Research Station on Commutative Algebra
June 13-17, 2016
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Commutative Algebra is a branch of Algebra, studying the properties of
commutative rings and objects. Commutative Algebra has been studied and
evolved solving problems from Algebraic Geometry, Number Theory, and
Computer Sciences. For example, Secant varieties and Fat points schemes
are related to Representation theory, Coding theory, Algebraic Complexity
Theory, Statistics, Polylogenetics, Data analysis, and Electrical engineering
(eg: Antenna Array Processing and Telecommunications).
Level Algebras and graded or nongraded Gorenstein Algebras
can be applied to Algebraic Geometry, Invariant theory, Algebraic and
enumerate combinatorics, Matroid theory, Design theory, Projective
geometry, and Partition theory. The Weak Lefschety Property is important
to understand the structures of Artinian algebras. Tropical geometry is a
new area of application of Commutative Algebra and Algebraic Geometry.
This workshop is a part of a research station project to improve the use
of these methods in policy analysis. Its goal is to promote Commutative
Algebra and applications. Its topics include:
Alessandra Bernardi (University of Trento): Fat and Thin Points for Tensor Decomposition file
Lefschetz properties and moving beyond the SHGH Conjecture file
Jeaman Ahn: Existence and Non-Existence of Gorenstein Sequences
Youngho Woo: Waring Rank of Some Polynomials and Strassen Additivity Conjecture
Kangjin Han (DGIST): Singular loci of 3rd secant varieties of Veronese embeddings file