Tootfinder

This giving circle has apparently stalled out, and could use a boost if you have a few bucks to spare:
https://chuffed.org/project/hope-giving-circle

Circle applies for a US national trust bank license, which would let it act as a custodian for its own reserves and hold crypto for its institutional clients (Hannah Lang/Reuters)
https://www.reuters.com/sustainability/boa

The Santa Barbara Ring Shout Project honors a tradition that our enslaved brothers did when they arrived in America.
It consists of calling and responding to the acapella style of singing.
SBRSP dances in a circle to the beat of a sticker, beating on a wood floor to make rhythm.
Ring Shout uses the entire body,
the main focus is rhythms.
SBRSP greatest accomplishment was joining the Gullah/Geechee shouters for a closeout exhibit of Lorenzo Turner's work …

Santa Barbara Ring Shout Project — Juneteenth
The Santa Barbara Ring Shout Project (SBRSP) honors a tradition that our enslaved brothers did when they arrived in America. It consists of calling and responding to the acapella style of singing. SBRSP dances in a circle to the beat of a sticker, beating on a wood floor to make rhythm. Ring Shout u

I fear that AI is the 12th circle of Dante's inferno: treachery against the soul itself.

Synchronization of mean-field models on the circle
Yury Polyanskiy, Philippe Rigollet, Andrew Yao
https://arxiv.org/abs/2507.22857 https://arxiv.org/pdf/25…

Synchronization of mean-field models on the circle
This paper considers a mean-field model of $n$ interacting particles whose state space is the unit circle, a generalization of the classical Kuramoto model. Global synchronization is said to occur if after starting from almost any initial state, all particles coalesce to a common point on the circle. We propose a general synchronization criterion in terms of $L_1$-norm of the third derivative of the particle interaction function. As an application we resolve a conjecture for the so-called self-…

Here's a handy reaction chart

google_plus: Google (2013)
Snapshot of connections among users of Google , collected in 2012. Nodes are users and a directed edge (i,j) represents user i added user j to i's circle.
This network has 211187 nodes and 1506896 edges.
Tags: Social, Online, Unweighted
https://networks.skewed.de/net/google_

Now I’m on MIRAC’s mailing list, so hopefully I don’t miss the next one.
Also, though…it is just deeply heartening to randomly encounter a protest: not a thing that I already knew about, but a thing that just •showed up• in my neighborhood. It makes me feel like the circle of resistance is much bigger than my own little circle. And it is.
That’s the feeling I want us to create: “Wow, these protests are everywhere.”

🇺🇦 #NowPlaying on KEXP's #SundaySoul
Circle:
🎵 My Lady
#Circle
https://ladydaisey.bandcamp.com/track/full-circle

#circle @…

POSTPONED! See reply.
TOMORROW: May 31, 2:00 PM until 6:00 PM
FREEDOM RISING
Union Station, Washington, DC
Art | Music | Freedom
#art #music #resist

🔊 #NowPlaying on #BBCRadio3:
#BetweenTheEars
- Miniatures
In this first weather-inspired miniature Between the Ears, Miyuki Jokiranta sinks into a mire near the arctic circle, discovering the gentle deceitfulness of the weather.
Relisten now 👇
https://www.bbc.co.uk/programmes/m002f0dh

google_plus: Google (2013)
Snapshot of connections among users of Google , collected in 2012. Nodes are users and a directed edge (i,j) represents user i added user j to i's circle.
This network has 211187 nodes and 1506896 edges.
Tags: Social, Online, Unweighted
https://networks.skewed.de/net/google_

Two folks here on the Fediverse, @… and @…, have set up a giving circle to help several families trying to survive in Gaza. This is direct mutual aid, with a direct impact.
I set up a recurring donation. If you have a little money yourself to chip in, it will have an impact.
https://chuffed.org/project/hope-giving-circle

Free Circle Actions on the Product of Three Spheres
Dimpi, Hemant Kumar Singh
https://arxiv.org/abs/2505.21993 https://arxiv.org/pdf/…

Free Circle Actions on the Product of Three Spheres
The orbit spaces of free S^0-actions on the mod 2 cohomology product of three spheres, S^n x S^m x S^l, 1 <= n <= m <= l have been determined in [6]. In this paper, we extend these findings to free S^1-actions on the rational cohomology product of three spheres. This extension also builds upon the work of Dotzel et al. [7], who studied free circle actions on the rational cohomology product of two spheres. Additionally, we establish Borsuk-Ulam type theorems.

Holomorphic 1-forms without zeros on K\"ahler threefolds
Simon Pietig
https://arxiv.org/abs/2506.22067 https://arxiv.org/pdf/250…

Holomorphic 1-forms without zeros on Kähler threefolds
We classify all smooth compact connected Kähler threefolds that admit the structure of a $C^\infty$-fiber bundle over the circle. This generalizes the work of Hao and Schreieder in the projective case. In contrast to the projective case, there cannot always exist a smooth morphism to a positive-dimensional torus. Instead, we show that such a compact Kähler threefold admits a finite étale cover that is bimeromorphic to a $\mathbb{P}^1$-, $\mathbb{P}^2$-, or Hirzebruch surface-bundle over a lo…

Arbitrarily Negative Energy for Small Kaluza-Klein Bubbles
Gary T. Horowitz (Ricky), Guanyu (Ricky), Lu
https://arxiv.org/abs/2507.22120 https://arxiv.or…

Arbitrarily Negative Energy for Small Kaluza-Klein Bubbles
We show that the ADM energy of a Kaluza-Klein bubble of nothing is unbounded from below even if the size of the circle at infinity and the size of the minimal sphere at the bubble are fixed. We demonstrate this by presenting a family of explicit time-symmetric initial data satisfying these boundary conditions with arbitrarily negative energy. In particular, this is true for very small bubbles, which indicates that the standard Kaluza-Klein vacuum is more unstable than previously thought.

