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Ian Thompson

Publications and source records attributed to Ian Thompson.

At least 19 recordsLinked to original sources
arXiv2026

Obstructions to the full Hao-Ng isomorphism

We show that the Hao-Ng isomorphism for full crossed products fails to hold. More precisely, for a non-degenerate $C^*$-correspondence $X$ over a $C^*$-algebra $\mathcal{A}$ and a generalized gauge action $G \curvearrowright X$ by a locally compact group $G$, we isolate three structural obstructions for the canonical commutation $\mathcal{O}_X\rtimes G \cong \mathcal{O}_{X\rtimes G}$ between full crossed product and Cuntz-Pimsner $C^*$-algebra. The first concerns hyperrigidity, the second concerns WEP of the coefficient $C^*$-algebra $\mathcal{A}$ for trivial actions, and the third concerns the coincidence of full and reduced crossed products by the action of $G$ on $\mathcal{A}$.

math.OA↗
arXiv2026

On the universal commuting dilation constant

The universal commuting dilation constant $C_d$ is the smallest constant $\alpha$ such that every $d$-tuple of contractions dilates to a commuting $d$-tuple of normal operators with norm at most $\alpha$. The work of several authors shows that $1.5438 \lesssim C_2 \leq 2$, and it has been asked on a few accounts whether $C_2 < 2$. We provide a positive answer that, in fact, produces a near optimal upper bound of $C_2 \leq \frac{2}{\sqrt{\phi}}$ where $\phi$ is the golden ratio. This tightens the gap on the universal commuting dilation constant to $1.5438 \lesssim C_2 \lesssim 1.5724$. We also tighten the known upper and lower bounds on $C_d$ for arbitrary $d$-tuples.

math.FA↗
arXiv2026

Two warm sub-Saturn mass planets identified from the TESS Full Frame Images

Context. Characterization of warm giants is crucial to constrain giant planet formation and evolution. Measuring the mass and radius of these planets, combined with their moderated irradiation, allows us to estimate their planetary bulk composition, which is a key quantity to comprehend giant planet formation and structure. Aims. We present the discovery of two transiting warm giant planets orbiting solar-type stars from the Transiting Exoplanet Survey Satellite (TESS), which were characterized by further spectroscopic and photometric ground-based observations. Methods. We performed a joint analysis of photometric data with radial velocities to confirm and characterize TOI-883 b and TOI-899 b, two sub-Saturns orbiting solar-like stars. Results. TOI-883 b and TOI-899 b have masses of $0.123 \pm 0.012$ $M_J$ and $0.213 \pm 0.024$ $M_J$, radius of $0.604 \pm 0.028$ $R_J$ and $0.991 \pm 0.044$ $R_J$, periods of $10.06$ d and $12.85$ d and equilibrium temperature of $1086 \pm 19$ K and $1040 \pm 19$ K, respectively. Conclusions. While having similar masses, orbital periods and stellar host properties, these planets seem to have different internal compositions, which could point to distinct formation histories. Both planets are suitable targets for atmospheric studies to further constrain formation scenarios of planets in the Neptune-Saturn mass range

astro-ph.EP↗
arXiv2025

Local presentability and monadicity of forgetful functors for operator algebraic categories

In recent work of Lindenhovius and Zamdzhiev, it was established that the category of complete operator spaces, with completely contractive linear maps as morphisms, is locally countably presentable. In this work, we extend their conclusion to the non-complete setting and prove that the categories of operator systems, (Archimedean) order unit spaces, and unital operator algebras are all locally countably presentable as well. This is established through an analysis of forgetful functors and the identification of Eilenberg-Moore categories. We provide a complete understanding of adjunction and monadicity for forgetful functors between these categories, together with the categories of $C^*$-algebras, Banach spaces, and normed spaces. In addition, for various subcategories of function-theoretic objects, we investigate completeness and local presentability through Kadison's duality theorem.

