Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.

Mathematics. --- Number Theory. --- Algebraic Geometry. --- Several Complex Variables and Analytic Spaces. --- Geometry, algebraic. --- Differential equations, partial. --- Number theory. --- Mathématiques --- Théorie des nombres --- Calabi-Yau manifolds --- String models --- Mathematical physics --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Calabi-Yau manifolds. --- String models. --- Models, String --- String theory --- Algebraic geometry. --- Functions of complex variables. --- Nuclear reactions --- Manifolds (Mathematics) --- Partial differential equations --- Algebraic geometry --- Geometry --- Number study --- Numbers, Theory of --- Complex variables --- Elliptic functions --- Functions of real variables

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both the arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on  Arithmetic and Geometry of  K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16–25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the large variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with three days of introductory lectures. A selection of four of these lectures is included in this volume. These lectures can be used as a starting point for graduate students and other junior researchers, or as a guide to the subject.

Mathematics --- Number theory --- Algebraic geometry --- Differential geometry. Global analysis --- Geometry --- Mathematical physics --- landmeetkunde --- differentiaal geometrie --- wiskunde --- fysica --- getallenleer --- geometrie

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Several important aspects of moduli spaces and irreducible holomorphic symplectic manifolds were highlighted at the conference “Algebraic and Complex Geometry” held September 2012 in Hannover, Germany. These two subjects of recent ongoing progress belong to the most spectacular developments in Algebraic and Complex Geometry. Irreducible symplectic manifolds are of interest to algebraic and differential geometers alike, behaving similar to K3 surfaces and abelian varieties in certain ways, but being by far less well-understood. Moduli spaces, on the other hand, have been a rich source of open questions and discoveries for decades and still continue to be a hot topic in itself as well as with its interplay with neighbouring fields such as arithmetic geometry and string theory. Beyond the above focal topics this volume reflects the broad diversity of lectures at the conference and comprises 11 papers on current research from different areas of algebraic and complex geometry sorted in alphabetic order by the first author. It also includes a full list of speakers with all titles and abstracts.

Mathematics --- Algebraic geometry --- Geometry --- landmeetkunde --- wiskunde --- geometrie