Binary matroids and degree-boundedness for pivot-minors
Rutger Campbell, James Davies, Robert Hickingbotham
https://arxiv.org/abs/2507.23182 https://arxiv.…

Binary matroids and degree-boundedness for pivot-minors
We prove that for every bipartite graph $H$ and positive integer $s$, the class of $K_{s,s}$-subgraph-free graphs excluding $H$ as a pivot-minor has bounded average degree. Our proof relies on the announced binary matroid structure theorem of Geelen, Gerards, and Whittle. Along the way, we also prove that every $K_{s,t}$-free bipartite circle graph with $s\le t$ has a vertex of degree at most $\max\{2s-2, t-1\}$ and provide examples showing that this is tight.

This https://arxiv.org/abs/2311.07309 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Non-singular extensions of circle-valued Morse functions
In this paper, we consider the non-singular extension problem for circle-valued Morse functions on closed orientable surfaces. The problem asks, given a circle-valued Morse function $f\colon M\to S^{1}$ on a closed orientable surface $M$, under what condition there exist a compact orientable 3-dimensional manifold $N$ with $\partial N = M$ and a submersion $G\colon N \to S^{1}$ such that $G|_{\partial N}=f$. We provide necessary and sufficient conditions for the existence of a non-singular…

Running in CIRCLE? A Simple Benchmark for LLM Code Interpreter Security
Gabriel Chua
https://arxiv.org/abs/2507.19399 https://arxiv.org/pdf/2507.19399

Running in CIRCLE? A Simple Benchmark for LLM Code Interpreter Security
As large language models (LLMs) increasingly integrate native code interpreters, they enable powerful real-time execution capabilities, substantially expanding their utility. However, such integrations introduce potential system-level cybersecurity threats, fundamentally different from prompt-based vulnerabilities. To systematically evaluate these interpreter-specific risks, we propose CIRCLE (Code-Interpreter Resilience Check for LLM Exploits), a simple benchmark comprising 1,260 prompts targe…

On an area-preserving inverse curvature flow for plane curves
Zezhen Sun, Yuting Wu
https://arxiv.org/abs/2507.22366 https://arxiv.org/pdf/2507.22366

On an area-preserving inverse curvature flow for plane curves
In this paper, we study a $1/κ^{n}$-type area-preserving non-local flow of convex closed plane curves for any $n>0$. We show that the flow exists globally, the length of evolving curve is non-increasing, and the limiting curve will be a circle in the $C^{\infty}$ metric as time $t\to\infty$.

Two folks here on the Fediverse, @… and @…, have set up a giving circle to help several families trying to survive in Gaza. This is direct mutual aid, with a direct impact.
I set up a recurring donation. If you have a little money yourself to chip in, it will have an impact.
https://chuffed.org/project/hope-giving-circle

google_plus: Google (2013)
Snapshot of connections among users of Google , collected in 2012. Nodes are users and a directed edge (i,j) represents user i added user j to i's circle.
This network has 211187 nodes and 1506896 edges.
Tags: Social, Online, Unweighted
https://networks.skewed.de/net/google_

circle singing and being open-hearted
#singing #BeBetter
https://muz4now.com/2009/circle-singin…

circle singing and being open-hearted
Stan Stewart - @muz4now

A priori bounds and equicontinuity of orbits for the intermediate long wave equation
Benjamin Harrop-Griffiths, Rowan Killip, Monica Visan
https://arxiv.org/abs/2506.23868

A priori bounds and equicontinuity of orbits for the intermediate long wave equation
We prove uniform-in-time a priori $H^s$ bounds for solutions to the intermediate long wave equation posed both on the line and on the circle, covering the range $-\frac12

This https://arxiv.org/abs/2410.03475 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Noncommutative metric geometry of quantum circle bundles
In this paper we investigate quantum circle bundles from the point of view of compact quantum metric spaces. The raw input data is a circle action on a unital $C^*$-algebra together with a quantum metric of spectral geometric origin on the fixed point algebra. Under a few extra conditions on the spectral subspaces we show that the spectral geometric data on the base algebra can be lifted to the total algebra. Notably, the lifted spectral geometry is independent of the choice of frames and is pe…

A Schwarz-Jack lemma, circularly symmetric domains and numerical ranges
Javad Mashreghi, Annika Moucha, Ryan O'Loughlin, Thomas Ransford, Oliver Roth
https://arxiv.org/abs/2506.23831