math.CT↗
arXiv2025

Couniversality for C*-algebras of residually finite-dimensional operator algebras

The C*-envelope of a non self-adjoint operator algebra is known to encode many properties of the underlying subalgebra. However, the C*-envelope does not always encode the residual finite-dimensionality of an operator algebra. To elucidate this failure, we study couniversal existence in the space of residually finite-dimensional (RFD) C*-algebras attached to a fixed operator algebra. We construct several examples of residually finite-dimensional operator algebras for which there does not exist a minimal RFD C*-algebra, answering a question of the first two authors. For large swathes of tensor algebras of C*-correspondences, we also prove that the space of RFD C*-algebras fails to be closed under infima of C*-covers. In the case of the disc algebra, we are able to achieve this failure for a single pair of RFD C*-algebras.

math.OA↗
arXiv2025

The Hao-Ng isomorphism theorem for reduced crossed products

We prove the Hao-Ng isomorphism for reduced crossed products by locally compact Hausdorff groups. More precisely, for a non-degenerate $\mathrm{C}^*$-correspondence $X$ and a generalized gauge action $G \curvearrowright X$ by a locally compact Hausdorff group $G$, we prove the commutation ${\mathcal{O}}_{X\rtimes_rG}\cong {\mathcal{O}}_X\rtimes_rG$ of the reduced crossed product with the Cuntz-Pimsner C*-algebra construction. This is done by proving that the reduced crossed product of an operator algebra commutes with the C*-envelope, which relies on refined W*-dynamical covers of C*-dynamical systems, unitary implementation of W*-dynamical systems, and an operator-valued extension of Maharam's lifting theorem.

math.OA↗
arXiv2024

Three Warm Jupiters orbiting TOI-6628, TOI-3837, TOI-5027 and one sub-Saturn orbiting TOI-2328

We report the discovery and characterization of three new transiting giant planets orbiting TOI-6628, TOI-3837 and TOI-5027, and one new warm sub-Saturn orbiting TOI-2328, whose transits events were detected in the lightcurves of the Transiting Exoplanet Survey Satellite \textbf{(TESS)} space mission. By combining TESS lightcurves with ground-based photometric and spectroscopic follow-up observations we confirm the planetary nature of the observed transits and radial velocity variations. TOI-6628~$b$ has a mass of 0.75$\pm$0.06~$M_\mathrm{J}$, a radius of 0.98$\pm$0.05~$R_J$ and is orbiting a metal-rich star with a period of 18.18424$\pm{0.00001}$ days and an eccentricity of 0.667$\pm0.016$, making it one of the most eccentric orbits of all known warm giants. TOI-3837~$b$ has a mass of 0.59$\pm$0.06~$M_\mathrm{J}$, a radius of 0.96$\pm$0.05~$R_J$ and orbits its host star every 11.88865$\pm$0.00003~days, with a moderate eccentricity of 0.198$^{+0.046}_{-0.058}$. With a mass of 2.01$\pm$0.13~$M_\mathrm{J}$ and a radius of 0.99$^{+0.07}_{-0.12}$ $R_J$, TOI-5027~$b$ orbits its host star in an eccentric orbit with $e$~=~0.395$^{+0.032}_{-0.029}$ every 10.24368$\pm{0.00001}$~days. TOI-2328~$b$ is a Saturn-like planet with a mass of 0.16$\pm$0.02~$M_\mathrm{J}$ and a radius of 0.89$\pm$0.04~$R_J$, orbiting its host star in a nearly circular orbit with $e$~=~0.057$^{+0.046}_{-0.029}$ at an orbital period of 17.10197$\pm{0.00001}$ days. All four planets have orbital periods above 10 days, and our planet interior structure models are consistsent a rocky-icy core with a H/He envelope, providing evidence supporting the core accretion model of planet formation for this kind of planets.

astro-ph.EP↗
arXiv2024

Rigidity of operator systems: tight extensions and noncommutative measurable structures

