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Classification of the topological holonomy groups in $SO(3)$
Naoya Ando
https://arxiv.org/abs/2507.20593 https://arxiv.org/pdf/2507.20593

Classification of the topological holonomy groups in $SO(3)$
In this paper, we obtain classification of the topological holonomy groups in $SO(3)$. Such a group is given by one of the following: a finite group (such groups are classified by Klein); a commutative infinite group which is generated by one or two elements, and dense in a subgroup of $SO(3)$ isomorphic to $SO(2)$; a non-commutative infinite group generated by two elements of order $2$, $\infty$ such that these rotation axes are orthogonal; a non-commutative infinite group which is dense in $S…

Sources: Instagram and TikTok are working on versions of their apps customized to run on TV screens, following YouTube's success in attracting a TV audience (The Information)
https://www.theinformation.com/articles/tiktok-instag…

TikTok, Instagram Plot TV Apps Following YouTube’s Success
Rejoice, couch potatoes. TikTok and Instagram, following YouTube’s lead, are working on ways to make it easier for viewers to watch videos from their apps on TV screens. The social media giants see an opportunity to grab some of the ad dollars flowing to the streaming TV market. Meta Platforms’ ...

Line bundles and exact sequences for the ideal class group and the Picard group
Abolfazl Tarizadeh
https://arxiv.org/abs/2508.19889 https://arxiv.org/pdf/2…

Line bundles and exact sequences for the ideal class group and the Picard group
For any extension of commutative rings $A\subseteq B$ we first naturally define a group $\Cl(A,B)$, that we call the ideal class group of this extension (we will see that both the classical ideal class group and, surprisingly, the Picard group are special cases of this structure), then, as a first main result, we obtain the following exact sequence of Abelian groups: ...

Avatars and Environments for Meetings in Social VR: What Styles and Choices Matter to People in Group Creativity Tasks?
Anya Osborne, Sabrina Fielder, Lee Taber, Tara Lamb, Joshua McVeigh-Schultz, Katherine Isbister
https://arxiv.org/abs/2506.21780

Avatars and Environments for Meetings in Social VR: What Styles and Choices Matter to People in Group Creativity Tasks?
Due to the COVID-19 pandemic, many professional entities shifted toward remote collaboration and video conferencing (VC) tools. Social virtual reality (VR) platforms present an alternative to VC for meetings and collaborative activities. Well-crafted social VR environments could enhance feelings of co-presence and togetherness at meetings, helping reduce the need for carbon-intensive travel to face-to-face meetings. This research contributes to creating meeting tools in VR by exploring the effe…

Sources: Instagram and TikTok are working on versions of their apps customized to run on TV screens, following YouTube's success in attracting a TV audience (The Information)
https://www.theinformation.com/articles/tiktok-instag…

TikTok, Instagram Plot TV Apps Following YouTube’s Success
Rejoice, couch potatoes. TikTok and Instagram, following YouTube’s lead, are working on ways to make it easier for viewers to watch videos from their apps on TV screens. The social media giants see an opportunity to grab some of the ad dollars flowing to the streaming TV market. Meta Platforms’ ...

Guide to the NFL's rookie class: Who is flying under the radar? Who will win OROY, DROY? https://www.espn.com/nfl/story/_/id/45979912/2025-nfl-rookies-guide-fantasy-picks-stat-projections-top-qbs-roy

The Plesken Lie algebra for associative algebras with anti-involution: semisimple cellular algebras
Thorsten Holm, Nils Wirries
https://arxiv.org/abs/2508.20628 https://

The Plesken Lie algebra for associative algebras with anti-involution: semisimple cellular algebras
Cohen and Taylor, following an idea of Plesken, introduced a Lie algebra to the complex group algebra of a finite group and determined its structure, based on the character theory of the group. We show how the definition of this Plesken Lie algebra can be extended to any associative algebra with an anti-involution. After some examples we consider semisimple cellular algebras and prove that their Plesken Lie algebras are direct sums of orthogonal Lie algebras, the sizes of which are determined b…

Characterization of hyperbolic groups via random walks
Victor Gerasimov, Leonid Potyagailo
https://arxiv.org/abs/2507.22005 https://arxiv.org/pdf/2507.2200…

Characterization of hyperbolic groups via random walks
Our first result gives a partial converse to a well-known theorem of A. Ancona for hyperbolic groups. We prove that a group $G$, equipped with a symmetric probability measure whose finite support generates $G$, is hyperbolic if it is nonamenable and satisfies the following condition: for a sufficiently small $\varepsilon >0$ and $r\geqslant0$, and for every triple $(x, y, z)$, belonging to a word geodesic of the Cayley graph, the probability that a random path from $x$ to $z$ intersects the c…

The systems group decided to welcome @… to the Brown CS department by filling his office with a … ton of crates. Way to get him, Carolyn and Justus!