A Schwarz-Jack lemma, circularly symmetric domains and numerical ranges
We prove a Schwarz-Jack lemma for holomorphic functions on the unit disk with the property that their maximum modulus on each circle about the origin is attained at a point on the positive real axis. With the help of this result, we establish monotonicity and convexity properties of conformal maps of circularly symmetric and bi-circularly symmetric domains. As an application, we give a new proof of Crouzeix's theorem that the numerical range of any $2\times 2$ matrix is a $2$-spectral set for t…

'There is not a singular voice': On trade, countries don't know who in Trump's circle to listen to (Politico)
https://www.politico.com/news/2025/06/22/there-is-not-a-singular-voice-countries-cant-figure-out-who-in-trumps-circle-to-listen-to-on-trade-00415851
http://www.memeorandum.com/250622/p56#a250622p56

It is a Sunday, and fittingly we were at an actual stone circle.
This is Long Meg and a few of her"daughters", a very #StandingStoneSunday

OpenStreetMap doesn't have as many streets documented as Google, but we can make it a killer app by mapping what Google won't! For an easy first destination, I propose we have a group of FOSS-loving volunteers commit ritual suicide and then map ring 2 of the 7th circle of Hell in accordance with Dante's Inferno

Fascism doesn’t belong here, or anywhere, ever!
Industrial Workers of the World
https://iww.org
International Workers Association
https://iwa-ait.org

Next evolution of Indy's coming!
✅ Indiana Jones and the Great Circle: The Order of Giants: What You Need to Know After the DLC's Reveal - Xbox Wire
https://news.xbox.com/en-us/2025/06/08/indiana-jones-great-circle-dlc-ord…

Indiana Jones and the Great Circle: The Order of Giants: What You Need to Know After the DLC's Reveal - Xbox Wire
Get ready for an all-new adventure with Indiana Jones and the Great Circle: The Order of Giants DLC, launching September 4. 

Contribute to this giving circle for families in Gaza if you can.
I realize that anything any of us can do right now feels impossibly small. Do not believe for one second that small things don’t matter.
https://chuffed.org/project/hope-giving-circle

I like Ike.
(That includes the 91% top marginal income tax rate for the wealthiest Americans during his presidency.)
#Eisenhower #HistoryMatters #TaxFairness

Back in Miami, Minkah Fitzpatrick hopes to secure long-term contract with Dolphins https://www.nfl.com/news/back-in-miami-minkah-fitzpatrick-hopes-to-secure-long-term-contract-with-dolphins

Sydney Sprague - "Flat Circle" (Music Video)
#music

No tracking across the web. No surveillance. No selling your data. That's it—that's the privacy policy.
"I fly with Gander. Because ragebait isn’t very Canadian."
#Gander Social Inc

C-FBI: A Combinatorial method using Convolutions for Circle Fitting in Blurry Images
Esteban Rom\'an Catafau, Torbj\"orn E. M. Nordling
https://arxiv.org/abs/2507.11476

C-FBI: A Combinatorial method using Convolutions for Circle Fitting in Blurry Images
This paper addresses the fundamental computer vision challenge of robust circle detection and fitting in degraded imaging conditions. We present Combinatorial Convolution-based Circle Fitting for Blurry Images (3C-FBI), an algorithm that bridges the gap between circle detection and precise parametric fitting by combining (1) efficient combinatorial edge pixel (edgel) sampling and (2) convolution-based density estimation in parameter space. We evaluate 3C-FBI across three experimental framewor…

On a complex topological orientation for circle-equivariant K-theory
J Morava
https://arxiv.org/abs/2505.21719 https://arxiv.org/pdf/…

On a complex topological orientation for circle-equivariant K-theory
The principal result of this note is the existence of a complex topological orientation for Atiyah-Segal $\mathbb{T}$-equivariant K-theory which indexes the projective space of lines in complex n-space by the Fourier expansion $1 + q + \dots + q^n$.

This https://arxiv.org/abs/2502.08656 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Parable of the Parabola
We study triangles and quadrilaterals which are inscribed in a circle and circumscribed about a parabola. Although these are particular cases of the celebrated Poncelet's Theorem, in this paper we {\it do not assume} the theorem but prove it along the way. Similarly, our arguments here \emph{are logically independent} from Cayley's condition, describing points of a finite order on an elliptic curve or any other use of the theory of elliptic curves. Instead, we use purely planimetric methods, in…

Floquet operator dynamics and orthogonal polynomials on the unit circle
Hsiu-Chung Yeh, Aditi Mitra
https://arxiv.org/abs/2506.20611 https://

Floquet operator dynamics and orthogonal polynomials on the unit circle
Operator spreading under stroboscopic time evolution due to a unitary is studied. An operator Krylov space is constructed and related to orthogonal polynomials on a unit circle (OPUC), as well as to the Krylov space of the edge operator of the Floquet transverse field Ising model with inhomogeneous couplings (ITFIM). The Verblunsky coefficients in the OPUC representation are related to the Krylov angles parameterizing the ITFIM. The relations between the OPUC and spectral functions are summariz…

Effect of Nozzle Geometry on the Performance of Non-Assist Flares
Ashray Mohit, Jenna Stolzman, Margaret Wooldridge, Jesse Capecelatro
https://arxiv.org/abs/2507.21827 https://

