In this paper we study the role of planarity in generalized scattering amplitudes, through several closely interacting structures in combinatorics, algebraic and tropical geometry. The generalized biadjoint scalar amplitude, introduced recently by...
We study magnetohydrodynamic (MHD) standing shocks in inflowing plasmas in a black hole magnetosphere. Fast and intermediate shock formation is explored in Schwarzschild and Kerr geometry to illustrate general relativistic effects. We find that non...
Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the analysis and rec...
geometry, a derived stack is, roughly, a stack together with a sheaf of commutative ring spectra. It generalizes a derived scheme. Derived stacks are the
T. Kobayashi conjectured in the 36th Geometry Symposium in Japan (1989) that a homogeneous space G/H of reductive type does not admit a compact Clifford-Klein form if rank G - rank K < rank H - rank K_H. We solve this conjecture affirmatively. We app...
We discuss Euclidean geometries in AdS$_3$ whose Lorentzian slicing gives rise to closed baby universes with a spatial geometry given by genus $g\geq 2$ surfaces. Our setup only involves a two-dimensional holographic CFT defined on a higher genus Rie...
The geometry very near the horizon of a near-extreme Reissner-Nordstrom black hole is described by the direct product of a near-$AdS_2$ spacetime with a two-sphere. While near-$AdS_2$ is locally diffeomorphic to $AdS_2$ the two connect differently wi...
In 2002, Isenberg-Mazzeo-Pollack (IMP) constructed a series of vacuum initial data sets via a gluing construction. In this paper, we investigate some local geometry of these initial data sets as well as implications regarding their spacetime developm...
A compact Polish foliated space is considered. Part of this work studies coarsely quasi-isometric invariants of leaves in some residual saturated subset when the foliated space is transitive. In fact, we also use "equi-" versions of this kind of inva...
Covering the face and all body parts, sometimes the only evidence to identify a person is their hand geometry, and not the whole hand- only two fingers (the index and the middle fingers) while showing the victory sign, as seen in many terrorists vide...
Implementation of a STEAM Makerspace to dynamize the teaching and learning processes of mathematics (with emphasis on geometry) of second-year students in the upper secondary level....
[CVPR 2025 Best Paper Award] VGGT: Visual Geometry Grounded Transformer (⭐ 12529)
Use the combined power of the Desmos Calculator and native construction and transformations tools to explore geometry as never before. Jump into a new dimension of math. Have you ever felt like two …
Smartphone-based earthquake early warning systems implemented by citizen science initiatives are characterized by a significant variability in their smartphone network geometry. This has an direct impact on the earthquake detection capability and per...
We prove a universal property for blow-ups in regularly immersed subschemes, based on a notion we call "virtual effective Cartier divisor". We also construct blow-ups of quasi-smooth closed immersions in derived algebraic geometry....
Human perception for effective object tracking in 2D video streams arises from the implicit use of prior 3D knowledge and semantic reasoning. In contrast, most generic object tracking (GOT) methods primarily rely on 2D features of the target and its...
The carousel model of pulsar emission attributes the phenomenon of subpulse drifting to a set of discrete sparks located very near the stellar surface rotating around the magnetic axis. Here, we investigate the subpulse drifting behaviour of PSR B003...
Naked singularities are hypothetical astrophysical entities featuring gravitational singularities without event horizons. In this study, we analyze the shadow properties of Kerr Modified Gravity (Kerr MOG) naked singularities (KMNSs). We show that th...
Newman-Janis algorithm for Kerr-Newman geometry is reanalyzed in the light of Cartan calculus....
In most mathematical work beyond practical geometry, angles are typically measured in radians rather than degrees. This is for a variety of reasons; for example, the trigonometric functions …