wrapping their bodies around masks of underworld deities. On the shoulder sit four cast bronze figures: on one side a youthful Dionysos with an exhausted maenad, on the other a sleeping Silenos and a maenad handling a snake. In the major repousse frieze on the body a bearded hunter is associated with Dionysian figures. What was the function of this extraordinary object? And what is the meaning of the intricate iconography? The krater is placed in its Macedonian archaeological context as an heirloom of the descendants of the man named in the Thessalian inscription on its rim, and in its art-historical context as a highly elaborated, early-4th-century version of a metal type known in Athens by about 470 B.C.

If crafts are big, then clay is colossal. From pins and pendants to bracelets, buttons, and embellishments, crafters of all ages are embracing the creativity that polymer clay inspires. The Complete Book of Polymer Clay is an encyclopedic book by renowned expert Lisa Pavelka includes the latest techniques, handy tips, and trade secrets. Pavelka presents a sweeping overview of materials, how-to fundamentals, and construction techniques. She also introduces six original projects with complete instructions showing readers how to make pendants, curio boxes, a necklace, and a bracelet. Clear, concise, and comprehensive, this is an essential addition to any crafter's library, no matter his or her skill level. For even more inspiration, this indispensable reference features a gallery of 50 original projects by Pavelka and other talented polymer clay designers.