Effect of Nozzle Geometry on the Performance of Non-Assist Flares
This study employs large-eddy simulations with a flamelet progress variable approach to systematically quantify the influence of nozzle geometry on combustion efficiency, mixing, and blowout resistance in non-assist methane flares. Five canonical nozzle shapes-circle, low aspect ratio ellipse, high aspect ratio ellipse, diamond, and square-were evaluated under relevant industrial flare conditions. Results demonstrate that cornered geometries enhance near-field recirculation, promote mixing, and…

Fiserv aims to launch its own stablecoin by 2025's end, and partners with PayPal and Circle to develop new products for financial institutions and merchants (Emily Mason/Bloomberg)
https://www.bloomberg.com/news/articles/20

Concentration inequalities for random dynamical systems
Graccyela Salcedo
https://arxiv.org/abs/2506.22823 https://arxiv.org/pdf/2506…

Concentration inequalities for random dynamical systems
We establish concentration inequalities for random dynamical systems (RDSs), assuming that the observables of interest are separately Lipschitz. Under a weak average contraction condition, we obtain deviation bounds for several random quantities, including time-average synchronization, empirical measures, Birkhoff sums, and correlation dimension estimators. We present concrete classes of RDSs to which our main results apply, such as finitely supported diffeomorphisms on the circle and projectiv…

Divya and Shantini have vetted that yes, these are real people in real crisis who need help.
The two of them aren’t professional fundraisers or anything. They’re just doing their best with the tools they have, trying desperately to help a few people.
Yes, I wish that we had proper organizations — NGOs, international aid, a functioning democracy! — to help •all• the people in need all at once. We don’t. Elbow grease is all we’ve got.
https://chuffed.org/project/hope-giving-circle

A p-adic criterion for Lehmer's conjecture
Anup B. Dixit, Sushant Kala
https://arxiv.org/abs/2507.20141 https://arxiv.org/pdf/2507.20141

A p-adic criterion for Lehmer's conjecture
For a non-zero algebraic number $α$ of degree $d$, let $h(α)$ denote its logarithmic Weil height. It is known that when $h(α)$ is small, and $d$ is large, the conjugates of $α$ are clustered near the unit circle and have angular equidistribution in the complex plane about the origin. In this paper, we establish a $p$-adic analogue of this result by obtaining lower bounds for $h(α)$ in terms of the number of its conjugates that lie in a finite extension of $\mathbb{Q}_p$, for some prime $p$…

This https://arxiv.org/abs/2505.06813 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Pure cactus groups and configuration spaces of points on the circle
In this article, we provide a summary of the results presented in the previous two papers of the authors and in the second author's Master thesis, which concern pure cactus groups and configuration spaces of points on the circle.

Divya and Shantini have vetted that yes, these are real people in real crisis who need help.
The two of them aren’t professional fundraisers or anything. They’re just doing their best with the tools they have, trying desperately to help a few people.
Yes, I wish that we had proper organizations — NGOs, international aid, a functioning democracy! — to help •all• the people in need all at once. We don’t. Elbow grease is all we’ve got.
https://chuffed.org/project/hope-giving-circle

things on linux can be mostly deterministic, until you get to the iptables circle of hell

If they bring Flash FM back in GTA VI they better have Maria Chambers voice DJ Toni again cuz that would be such a full circle moment.

🇺🇦 #NowPlaying on BBCRadio3's #RoundMidnight
Terry Callier:
🎵 Golden Circle
#TerryCallier
https://open.spotify.com/track/5BJZmEkHtvSlhievzRYvVM

A New Approach to the Construction of Subdivision Algorithms
Alexander Dietz
https://arxiv.org/abs/2507.20897 https://arxiv.org/pdf/2507.20897

A New Approach to the Construction of Subdivision Algorithms
In this thesis, a new approach for constructing subdivision algorithms for generalized quadratic and cubic B-spline subdivision for subdivision surfaces and volumes is presented. First, a catalog of quality criteria for these subdivision algorithms is developed, serving as a guideline for the construction process. The construction begins by generating the desired subdominant eigenvectors as the vertices of regular convex 3-polytopes for volumes using circle packings. Subsequently, these polyt…

Nonlinear Aggregation of Phase Elements on the Unit Circle under Parametric External Fields
Isshin Arai, Tomoaki Itano, Masako Sugihara-Seki
https://arxiv.org/abs/2507.19053 htt…

Nonlinear Aggregation of Phase Elements on the Unit Circle under Parametric External Fields
We investigate nonlinear aggregation dynamics of phase elements distributed on the unit circle under parametrically modulated external fields. Our model, inspired by flaky particle rotation in fluids, employs the equation ${dα/dt} = λ(t)\sin 2(α- ϕ(t))$ with $λ(t) = \cos(ω_1 t)$ and $ϕ(t) = ω_2 t$, representing a switching rotating attractive device where the attractive strength oscillates while the attractive point rotates at independent frequencies. Through numerical simulations and a…

On the intersection of Cantor set with the unit circle and some sequences
Kan Jiang, Derong Kong, Wenxia Li, Zhiqiang Wang
https://arxiv.org/abs/2507.16510 https://

On the intersection of Cantor set with the unit circle and some sequences
For $λ\in(0,1/2)$ let $K_λ$ be the self-similar set in $\mathbb{R}$ generated by the iterated function system $\{f_0(x)=λx, f_1(x)=λx+1-λ\}$. In this paper, we investigate the intersection of the unit circle $\mathbb{S} \subset \mathbb{R}^2$ with the Cartesian product $K_λ \times K_λ$. We prove that for $λ\in(0, 2 - \sqrt{3}]$, the intersection is trivial, i.e., \[ \mathbb{S} \cap (K_λ \times K_λ) = \{(0,1), (1,0)\}. \] If $λ\in [0.330384,1/2)$, then the intersection $\mathbb{S} \cap…

Replaced article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- The convergence of inversive distance circle packings to the Riemann mapping
Yuxiang Chen, Yanwen Luo, Xu Xu

Food Lion had a bottle of Cabernet with a dollar off offer if you bought meat. Just make a copy of your receipt, circle the meat items, and mail it in. Current postage costs 78 cents. Wot??.?

