Research Station on Commutative Algebra

June 13-17, 2016

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Date: June 13th ~ 17th 2016

Place: Yangpyeong Bloomvista(http://www.bloomvista.co.kr)

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:

Secant varieties

Fat points schemes

Gorenstein algebras including level algebras

Artinian algebras having the weak Lefschetz property,

Tropical algebra, and

Other topics related to commutative algebra

The workshop provides an opportunity for discussions with the invited

speakers on interesting questions, unsolved problems and potential

applications of the topics in diverse contexts.

Lecture series given by

Alessandra Bernardi (University of Trento): Fat and Thin Points for Tensor Decomposition file

Maria Virginia Catalisano (University of Genoa): Higher secant varieties of classical projective varieties file

Anthony Iarrobino (Northeastern University): Gorenstein Algebras: graded or nongraded

Juan Migliore (University of Notre Dame): A Survey on the Weak (and Strong) Lefschetz property file
Lefschetz properties and moving beyond the SHGH Conjecture file

Mounir Nisse (KIAS): Tropical algebra

Seminar Talks given by

Sijong Kwak (KAIST): CM regularity
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

Organizers:

Yong-Su Shin (Sungshin Women’s University)

Young Rock Kim (Hankuk University of Foreign Studies)

Contact:

Hyemi Kim (hmkim@kias.re.kr)