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Fiberwise Gromov-Witten theory, quantum spectra of flag bundles, and prime factorization of integers
Giordano Cotti
https://arxiv.org/abs/2510.05500 https://

Fiberwise Gromov-Witten theory, quantum spectra of flag bundles, and prime factorization of integers
This work investigates the vertical quantum cohomology and quantum spectra of flag bundles, uncovering new links between the Gromov-Witten theory of homogeneous fibrations and analytic number theory. Building on previous constructions by Astashkevich and Sadov (arXiv:hep-th/9401103) and by Biswas, Das, Oh, and Paul (arXiv:2408.06616), we establish functorial and inductive properties of vertical quantum cohomology, and relate the vertical and absolute quantum spectra. We show that the degeneracy…

Discrete measured groupoid von Neumann algebras via the Gaussian deformation
Felipe Flores, James Harbour
https://arxiv.org/abs/2509.15161 https://arxiv.or…

Discrete measured groupoid von Neumann algebras via the Gaussian deformation
Given a discrete measured groupoid $\mathcal{G}$, we study properties of the corresponding von Neumann algebra $L(\mathcal{G})$ using the techniques of Popa's deformation/rigidity theory. More specifically, we define and study the Gaussian deformation associated with any $1$-cocycle of $\mathcal{G}$ and use it to prove primeness and fullness under appropriate assumptions. We also characterize the maximal rigid subalgebras of $L(\mathcal{G})$ and produce unique prime factorization results for al…