Noetherianity up to Symmetry

By Jan Draisma. 2013

51 citations recorded by the source corpus.

These lecture notes for the 2013 CIME/CIRM summer school Combinatorial Algebraic Geometry deal with manifestly infinite-dimensional algebraic varieties with large symmetry groups. So large, in fact, that subvarieties stable under those symmetry groups are defined by finitely many orbits of equations—whence the title Noetherianity up to symmetry. It is not the purpose of these notes to give a systematic, exhaustive treatment of such varieties, but rather to discuss a few “personal favourites”: exciting examples drawn from applications in algebraic statistics and multilinear algebra. My hope is that these notes will attract other mathematicians to this vibrant area at the crossroads of combinatorics, commutative algebra, algebraic geometry, statistics, and other applications.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/1a92b6e14ff59beb8db5b5ef6a9ed04a119132e1

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In Algebra and Number Theory

1. Uwe Nagel
2. Tim Romer
3. Juan Migliore
4. Karim A. Adiprasito

In Computational Theory and Mathematics

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2. Tim Romer
3. Juan Migliore
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In Discrete Mathematics and Combinatorics

1. Uwe Nagel
2. Tim Romer

Citations in the corpus

• FI- and OI-modules with varying coefficients (2017, background): “(i) In the case A = P, the above colimit has been studied, for example, in [7, 14, 18] by using the monoid of increasing maps Inc(N) = {π : N → N | π(i) < π(i+ 1) for all i ≥ 1}.”