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Construction of the smallest Ree-Tits unital from the special linear group of degree two over the field with eight elements
Markus Johannes Stroppel
https://arxiv.org/abs/2506.02732

Construction of the smallest Ree-Tits unital from the special linear group of degree two over the field with eight elements
We construct the smallest Ree-Tits unital from a group of matrices that is isomorphic to the commutator group of the corresponding Ree group. The matrix description is used to determine configurations in the unital via explicit computations. Embeddings into larger Ree-Tits unitals are made explicit.

Live streaming some #LOTRO from my #Linux PC tonight! Come hang out and explore Middle-earth with me! https://www.twitch.tv/tuxramus

Unified description of cuprate superconductors by fractionalized electrons emerging from integrated analyses of photoemission spectra and quasiparticle interference
Shiro Sakai, Youhei Yamaji, Fumihiro Imoto, Tsuyoshi Tamegai, Adam Kaminski, Takeshi Kondo, Yuhki Kohsaka, Tetsuo Hanaguri, Masatoshi Imada
https://arxiv.org/abs/2508.01297

Unified description of cuprate superconductors by fractionalized electrons emerging from integrated analyses of photoemission spectra and quasiparticle interference
Electronic structure of high-temperature superconducting cuprates is studied by analyzing experimental data independently obtained from two complementary spectroscopies, one, quasiparticle interference (QPI) measured by scanning-tunneling microscopy and the other, angle-resolved photoemission spectroscopy (ARPES) and by combining these two sets of data in a unified theoretical analysis. Through explicit calculations of experimentally measurable quantities, we show that a simple two-component fe…

Theta-invariants of $\mathbb{Z}\pi$-homology equivalences to spherical 3-manifolds
Hisatoshi Kodani, Tadayuki Watanabe
https://arxiv.org/abs/2507.12121 htt…

Theta-invariants of $\mathbb{Z}π$-homology equivalences to spherical 3-manifolds
We study Bott and Cattaneo's $Θ$-invariant of 3-manifolds applied to $\mathbb{Z}π$-homology equivalences from 3-manifolds to a fixed spherical 3-manifold. The $Θ$-invariants are defined by integrals over configuration spaces of two points with local systems and by choosing some invariant tensors. We compute upper bounds of the dimensions of the space spanned by the Bott--Cattaneo $Θ$-invariants and of that spanned by Garoufalidis and Levine's finite type invariants of type 2. The computatio…

My Linux rig is ready for battle! Tonight, it's all about racking up those Conquest points in SWTOR. Come join the push and let's conquer the galaxy together! #StarWars

LOTRO stream is LIVE! Back to Middle-earth on my Linux rig. Come say hi on Twitch! #LOTRO

STO stream is LIVE from Linux! Get ready for some space adventures on Twitch! #STO #LinuxGaming

LOTRO stream is LIVE! Join the fellowship on Twitch! #LOTRO #MMORPG

SWTOR stream is LIVE! Come explore the Old Republic with me on Twitch! (Running on Linux!) #SWTOR

Tonight's adventure: streaming some #LOTRO from my #TuxPoweredPC! Come join me for some Middle-earth exploration and see what quests we can conquer. #LordOfTheRingsOnline