Dupont Circle: The Birthplace of Television
https://wtop.com/dc/2025/06/only-on-wtop-tour-dupont-circle-building-being-celebrated-as-the-birthplace-of-television/

ONLY ON WTOP: Tour Dupont Circle building being celebrated as ‘the birthplace of television’
In a city full of national monuments, an enterprising landlord is declaring the D.C. building of legendary Kramers bookstore as “the birthplace of television.”

Shares of Circle jumped 124%, opening at $69.50 on the NYSE, after the stablecoin company raised almost $1.1B in an IPO (Tanaya Macheel/CNBC)
https://www.cnbc.com/2025/06/05/stablecoin-issuer-circle-soars-in-…

Stablecoin issuer Circle soars 124% in NYSE debut after pricing IPO above expected range
Circle joins Coinbase, Mara Holdings and Riot Platforms as one of the few pure-play crypto companies to list in the U.S. 

This https://arxiv.org/abs/2505.06234 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Largest Circle Enclosing $n$ Lattice Points
In this paper, we propose a class of elementary plane geometry problems closely related to the title of this paper. Here, a circle is the 1-dimensional curve bounding a disk. For any nonnegative integer, a circle is called $n$-enclosing if it contains exactly $n$ lattice points on the $xy$-plane in its interior. The main questions are when the largest $n$-enclosing circle exists and what the largest radius is. We study the small integer cases by hand and extend to all $n<1100$ with the aid of a…

I tried hunting POTA with five different #HamRadio antenna arrangements while taking a short holiday at the beach over the past few days. I tried the built-in antenna on my KX3, a 20m vertical with radials on a deck, the same vertical with radials stuck with a stake into the top of a sand dune, and two inverted-V 40m end-fed half wave arrangements on a spiderbeam, a north/south and an e…

Robust signal decompositions on the circle
Aral Kose, Daniel Liberzon
https://arxiv.org/abs/2507.07007 https://arxiv.org/pdf/2507.070…

Robust signal decompositions on the circle
We consider the problem of decomposing a piecewise constant function on the circle into a sum of indicator functions of closed circular disks in the plane, whose number and location are not a priori known. This represents a situation where an agent moving on the circle is able to sense its proximity to some landmarks, and the goal is to estimate the number of these landmarks and their possible locations -- which can in turn enable control tasks such as motion planning and obstacle avoidance. Mo…

A Comparison of Bacterial Colonies Count from Petri Dishes Utilizing Hough Transform and Traditional Manual Counting
Areesha Rehman, Zikria Saleem, Jarrar Amjad, Syed Rehan Shah, Kamran Siddique
https://arxiv.org/abs/2505.20365

A Comparison of Bacterial Colonies Count from Petri Dishes Utilizing Hough Transform and Traditional Manual Counting
Bacterial colony enumeration is an essential stage in microbiological research, allowing susceptibility to antibiotics assessment, monitoring of the environment, and clinical diagnostics. Traditional manual counting methods are costly and susceptible to human mistakes, prompting the creation of automated detection systems. This research compares the efficacy of the Hough Circle Transform method for automated colony detection to hand counting of E. coli, S. aureus, and P. aeruginosa colonies on …

The Wave Equation in the Context of Reduced Groups $C^*$-Algebras
Fan Huang
https://arxiv.org/abs/2505.22930 https://arxiv.org/pdf/25…

The Wave Equation in the Context of Reduced Groups $C^*$-Algebras
Motivated by the identification $C(\mathbb{T})\cong C_r^*(\mathbb{Z})$ and the wave equation on the circle, we explore the wave equation in the context of reduced group $C^*$-algebras $C_r^*(G)$ for countably infinite, possibly non-abelian groups $G$. Using a one-parameter group of $*$-automorphisms whose infinitesimal generator paves the way to an analogue of the Laplacian, we establish the existence and uniqueness of solutions to the wave equation within this framework.

Blech, I think I almost understand this piece of PDF; 7 objects later and it's drawn a composited semi transparent green circle.

