Related papers: Integral points on affine surfaces fibered over $\…
We present surface normal estimation using a single near infrared (NIR) image. We are focusing on fine-scale surface geometry captured with an uncalibrated light source. To tackle this ill-posed problem, we adopt a generative adversarial…
Ultra-fine-grained image recognition (UFGIR) categorizes objects with extremely small differences between classes, such as distinguishing between cultivars within the same species, as opposed to species-level classification in fine-grained…
In the article it was shown the convergence of special integral of two dimensional Terry's problem. Main tools of the article are an investigation of real algebraic varieties and estimations of areas of algebraic surfaces.
We contribute a new algebraic method for computing the orthogonal projections of a point onto a rational algebraic surface embedded in the three dimensional projective space. This problem is first turned into the computation of the finite…
Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces that we call discrete affine minimal surfaces. We show that…
This is a book aimed at graduate students and researchers in symplectic geometry, based on a course I taught in 2019. The primary message is that the base of a Lagrangian torus fibration inherits an integral affine structure, which you can…
We construct locally recoverable codes with hierarchy from surfaces in $\mathbb{A}^3$ admitting a fibration by curves of Artin-Schreier or Kummer type. We derive the parameters of our codes by leveraging the geometry and arithmetic of the…
A surface integral equation solver is proposed for fast and accurate simulation of interconnects embedded in stratified media. A novel technique for efficient computation of the multilayer Green's function is proposed. Using the Taylor…
This work focuses on the properties of dusty tori in active galactic nuclei (AGN) derived from the comparison of SDSS type 1 quasars with mid-Infrared (MIR) counterparts and a new, detailed torus model. The infrared data were taken by the…
We present the ongoing development of a commercially available Micron Optics fiber-Fabry Perot Interferometer as a precise, stable, easy to use, and economic spectrograph reference with the goal of achieving <1 m/s long term stability.…
We study slopes of finite cyclic covering fibrations of a fibered surface. We give the best possible lower bound of the slope of these fibrations. We also give the slope equality of finite cyclic covering fibrations of a ruled surface and…
Following Steinberg, we construct an adjoint quotient for the Vinberg semi-group and a section to this quotient. Then, after Ng\^o, we show the existence of a regular centralizer on it and use it to compute the affine Springer fibers for…
Infrared nanospectroscopy based on Fourier transform infrared near-field spectroscopy (nano-FTIR) is an emerging nanoanalytical tool with large application potential for label-free mapping and identification of organic and inorganic…
We study unramified sections of the fundamental group sequence of smooth projective curves of genus $\geq 2$ over $p$-adic fields together with an integral model. We are particularly interested in the induced specialized sections of the…
We characterise integral points of bounded log-anticanonical height on a quartic del Pezzo surface of singularity type $\mathbf{A}_3$ over imaginary quadratic fields with respect to its singularity and its lines. Furthermore, we count these…
We give a general structure theorem for affine A 1-fibrations on smooth quasi-projective surfaces. As an application, we show that every smooth A 1-fibered affine surface non-isomorphic to the total space of a line bundle over a smooth…
We study the geometry of elliptic fibrations satisfying the conditions of Step 2 of Tate's algorithm with a discriminant of valuation 4. We call such geometries USp(4)-models, as the dual graph of their special fiber is the twisted affine…
This research monograph focuses on the arithmetic, over number fields, of surfaces fibred into curves of genus 1 over the projective line, and of intersections of two quadrics in projective space. The first half takes up and develops…
Consider a fibered power of an elliptic surface. We characterize its subvarieties that contain a Zariski dense set of points that are torsion points in fibers with complex multiplication. This result can be viewed as a mix of the…
Fiber-integrated micro-optical elements promise a scalable approach to photon collection and beam shaping for quantum information processing. Here, we demonstrate single-step fabrication of micro-spherical, micro-spiral, and micro-axicon…