Combinatorial geometry takes the lead

DOI10.4171/icm2022/201arXiv2207.03875OpenAlexW4389775624MaRDI QIDQ6200333

Andrei Okounkov

Publication date: 22 March 2024

Published in: International Congress of Mathematicians (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.03875

zbMATH Keywords

graded algebrastropical realization of matroids

Mathematics Subject Classification ID

Combinatorial aspects of tropical varieties (14T15) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Combinatorial aspects of matroids and geometric lattices (05B35)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Hodge theory of Soergel bimodules.
• Hard Lefschetz theorem for nonrational polytopes
• On the shape of Bruhat intervals
• The moduli space of matroids
• The number of faces of a simplicial convex polytope
• Enumeration of points, lines, planes, etc.
• Matroids over partial hyperstructures
• Tropical cycles and Chow polytopes
• A counterexample to the generalisation of Sperner's theorem
• Linear Algebra Done Right
• Unimodal, log-concave and Pólya frequency sequences in combinatorics
• Whitney Number Inequalities for Geometric Lattices
• Non‐Algebraic Matroids exist
• Hodge theory in combinatorics
• Algebraic Combinatorics
• Almost all matroids are nonrepresentable
• The Slimmest Geometric Lattices
• COMBINATORIAL APPLICATIONS OF THE HODGE–RIEMANN RELATIONS
• WHAT IS...Tropical Geometry?
• A rank inequality for finite geometric lattices
• The Lines and Planes Connecting the Points of a Finite Set
• Tropical algebraic geometry
• The closure of a linear space in a product of lines