X-ray Emission Spectropolarimetry of Strongly Anisotropic Single Crystal Systems using a Rowland Circle Geometry
Jared E. Abramson, Charles A. Cardot, Josh J. Kas, John J. Rehr, Werner Kaminsky, Herwig Michor, Marta Roman, Petra Becker, Gerald T. Seidler
https://arxiv.org/abs/2507.18839

X-ray Emission Spectropolarimetry of Strongly Anisotropic Single Crystal Systems using a Rowland Circle Geometry
Polarization dependence has historically seen extensive use in x-ray spectroscopy to determine magnetic and local geometric properties, but more broadly as a way to gain extra sensitivity to electronic structure at the level of individual magnetic orbitals. This is often done in the context of x-ray absorption through techniques like x-ray magnetic circular dichroism or x-ray linear dichroism, but it has seen little application to x-ray emission. Here we explore the information contained in the…

Towards Open-Closed Categorical Enumerative Invariants: Circle-Action Formality Morphism
Jakob Ulmer
https://arxiv.org/abs/2507.15445 https://

Towards Open-Closed Categorical Enumerative Invariants: Circle-Action Formality Morphism
Categorical enumerative invariants of a Calabi-Yau category, encoded as the partition function of the associated closed string field theory (SFT), conjecturally equal Gromov-Witten invariants when applied to Fukaya categories. Part of this theory is a formality $L_\infty$ morphism which depends on a splitting of the non-commutative Hodge filtration. Our main result is providing an open-closed formality morphism; the algebraic structures involved conjecturallygive a home to open-closed GW invari…

Rational points on varieties defined by multihomogeneous diagonal forms
Doyon Kim, Tian Wang
https://arxiv.org/abs/2507.20878 https://arxiv.org/pdf/2507.20…

Rational points on varieties defined by multihomogeneous diagonal forms
We give an asymptotic formula for the number of rational points of bounded height on algebraic varieties defined by systems of multihomogeneous diagonal equations. The proof uses the Hardy-Littlewood circle method and the hyperbola method developed by Blomer and Brüdern.

Free commutative skew braces
Thomas Letourmy
https://arxiv.org/abs/2506.19765 https://arxiv.org/pdf/2506.19765

Free commutative skew braces
The main result of this paper is an explicit construction of the free commutative skew brace -- that is, a skew brace whose circle group is commutative -- on an arbitrary generating set $X$. We embed this object into a set of rational functions and show that a simple linear equation characterizes the image of this embedding. As a consequence, comparing elements in this skew brace is no more difficult than comparing elements in the free commutative group generated by $X$.

20 years later, full circle. ⭕️ https://bonn.social/@Sascha/114686955069707737

Hace unas semanas vi «Kingsman: The Secret Service» y me gustó harto, así que por estos días fui por la secuela «Kingsman: The Golden Circle» y me llevé una decepción total.
👇🏻
★★ en #Letterboxd https://boxd.it/akISiV

Google adds new AI and gaming features to Android's Circle to Search, and Gemini Live support for foldables and third-party apps, starting with Samsung devices (Jess Weatherbed/The Verge)
https://www.theverge.com/news/702291/android-google-a…

Android’s Circle to Search feature gets AI and gaming upgrades
Google is adding AI Mode to Android’s Circle to Search tool and expanding Gemini Live support for Samsung devices.

@… @… honestly, that’s not a bad idea. 😝
@… suggested putting a sticker over the “PAR” that ma…

Raiders WR Jack Bech, Broncos CB Jahdae Barron—An AFC West Matchup To Circle https://raiderramble.com/2025/07/13/raiders-wr-jack-bech-broncos-cb-jahdae-barron-an-afc-west/

National Park Service closes Dupont Circle ahead of WorldPride Parade;
“Entirely unnecessary and infuriating situation," says one D.C. lawmaker.
https://51st.news/national-park-service-closes-dupont-circle-worldpride-parade/

National Park Service closes Dupont Circle ahead of WorldPride Parade
“Entirely unnecessary and infuriating situation," says one D.C. lawmaker.

Crews close off Dupont Circle Park for WorldPride festivities this weekend (Marissa J. Lang/Washington Post)
https://www.washingtonpost.com/dc-md-va/2025/06/06/dupont-circle-park-closing-world-pride-dc-2025/
http://www.memeorandum.com/250606/p45#a250606p45

Convergence of discrete conformal mappings on surfaces
David Glickenstein, Lee Sidbury
https://arxiv.org/abs/2507.17037 https://arxiv.org/pdf/2507.17037

Convergence of discrete conformal mappings on surfaces
Discrete conformal mappings based on circle packing, vertex scaling, and related structures has had significant activity since Thurston proposed circle packing as a way to approximate conformal maps in the 1980s. The first convergence result of Rodin-Sullivan (1987) proved that circle packing maps do indeed converge to conformal maps to the disk. Recent results have shown convergence of maps of other discrete conformal structures to conformal maps as well. We give a general theorem of convergen…

Why is no one in the press asking the Manhattan DA or NY State AG what they are gonna do about this
-- cause we know Trump’s SEC and US DOJ aren’t going to do anything about this,

google_plus: Google (2013)
Snapshot of connections among users of Google , collected in 2012. Nodes are users and a directed edge (i,j) represents user i added user j to i's circle.
This network has 211187 nodes and 1506896 edges.
Tags: Social, Online, Unweighted
https://networks.skewed.de/net/google_

Optimal polynomial approximants and orthogonal polynomials on the unit circle. An electrostatic approach
Ram\'on Orive, Joaqu\'in S\'anchez-Lara, Daniel Seco
https://arxiv.org/abs/2507.15488

