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Using toric geometry

Abstract

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Next lectures
29.05.2024, 10:00 (G3 10 (Lecture hall))
05.06.2024, 10:00 (G3 10 (Lecture hall))
13.06.2024, 10:00 (G3 10 (Lecture hall))
19.06.2024, 14:30 (G3 10 (Lecture hall))
26.06.2024, 10:00 (G3 10 (Lecture hall))
Toric varieties form a well understood class of algebraic varieties. They often arise as the image of a monomial map. These lectures offer an introduction to basic toric geometry and its applications in mathematics and other sciences. Covered topics include toric ideals, semigroup algebras, Cox rings, discriminants and algebraic moment maps. We will also discuss standard constructions of toric varieties from cones, polytopes and fans, and the role of toric varieties in convex optimization, algebraic statistics, and equation solving.

Keywords
toric varieties, polytopes, fans, monomial algebras, Cox rings, discriminant, moment map

Prerequisites
Basic algebraic geometry: affine/projective varieties and their coordinate rings.

Remarks and notes
There will be one lecture and one exercise session per week.

Links

lecture
01.04.24 31.07.24

Regular lectures Summer semester 2024

MPI for Mathematics in the Sciences / University of Leipzig see the lecture detail pages

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail

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