MAT 614 Topics in Algebraic Geometry: Tropical Geometry Fall 2010 | |

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## Welcome to MAT 614The course should introduce to Tropical Geometry, a subject that is shaping during the last decade. It is a sort of Algebraic Geometry over hyperfields of characteristic 1 and 2. In Tropical Geometry varieties are polyhedra of special type, regular functions are piecewise linear convex functions with integral slopes. However there are strong and useful relations to the classical algebraic geometry over the fields of complex numbers and real numbers, as well as over fields with non-Archimedean norms. Tropical Geometry has applications to the classical enumerative problems. On the other hand, it opens its own new world, in which one can find counter-parts of most of the classical algebraic geometry. Sometimes the passage to the tropical geometry makes the theory easier.
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