Optimal polynomial approximants and orthogonal polynomials on the unit circle. An electrostatic approach
We explore the connection between two seemingly distant fields: the set of cyclic functions $f$ in a Hilbert space of analytic functions over the unit disc $\D$, on the one hand, and the families of orthogonal polynomials for a weight on the unit circle $\T$ (OPUC), on the other. This link is established by so-called Optimal Polynomial Approximants (OPA) to $1/f$, that is, polynomials $p_n$ minimizing the norm of $1-p_nf$, among all polynomials $p_n$ of degree up to a given $n$. Here, we focu…

Characterizing infinite torsion subgroups of the circle through arithmetic-type sequences
Ayan Ghosh, Pratulananda Das
https://arxiv.org/abs/2506.15257 htt…

Characterizing infinite torsion subgroups of the circle through arithmetic-type sequences
In a recent work [Das et al., Bull. Sci. Math. 199 (2025), 103580], the structure of characterized subgroups corresponding to arithmetic-type sequences was investigated. Building upon this work, we further show that a characterized subgroup associated with an arithmetic-type sequence is countable if and only if it is torsion. Further we prove that any infinite torsion subgroup of the circle can be characterized by an arithmetic-type sequence with bounded ratio. Moreover, our findings demonstrat…

🇺🇦 #NowPlaying on KEXP's #SonicReducer
Circle Jerks:
🎵 Letter Bomb
#CircleJerks
https://wastedx.bandcamp.com/track/letter-bomb-circle-jerks
https://open.spotify.com/track/6WCEWks9hFSn158EhOONjy

Characterizing circle graphs with binomial partial Petrial polynomials
Ruiqing Feng, Qi Yan, Xuan Zheng
https://arxiv.org/abs/2507.02421 https://

Characterizing circle graphs with binomial partial Petrial polynomials
The partial Petrial polynomial was first introduced by Gross, Mansour, and Tucker as a generating function that enumerates the Euler genera of all possible partial Petrials on a ribbon graph. Yan and Li later extended this polynomial invariant to circle graphs by utilizing the correspondence between circle graphs and bouquets. Their explicit computation demonstrated that paths produce binomial polynomials, specifically those containing exactly two non-zero terms. This discovery led them to pose…

An isometry theorem for persistent homology of circle-valued functions
Nathan Broomhead, Mariam Pirashvili
https://arxiv.org/abs/2506.02999 https://…

An isometry theorem for persistent homology of circle-valued functions
This paper explores persistence modules for circle-valued functions, presenting a new extension of the interleaving and bottleneck distances in this setting. We propose a natural generalisation of barcodes in terms of arcs on a geometric model associated to the derived category of quiver representations. The main result is an isometry theorem that establishes an equivalence between the interleaving distance and the bottleneck distance for circle-valued persistence modules.

Yo también quiero ser popular, así que les comparto el tradicional #LastFourWatched en otro #LetterboxdFriday
Career Opportunities (3★)
Kingsman: The Golden Circle (2★)
They Live (3½★)
Trouble (1★)
👉🏻

Dupont Circle park to close during WorldPride, Park Service says (Washington Post)
https://www.washingtonpost.com/dc-md-va/2025/06/02/world-pride-dupont-circle-park-dc/
http://www.memeorandum.com/250603/p2#a250603p2

The hyperbolic circle problem over Heegner points
Dimitrios Chatzakos, Giacomo Cherubini, Stephen Lester, Morten S. Risager
https://arxiv.org/abs/2506.13883

The hyperbolic circle problem over Heegner points
For the full modular group, we obtain a logarithmic improvement on Selberg's long-standing bound for the error term of the counting function in the hyperbolic circle problem over Heegner points of different discriminants. The main ingredients in our method are Waldspurger's formula, twisted first moments of certain Rankin-Selberg convolutions, and a new fractional moment estimate.

Envelopes of lines, unfoldings and breaking symmetry
Peter Giblin, Alexander Wettig
https://arxiv.org/abs/2506.16547 https://arxiv.or…

Envelopes of lines, unfoldings and breaking symmetry
We generalise the well-known ``embroidery'' envelopes of chords joining points at angles $t$ and $mt$ of a single circle in several ways. Firstly we allow $m$ to be rational (possibly negative) instead of integral, finding formulas for the number of cusps, points at infinity and self-intersections of these envelopes. Secondly we use two concentric circles instead of one, taking the chords to join a point of one circle to a point of the other. This construction allows the formation of different …

Infinite Ideal Polyhedra in Hyperbolic 3-Space: Existence and Rigidity
Huabin Ge, Hao Yu, Puchun Zhou
https://arxiv.org/abs/2506.19528 https://

Infinite Ideal Polyhedra in Hyperbolic 3-Space: Existence and Rigidity
In the seminal work [27], Rivin obtained a complete characterization of finite ideal polyhedra in hyperbolic 3-space by the exterior dihedral angles. Since then,the characterization of infinite hyperbolic polyhedra has become an extremely challenging open problem. To resolve this problem, we study ideal circle patterns (ICPs) and use them to characterize infinite ideal polyhedra (IIPs). Specifically, we establish the existence and rigidity of embedded ICPs on the plane. We further prove the uni…

Scaling of the rotation number for perturbations of rational rotations
Paul Glendinning
https://arxiv.org/abs/2506.19508 https://arxi…

