Computational Invariant Theory

By Harm Derksen, G. Kemper. 2002

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Potential energy surfaces from high fidelity fitting of ab initio points: the permutation invariant polynomial - neural network approach (2016, background): “These authors, and subsequent investigators [29, 63], recognised that a permutation invariant PES should involve not only the primary but also secondary invariant polynomials [64].”
Permutationally invariant potential energy surfaces in high dimensionality (2009, background): “The mathematical background is classical, and can found in the monograph by Derksen and Kemper 65 , which emphasizes the constructive computer-algebra aspects of the theory.”
The Interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmetic Combinatorics (2015, background): “Bounding the Noether number has always been an objective of i nvariant theory (for recent surveys we refer to [ 81, 60]; degree bounds are discussed in [ 17, 78, 26, 10, 54]; see [16] for algorithmic aspects).”
On the Castelnuovo-Mumford regularity of rings of polynomial invariants (2011, background): “The first part was conjectured by Kemper [19].”
Towards non-reductive geometric invariant theory (2007, background): “Since X is Noetherian one sees that flnite separating sets of invariants always exist (the analogous result in [ 9 ] is Theorem 2.3.15).”