Let $A$ be a unital $C^*$-algebra generated by some separable operator system $S$. More than a decade ago, Arveson conjectured that $S$ is hyperrigid in $A$ if all irreducible representations of $A$ are boundary representations for $S$. Recently, a counterexample to the conjecture was found by Bilich and Dor-On. To circumvent the difficulties hidden in this counterexample, we exploit some of Pedersen's seminal ideas on noncommutative measurable structures and establish an amended version of Arveson's conjecture. More precisely, we show that all irreducible representations of $A$ are boundary representations for $S$ precisely when all representations of $A$ admit a unique "tight" completely positive extension from $S$. In addition, we prove an equivalence between uniqueness of such tight extensions and rigidity of completely positive approximations for representations of nuclear $C^*$-algebras, thereby extending the classical principle of Korovkin--Saskin for commutative algebras of continuous functions.

math.OA↗
arXiv2023

An approximate unique extension property for completely positive maps

We study the closure of the unitary orbit of a given point in the non-commutative Choquet boundary of a unital operator space with respect to the topology of pointwise norm convergence. This may be described more extensively as the $\ast$-representations of the $\mathrm{C}^{\ast}$-envelope that are approximately unitarily equivalent to one that possesses the unique extension property. Although these $\ast$-representations do not necessarily have the unique extension property themselves, we show that their unital completely positive extensions display significant restrictions. When the underlying operator space is separable, this allows us to connect our work to Arveson's hyperrigidity conjecture. Finally, as an application, we reformulate the classical \v{S}a\v{s}kin Theorem and Arveson's essential normality conjecture.

math.OA↗
arXiv2023

Jensen polynomials associated with Wright's circle method: Hyperbolicity and Tur\'an inequalities

We study the Fourier coefficients of functions satisfying a certain version of Wright's circle method with finitely many major arcs. We show that the Jensen polynomials associated with such Fourier coefficients are asymptotically hyperbolic, building on the framework of Griffin--Ono--Rolen--Zagier and others. Consequently, we prove that the Fourier coefficients asymptotically satisfy all higher-order Tur\'an inequalities. As an application, we apply our results to both $(q^t;q^t)_\infty^{-r}$, which counts $r$-coloured partitions into parts divisible by $t$, and to the function $(q^{a};q^{p})_\infty^{-1}$ where $p$ is prime and $0\leq a<p$, a ubiquitous function throughout number theory.

math.NT↗
arXiv2022

The MegaMapper: A Stage-5 Spectroscopic Instrument Concept for the Study of Inflation and Dark Energy

In this white paper, we present the MegaMapper concept. The MegaMapper is a proposed ground-based experiment to measure Inflation parameters and Dark Energy from galaxy redshifts at $2<z<5$. In order to achieve path-breaking results with a mid-scale investment, the MegaMapper combines existing technologies for critical path elements and pushes innovative development in other design areas. To this aim, we envision a 6.5-m Magellan-like telescope, with a newly designed wide field, coupled with DESI spectrographs, and small-pitch robots to achieve multiplexing of at least 26,000. This will match the expected achievable target density in the redshift range of interest and provide a 10x capability over the existing state-of the art, without a 10x increase in project budget.

astro-ph.IM↗
arXiv2022

Minimal boundaries for operator algebras

We study boundaries for unital operator algebras. These are sets of irreducible $*$-representations that completely capture the spatial norm attainment for a given subalgebra. Classically, the Choquet boundary is the minimal boundary of a function algebra and it coincides with the collection of peak points. We investigate the question of minimality for the non-commutative counterpart of the Choquet boundary and show that minimality is equivalent to what we call the Bishop property. Not every operator algebra has the Bishop property, but we exhibit classes of examples that do. Throughout our analysis, we exploit various non-commutative notions of peak points for an operator algebra. When specialized to the setting of $C^*$-algebras, our techniques allow us to provide a new proof of a recent characterization of those $C^*$-algebras admitting only finite-dimensional irreducible representations.

