Oberwolfach Reports (OWR)
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Browsing Oberwolfach Reports (OWR) by Author "Batyrev, Victor"
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- ItemConvex and Algebraic Geometry(Zürich : EMS Publ. House, 2006) Batyrev, Victor; Teissier, BernardThe subjects of convex and algebraic geometry meet primarily in the theory of toric varieties. Toric geometry is the part of algebraic geometry where all maps are given by monomials in suitable coordinates, and all equations are binomial. The combinatorics of the exponents of monomials and binomials is sufficient to embed the geometry of lattice polytopes in algebraic geometry. Recent developments in toric geometry that were discussed during the workshop include applications to mirror symmetry, motivic integration and hypergeometric systems of PDE’s, as well as deformations of (unions of) toric varieties and relations to tropical geometry.
- ItemToric Geometry(Zürich : EMS Publ. House, 2009) Batyrev, Victor; Karshon, YaelToric Geometry originated from investigations of torus actions on geometric and algebraic objects. It is addressed through algebraic geometry, symplectic geometry, equivariant topology, as well as the theory of convex polyhedra within discrete mathematics. In spite of using their own language these completely different disciplines often observe similar or even identical combinatorial phenomena. Thus toric geometry leads to a fascinating and fruitful interplay between these disciplines.
- ItemToric Geometry(Zürich : EMS Publ. House, 2012) Batyrev, Victor; Karshon, YaelToric Geometry plays a major role where a wide variety of mathematical fields intersect, such as algebraic and symplectic geometry, algebraic groups, and combinatorics. The main feature of this workshop was to bring people from these area together to learn about mutual, possibly up till now unnoticed similarities in their respective research.