Noetherianity up to conjugation of locally diagonal inverse limits

We prove that the inverse limit of the sequence dual to a sequence of Lie algebras is Noetherian up to the action of the direct limit of the corresponding sequence of classical algebraic groups when the sequence of groups consists of diagonal embeddings. We also classify all conjugation-stable closed subsets of the space of $\mathbb{N}\times\mathbb{N}$ matrices.Comment: 43 pages, final revisio

A note on ED degrees of group-stable subvarieties in polar representations

In a recent paper, Drusvyatskiy, Lee, Ottaviani, and Thomas establish a "transfer principle" by means of which the Euclidean distance degree of an orthogonally-stable matrix variety can be computed from the Euclidean distance degree of its intersection with a linear subspace. We generalise this principle

Notes on Lai Chin personal pronouns and overt case marking

published or submitted for publicationis peer reviewe

Detection of steam in the circumstellar disk around a massive Young Stellar Object

We report on the observation of hot water vapor (steam) in the inner AU of a young massive star located in the star-forming region IRAS 08576-4334. The water lines are detected in a medium resolution (R=10,000) K-band spectrum taken by the infrared spectrometer ISAAC mounted on the VLT-ANTU. The water vapor is at a mean temperature of 1565+/-510 K, cooler than the hot CO found in the same object, which is at 1660K and the column density is N(H2O)=(2.5 +/- 0.4)x1E18 cm-2. The profile of both H2O and CO lines is best reproduced by the emission from a Keplerian disk. To interpret the data, we also investigate the formation of molecules and especially CO and water vapor in the inner hot and dense part of disks around young high mass stars using a pseudo time-dependent gas-phase chemical model. Molecules are rapidly photodissociated but this destruction is compensated by an efficient formation due to fast neutral-neutral reactions. The ability of CO molecules to self-shield significantly enhances its abundance. Water molecules are sufficiently abundant to be detectable. The observed H2O/CO ratio is reproduced by gas at 1600K and an enhanced UV field over gas density ratio I_UV/nH=1E(-4)- 1E(-6). The simulations support the presence of CO and H2O molecules in the inner disks around young massive stars despite the strong UV radiation and show that the OH radical plays an essential role in hot gas chemistry.Comment: 15 pages, 11 figures, Accepted to A&

Polynomials and tensors of bounded strength

Notions of rank abound in the literature on tensor decomposition. We prove that strength, recently introduced for homogeneous polynomials by Ananyan-Hochster in their proof of Stillman's conjecture and generalised here to other tensors, is universal among these ranks in the following sense: any non-trivial Zariski-closed condition on tensors that is functorial in the underlying vector space implies bounded strength. This generalises a theorem by Derksen-Eggermont-Snowden on cubic polynomials, as well as a theorem by Kazhdan-Ziegler which says that a polynomial all of whose directional derivatives have bounded strength must itself have bounded strength.Comment: Improved the bounds on strength as a function of the dimension of the space where one first sees nontrivial equations for the tensor property