![]() Furthermore, the 2-Fano condition has been studied for smooth toric varieties in. Currently, all known examples have Picard number one, and can be described as zero loci of sections of certain vector bundles. Some effort has been put into understanding the structure of 2-Fano varieties. Conjecturally, 2-Fano manifolds have rational polyhedral cones of effective 2-cycles, and two-dimensional families of 2-Fano manifolds admit sections (provided there is no Brauer-Manin obstruction). De Jong and Starr introduced 2-Fano manifolds in, as manifolds with both first and second Chern character positive. This condition has far reaching implications for example, the cone of effective 1-cycles is rational polyhedral, and one-dimensional families of such manifolds admit sections. ![]() Fano manifolds are manifolds whose first Chern class intersects all curves positively. The project will be centered around investigating the structure of higher Fano manifolds. Leadership: Carolina Araujo, (IMPA), Roya Beheshti (Washington University) & Ana-Maria Castravet (University of Versailles, France) They should also address their familiarity with the suggested prerequisites. In their personal statements, applicants should rank in order their top three choices of projects. Several of the proposed projects extensively involve experimentation and computation, which will increase the likelihood that concrete progress is made over the course of five days and provide useful training in computational mathematics. The groups will work on open-ended projects in diverse areas of current interest, including moduli spaces and combinatorics, degenerations, and birational geometry. Successful applicants will be assigned to a group based on their research interests. This workshop capitalizes on momentum from a series of recent events for women in algebraic geometry, starting in 2015 with the IAS Program for Women in Mathematics on algebraic geometry. ![]() The goals of this workshop are: to advance the frontiers of modern algebraic geometry, including through explicit computations and experimentation, and to strengthen the community of women and non-binary mathematicians working in algebraic geometry. Bruce Reznick, Combinatorial methods in algebra, analysis, number theory, combinatorics, geometry.The Women in Algebraic Geometry Collaborative Research Workshop will bring together researchers in algebraic geometry to work in groups of 4-6, each led by one or two senior mathematicians.James Pascaleff, Symplectic topology and mirror symmetry.Rob Leigh (Department of Physics), String theory, non-commutative geometry.Rinat Kedem, Mathematical physics, representation theory of infinite dimensional Lie algebras, quantum groups, and vertex algebras, integrable models statistical mechanics and quantum field theory.Maarten Bergvelt, Representation theory of infinite dimensional Lie algebras, algebraic geometry, super geometry.John D'Angelo, Several complex variables and complex geometry.Mao Li, Higgs bundles, D modules and geometric Langlands conjecture.Aron Heleodoro, Algebraic Geometry, Geometric Representation Theory and K-theory.Sheldon Katz, Algebraic geometry, string theory.Jeremiah Heller, Motivic homotopy theory, algebraic cycles and K-theory.Haboush, Algebraic groups and homogeneous spaces. Iwan Duursma, Number theory, Arithmetic geometry, Coding Theory and Cryptography.Christopher Dodd, Algebraic and Arithmetic Geometry, D-modules, Geometric Representation Theory.Steven Bradlow, Differential geometry, gauge theory, holomorphic vector bundles, moduli spaces.The document Graduate Studies in Algebraic Geometry outlines the general areas of Algebraic Geometry studied here and describes the advanced undergraduate and graduate courses that are under development or offered regularly. The future looks very bright indeed with promising new directions for research being undertaken, many of which connect algebraic geometry to other areas of mathematics as well as to physics. It is an old subject with a rich classical history, while the modern theory is built on a more technical but rich and beautiful foundation. Algebraic Geometry in simplest terms is the study of polynomial equations and the geometry of their solutions.
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