We construct a new grading on the Goldman Lie algebra of a closed oriented surface by the winding number. This grading induces a grading on the HOMFLY-PT skein algebra and related algebras. Our work supports the conjectures of B. Cooper and P. Samuel...
SIDH is a post-quantum key exchange algorithm based on the presumed difficulty of finding isogenies between supersingular elliptic curves. However, SIDH and related cryptosystems also reveal additional information: the restriction of a secret isogeny...
This paper presents division polynomials for twisted Edwards curves. Their chief property is that they characterise the $n$-torsion points of a given twisted Edwards curve. We also present results concerning the coefficients of these polynomials, w...
We consider algebraic affine and projective curves of Edwards \cite{E, SkOdProj} over a finite field $\text{F}_{p^n}$. Most cryptosystems of the modern cryptography \cite{SkBlock} can be naturally transform into elliptic curves \cite{Kob}. We researc...
Letting $p$ vary over all primes and $E$ vary over all elliptic curves over the finite field $\mathbb{F}_p$, we study the frequency to which a given group $G$ arises as a group of points $E(\mathbb{F}_p)$. It is well-known that the only permissible g...
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V446 Her is the best example of an old nova which has developed dwarf nova eruptions in the post-nova state. We report on observed properties of the long-term light curve of V446 Her, using photometry over 19 years. Yearly averages of the outburst ma...
A global action is an algebraic analogue of a topological space. It consists of group actions $G_α\curvearrowright X_α$, $(α\inΦ)$, which fulfill a certain compatibility condition. We investigate the homotopy theory of global actions. The main re...
Load curve data in power systems refers to users' electrical energy consumption data periodically collected with meters. It has become one of the most important assets for modern power systems. Many operational decisions are made based on the informa...
In this paper we discuss the difficulties of mounting successful attack against crypto implementations when essential information is missing. We start with a detailed description of our attack against our own design, to highlight which information is...
We study very small trees from the point of view of reducing systems of free factors, which are analogues of reducing systems of curves for a surface lamination; a non-trivial, proper free factor $F \leq \FN$ reduces $T$ if and only if $F$ acts on so...
We give a description of the boundary of a complex of free factors that is analogous to E. Klarreich's description of the boundary of a curve complex. The argument uses the geometry of folding paths developed by Bestvina and Feighn as well as structu...
We study tropical Tevelev degrees arising from maps between certain tropical moduli spaces of curves. Building on work of Dawson and Cavalieri, who defined and computed tropical Tevelev degrees in the case of degree $d = g+1$ and $n = g+3$ marked poi...
This paper provides specific results on the Igusa local zeta function for the curves $x^n+y^m$. In addition to specific results, we give an introduction to $p$-adic analysis and a discussion of various methods which have been used to compute these ze...
Core Animation Examples (Basics, Replicator, Reflection, Wiggle Jiggle, Lissajous Curve, Sine Wave, etc.) (⭐ 250)
In a series of papers, published in Mathematische Annalen, Bianchi and Blumenthal introduced the notions of Bianchi orbifolds and Hilbert-Blumnethal surfaces as generalizations of modular curves associated to quadratic fields. In this paper, in the s...
The canonical ring $S_D = \bigoplus_{d \geq 0} H^0(X, \lfloor dD \rfloor)$ of a divisor D on a curve X is a natural object of study; when D is a Q-divisor, it has connections to projective embeddings of stacky curves and rings of modular forms. We st...
We describe a method for determining the limb polarization and limb darkening of stars in eclipsing binary systems, by inverting photometric and polarimetric light curves. Because of the ill-conditioning of the problem, we use the Backus-Gilbert...
This paper focuses on packaging design using origami techniques, specifically designs incorporating curves, known as pillow boxes. While conventional paper packaging boxes are typically cuboid, pillow box designs include curved surfaces, offering bot...
A handlebar moustache is a moustache with particularly lengthy and upwardly curved extremities. These moustache styles are named for their resemblance