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

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.

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.

A compelling exploration of the convergence of Jane Austen’sliterary themes and characters with David Hume’s views onmorality and human nature. Argues that the normative perspectives endorsed in JaneAusten's novels are best characterized in terms of a Humeanapproach, and that the merits of Hume's account of ethical,aesthetic and epistemic virtue are vividly illustrated by Austen'swriting. Illustrates how Hume and Austen complement one another, eachproviding a lens that allows us to expand and elaborate on theideas of the other Proposes that literature may serve as a thought experiment,articulating hypothetical cases which allow the reader to test hermoral intuitions Contributes to ongoing debates on the philosophy of literature,ethics, and emotion

Autobiographical poetry from one of Kentucky’s rising Affrilachian literary stars. Bernard Clay’s autobiographical poetry debut, English Lit, juxtaposes the roots of Black male identity against an urban and rural Kentucky landscape. Hailed as one of the most authentic voices of his generation, Clay artfully renders coming-of-age in the predominately Black West End of Louisville, Kentucky. Balancing the spirited grit of a farmer and the careful lyricism of a poet, English Lit is a triumph of new Affrilachian—African American and Appalachian—literature.