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Geodesic orbit pseudo-Riemannian H-type nilmanifolds: case of minimal admissible Clifford modules
Kenro Furutani, Irina Markina, Yurii Nikonorov
https://arxiv.org/abs/2507.00470

Geodesic orbit pseudo-Riemannian H-type nilmanifolds: case of minimal admissible Clifford modules
We investigate the geodesic orbit property of pseudo-Riemannian nilmanifolds, specifically those known in the literature as pseudo $H$-type Lie groups -- i.e., 2-step nilpotent Lie groups of Heisenberg type equipped with a left invariant pseudo-Riemannian metric. The study of homogeneous geodesics on Riemannian $H$-type Lie groups was completed by C.~Riehm in 1984. In this work, we extend these results to the pseudo-Riemannian $H$-type Lie groups and provide a complete characterization of the g…

A White Paper on The Multi-Messenger Science Landscape in India
Samsuzzaman Afroz, Sanjib Kumar Agarwalla, Dipankar Bhattacharya, Soumya Bhattacharya, Subir Bhattacharyya, Varun Bhalerao, Debanjan Bose, Chinmay Borwanker, Ishwara Chandra C. H., Aniruddha Chakraborty, Indranil Chakraborty, Sovan Chakraborty, Debarati Chatterjee, Varsha Chitnis, Moon Moon Devi, Sanjeev Dhurandhar, Amol Dighe, Bitan Ghosal, Sourendu Gupta, Arpan Hait, Md Emanuel Hoque, Pratik Majumdar, Nilmani Mathur, Har…

A White Paper on The Multi-Messenger Science Landscape in India
The multi-messenger science using different observational windows to the Universe such as Gravitational Waves (GWs), Electromagnetic Waves (EMs), Cosmic Rays (CRs), and Neutrinos offer an opportunity to study from the scale of a neutron star to cosmological scales over a large cosmic time. At the smallest scales, we can explore the structure of the neutron star and the different energetics involved in the transition of a pre-merger neutron star to a post-merger neutron star. This will open up a…

The Piltz divisor Problem in Number Fields Using The Resonance Method
Nilmoni Karak, Kamalakshya Mahatab
https://arxiv.org/abs/2506.22587 https://

The Piltz divisor Problem in Number Fields Using The Resonance Method
The Piltz divisor problem is a natural generalization of the classical Dirichlet divisor problem. In this paper, we study this problem over number fields and obtain improved $Ω-$bounds for its error terms. Our approach involves generalizing a Voronoi-type formula due to Soundararajan in the number field setting, and applying a recent result due to the second author.

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Omega Estimate for the Lattice Point Discrepancy of a Body of Revolution Using The Resonance Method
Nilmoni Karak
https://arxiv.org/abs/2506.22590 https://…

Omega Estimate for the Lattice Point Discrepancy of a Body of Revolution Using The Resonance Method
Using a recent method developed by Mahatab, we obtain an improved $Ω$-bound for the error term arising in lattice counting problem of bodies of revolution in $\mathbb R^3$ around a coordinate axis and having smooth boundary with bounded nonzero curvature. This strengthens an earlier result by Kühleitner and Nowak.

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Large and iterated finite group actions on manifolds admitting non-zero degree maps to nilmanifolds
Jordi Daura Serrano
https://arxiv.org/abs/2506.11174 ht…

Large and iterated finite group actions on manifolds admitting non-zero degree maps to nilmanifolds
Let M be a closed connected oriented manifold admitting a non-zero degree map to a nilmanifold. In the first part of the paper we study effective finite group actions on M. In particular, we prove that Homeo(M) is Jordan, we bound the discrete degree of symmetry of M and we study the number and the size of stabilizers of an effective action of a finite group G on M. We also study the toral rank conjecture and Carlsson's conjecture for large primes for this class of manifolds. In the second part…

The first phase of mass transfer in low-mass binaries: neither stable nor a common envelope
Gijs Nelemans, Holly Preece, Karel Temmink, James Munday, Onno Pols
https://arxiv.org/abs/2506.16832

The first phase of mass transfer in low-mass binaries: neither stable nor a common envelope
The masses of the white dwarfs in a binary carry information about previous mass-transfer phases. The core mass -- radius relation of low-mass giants gives the size of the progenitor of a helium white dwarf at the moment it last filled its Roche lobe. Previously, we used this information for a few observed systems to propose a new mass-transfer type, based on an angular momentum balance. Our aim is to investigate if stable mass transfer instead of the angular momentum prescription is consiste…

On Jiang's Bounded Index Property for products of nilmanifolds
Peng Wang, Qiang Zhang
https://arxiv.org/abs/2507.06132 https://ar…

On Jiang's Bounded Index Property for products of nilmanifolds
In 2023, Zhang and Zhao presented the first examples of aspherical manifolds lacking the Bounded Index Property (BIP) for fixed points. This answered a question posed by Jiang in 1998 in the negative. In this paper, we first extend the notion of BIP to that of iterations of selfmaps (BIP$_k$), and then demonstrate BIP$_k$ for certain products $M\times N$ of nilmanifolds. Finally, we give characterizations for the Lefschetz number, the Nielsen number, and the minimal number of fixed points of se…

p-K\"ahler structures on compact complex manifolds
Ettore Lo Giudice
https://arxiv.org/abs/2506.13546 https://arxiv.org/pdf/2506…

p-Kähler structures on compact complex manifolds
Let $(M,J)$ be a complex manifold of complex dimension $n$. A $p$-Kähler structure on $(M,J)$ is a real, closed $(p,p)$-transverse form. In this paper, we address the conjecture of L. Alessandrini and G. Bassanelli on $(n-2)$-Kähler nilmanifolds equipped with nilpotent complex structures and holomorphically parallelizable nilmanifolds. We also derive necessary conditions for the existence of smooth curves of $p$-Kähler structures, starting from a fixed $p$-Kähler structure, along a differen…