Scaling of the rotation number for perturbations of rational rotations
The parameter dependence of the rotation number in families of circle maps which are perturbations of rational rotations is described. We show that if, at a critical parameter value, the map is a (rigid) rotation $x\to x+\frac{p}{q}~({\rm mod}~1)$ with $p$ and $q$ coprime, then the rotation number is differentiable at that point provided a transversality condition holds, and hence that the rotation number scales linearly at this parameter. We provide an explicit and computable expression for th…

marker_cafe: The Marker Cafe (2011)
Snapshot of connections among users of the Israeli social network Marker Cafe, collected in 2011. Nodes are users and a directed edge (i,j) represents user i added user j to i's circle.
This network has 69413 nodes and 1644849 edges.
Tags: Social, Online, Unweighted
https://

Source: Circle priced its upsized IPO at $31 per share, above marketed range of $27 to $28, raising nearly $1.1B and valuing the company at approximately $6.9B (Anthony Hughes/Bloomberg)
https://www.bloomberg.com/news/articles/20

Generalized Hardy's identity for the astroid-type p-circle lattice point problem
Masaya Kitajima
https://arxiv.org/abs/2506.03331 https://

Generalized Hardy's identity for the astroid-type p-circle lattice point problem
Let $r$ be a positive real number and $p$ satisfy $(2/p)\in\mathbb{N}$. Then, we consider the lattice point problem of the closed curves astroid-type $p$-circle $\{x\in\mathbb{R}^{2}|\ |x_{1}|^{p}+|x_{2}|^{p}=r^{p}\}$ which generalize the circle. In investigating the asymptotic behavior of the error term in the area approximation of the circle, G.H. Hardy conjectured an infimum for the evaluation in 1917. One of the grounds for this conjecture is the Hardy's identity, w…

Combinatorial p-th Calabi flow for finite and infinite ideal circle patterns
Xiaorui Yang, Hao Yu
https://arxiv.org/abs/2506.07130 https://

Combinatorial p-th Calabi flow for finite and infinite ideal circle patterns
This paper presents a comprehensive study of the combinatorial $p$-th Calabi flow for both finite and infinite ideal circle patterns. In the finite case, we establish a sharp criterion: the combinatorial $p$-th Calabi flow with $p>1$ converges if and only if a constant curvature metric exists in the underlying geometric background. In the infinite setting, we prove the long-time existence of solutions to the combinatorial $p$-th Calabi flow for $p \geq 2$, representing a significant advance in …

On the Moments of Exponential Sums over r-Free Polynomials
Ben Doyle
https://arxiv.org/abs/2506.20581 https://arxiv.org/pdf/2506.2058…

On the Moments of Exponential Sums over r-Free Polynomials
Let $\mathbb{F}_q[t]$ denote the ring of polynomials over the finite field $\mathbb{F}_q$. Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of $k$th moments of exponential sums over $r$-free polynomials in $\mathbb{F}_q[t]$ for all $k>0$. In the supercritical case $k>1+1/r$, we acquire an asymptotic formula using a function field analogue of the Hardy-Littlewood circle method.

This giving circle is keeping a few people alive in Gaza, and they’ve stalled out really frustratingly close to their goal. If you want to feel like you did something good today in the face of all the awful, maybe consider chipping in a little.
https://chuffed.org/project/hope-giving-circle

Isolated singularities in $G_2$-structures with torsion
Henrique S\'a Earp, Jakob Stein
https://arxiv.org/abs/2506.15482 https://…

Isolated singularities in $G_2$-structures with torsion
We revisit the study of $G_2$-structures with special torsion, and isolated singularities. Many of the known examples with conical singularities admit additional symmetries, and we describe circle-invariant $G_2$-structures in this context. Finally, we show that collapsing the circle fibres of a contact Calabi-Yau manifold at isolated points cannot produce a $G_2$-structure with bounded torsion.

Chime priced its US IPO at $27 a share, above the expected range, raising ~$700M and another $165M from shares sold by investors, valuing the company at $11.6B (MacKenzie Sigalos/CNBC)
https://www.cnbc.com/2025/06/11/chime-ipo-fintech.html

Chime prices IPO at $27 per share, valuing fintech company at $11.6 billion ahead of Nasdaq debut
Chime's debut set for Thursday follows recent listings from eToro and Circle, with investors watching closely to gauge broader appetite for fintech offerings.

The hyperbolic lattice counting problem in large dimensions
Christos Katsivelos
https://arxiv.org/abs/2506.17753 https://arxiv.org/pd…

The hyperbolic lattice counting problem in large dimensions
For $n\geq 3$ and $Γ$ a cocompact lattice acting on the hyperbolic space $\mathbb{H}^n$, we investigate the average behaviour of the error term in the circle problem. First, we explore the local average of the error term over compact sets of $Γ\backslash\mathbb{H}^n$. Our upper bound depends on the quantum variance and the spectral exponential sums appearing in the study of the Prime geodesic theorem. We also prove $Ω$-results for the mean value and the second moment of the error term.

google_plus: Google (2013)
Snapshot of connections among users of Google , collected in 2012. Nodes are users and a directed edge (i,j) represents user i added user j to i's circle.
This network has 211187 nodes and 1506896 edges.
Tags: Social, Online, Unweighted
https://networks.skewed.de/net/google_