math.OA↗
arXiv2022

The number of locally invariant orderings of a group

We show that if a nontrivial group admits a locally invariant ordering, then it admits uncountably many locally invariant orderings. For the case of a left-orderable group, we provide an explicit construction of uncountable families of locally invariant orderings; for a general group we provide an existence theorem that applies compactness to yield uncountably many locally invariant orderings. Along the way, we define and investigate the space of locally invariant orderings of a group, the natural group actions on this space, and their relationship to the space of left-orderings.

math.GR↗
arXiv2021

Maximal C^*-covers and residual finite-dimensionality

We study residually finite-dimensional (or RFD) operator algebras which may not be self-adjoint. An operator algebra may be RFD while simultaneously possessing completely isometric representations whose generating C*-algebra is not RFD. This has provided many hurdles in characterizing residual finite-dimensionality for operator algebras. To better understand the elusive behaviour, we explore the C*-covers of an operator algebra. First, we equate the collection of C*-covers with a complete lattice arising from the spectrum of the maximal C*-cover. This allows us to identify a largest RFD C*-cover whenever the underlying operator algebra is RFD. The largest RFD C*-cover is shown to be similar to the maximal C*-cover in several different facets and this provides supporting evidence to a previous query of whether an RFD operator algebra always possesses an RFD maximal C*-cover. In closing, we present a non self-adjoint version of Hadwin's characterization of separable RFD C*-algebras.

math.OA↗
arXiv2020

Finite-dimensionality in the non-commutative Choquet boundary: peaking phenomena and $\mathrm{C}^*$-liminality

We explore the finite-dimensional part of the non-commutative Choquet boundary of an operator algebra. In other words, we seek finite-dimensional boundary representations. Such representations may fail to exist even when the underlying operator algebra is finite-dimensional. Nevertheless, we exhibit mechanisms that detect when a given finite-dimensional representation lies in the Choquet boundary. Broadly speaking, our approach is topological and requires identifying isolated points in the spectrum of the $\mathrm{C}^*$-envelope. This is accomplished by analyzing peaking representations and peaking projections, both of which being non-commutative versions of the classical notion of a peak point for a function algebra. We also connect this question with the residual finite-dimensionality of the $\mathrm{C}^*$-envelope and to a stronger property that we call $\mathrm{C}^*$-liminality. Recent developments in matrix convexity allow us to identify a pivotal intermediate property, whereby every matrix state is locally finite-dimensional.

math.OA↗
arXiv2020

Low Distortion Block-Resampling with Spatially Stochastic Networks

We formalize and attack the problem of generating new images from old ones that are as diverse as possible, only allowing them to change without restrictions in certain parts of the image while remaining globally consistent. This encompasses the typical situation found in generative modelling, where we are happy with parts of the generated data, but would like to resample others ("I like this generated castle overall, but this tower looks unrealistic, I would like a new one"). In order to attack this problem we build from the best conditional and unconditional generative models to introduce a new network architecture, training procedure, and algorithm for resampling parts of the image as desired.

stat.ML↗
arXiv2019

From bound states to the continuum

This white paper reports on the discussions of the 2018 Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program "From bound states to the continuum: Connecting bound state calculations with scattering and reaction theory". One of the biggest and most important frontiers in nuclear theory today is to construct better and stronger bridges between bound state calculations and calculations in the continuum, especially scattering and reaction theory, as well as teasing out the influence of the continuum on states near threshold. This is particularly challenging as many-body structure calculations typically use a bound state basis, while reaction calculations more commonly utilize few-body continuum approaches. The many-body bound state and few-body continuum methods use different language and emphasize different properties. To build better foundations for these bridges, we present an overview of several bound state and continuum methods and, where possible, point to current and possible future connections.

nucl-th↗