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Bericht: Entlassungen bei "Oblivion Remastered"-Studio Virtuos
Beim Entwicklerstudio Virtuos sollen 300 Stellen gestrichen werden, berichtet ein Journalist. Betroffen ist demnach auch das Team hinter "Oblivion Remastered".

Vertex functions for bow varieties and their Mirror Symmetry
Tommaso Maria Botta, Hunter Dinkins
https://arxiv.org/abs/2507.13219 https://

Vertex functions for bow varieties and their Mirror Symmetry
In this paper, we study the vertex functions of finite type $A$ bow varieties. Vertex functions are $K$-theoretic analogs of $I$-functions, and 3d mirror symmetry predicts that the $q$-difference equations satisfied by the vertex functions of a variety and its 3d mirror dual are the same after a change of variable swapping the roles of the various parameters. Thus the vertex functions are related by a matrix of elliptic functions, which is expected to be the elliptic stable envelope of M. Agana…

Spanning path-cycle systems with given end-vertices in regular graphs (full version)
Yoshimi Egawa, Mikio Kano, Kenta Ozeki
https://arxiv.org/abs/2508.11302 https://

Spanning path-cycle systems with given end-vertices in regular graphs (full version)
We prove the following theorem. Let $r\ge 4$ be an integer, and $G$ be a $K_{1,r}$-free $r$-edge-connected $r$-regular graph. Then, for every set $W$ of even number of vertices of $G$ such that the distance between any two vertices of $W$ in $G$ is at least 3, $G$ has vertex-disjoint paths and cycles $P_1, \ldots, P_m, C_1, \ldots, C_n$ such that (i) $V(G)=V(P_1) \cup \cdots \cup V(P_m) \cup V(C_1) \cup \cdots \cup V(C_n)$, (ii) each path $P_i$ connects two vertices of $W$, and (iii) the set of…

US appeals court rules in Apple's favor by throwing out a $300M verdict that found it infringed on Optis' wireless tech patents, sending the case to a new trial (Blake Brittain/Reuters)
https://www.reuters.com/legal/litigation/a

VARRHO & StereoKollektor – Vertical Protocol
#breakbeats

Locally analytic completed cohomology of Shimura varieties of Hodge type
Kensuke Aoki
https://arxiv.org/abs/2508.11099 https://arxiv.org/pdf/2508.11099

Locally analytic completed cohomology of Shimura varieties of Hodge type
For Shimura varieties of Hodge type, we show that there are natural isomorphisms between locally analytic complete cohomology groups and cohomology groups for flag varieties with coefficient which is given by their perfectoid covers. This result is a generalization of that of Pan for the modular curve and Qiu-Su for unitary Shimura curves.

heise | heise Update vom 18. Juli 2025: Lesetipps fürs Wochenende
Der wöchentliche Newsletter von heise diesmal mit Vorratskammer-Inventur, Aktien-Crawlern, smarten Ventilatoren, Tesla-Absturz und KI-Fahrstuhlmusik.

On quadratic persistence and Pythagoras numbers of totally real projective varieties
Jong In Han, Jaewoo Jung, Euisung Park
https://arxiv.org/abs/2506.13247

On quadratic persistence and Pythagoras numbers of totally real projective varieties
In this paper, we study the relationship between quadratic persistence and the Pythagoras number of totally real projective varieties. Building upon the foundational work of Blekherman et al. in arXiv:1902.02754, we extend their characterizations of arithmetically Cohen-Macaulay varieties with next-to-maximal quadratic persistence to arbitrary case. Our main result classifies totally real non-aCM varieties of codimension $c$ and degree $d$ that exhibit next-to-maximal quadratic persistence in t…

Perfect codes in Cayley graphs of abelian groups
Peter J. Cameron, Roro Sihui Yap, Sanming Zhou
https://arxiv.org/abs/2507.11871 https://

Perfect codes in Cayley graphs of abelian groups
A perfect code in a graph $Γ= (V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent and every vertex in $V \setminus C$ is adjacent to exactly one vertex in $C$. A total perfect code in $Γ$ is a subset $C$ of $V$ such that every vertex of $Γ$ is adjacent to exactly one vertex in $C$. In this paper we prove several results on perfect codes and total perfect codes in Cayley graphs of finite abelian groups.

Finding a long cycle in a percolated vertex expander
Lawrence Hollom
https://arxiv.org/abs/2506.12162 https://arxiv.org/pdf/2506.1216…

Finding a long cycle in a percolated vertex expander
Given a graph $G$, the percolated graph $G_p$ has each edge independently retained with probability $p$. Collares, Diskin, Erde, and Krivelevich initiated the study of large structures in percolated single-scale vertex expanders, wherein every set of exactly $k$ vertices of $G$ has at least $dk$ neighbours before percolation. We extend their result to a conjectured stronger form, proving that if $p = (1+\varepsilon)/d$ and $G$ expands as above, then $G_p$ fails to contain a cycle of length $Ω_…