Related papers: Excavation Problems in Elamite Mathematics
We describe a tabulation of (conjecturally) modular elliptic curves over the field Q(sqrt(5)) up to the first curve of rank 2. Using an efficient implementation of an algorithm of Lassina Dembele, we computed tables of Hilbert modular forms…
In this review, we count and classify certain sublattices of a given lattice, as motivated by crystallography. We use methods from algebra and algebraic number theory to find and enumerate the sublattices according to their index. In…
We provide a geometric proof of the Schubert calculus interpretation of the Horn conjecture, and show how the saturation conjecture follows from it. The geometric proof gives a strengthening of Horn and saturation conjectures. We also…
We study relations between special elliptic isometries in the complex hyperbolic plane. Relations of lengths 2, 3, and 4 are fully classified. Some relative SU(2,1)-character varieties of the quadruply punctured sphere are described and…
We describe an approach to the question of finding real solutions to problems of enumerative geometry, in particular the question of whether a problem of enumerative geometry can have all of its solutions be real. We give some methods to…
We study elliptic fibrations that geometrically engineer an SU(2)$\times$ G$_2$ gauge theory realized by Weierstrass model for the collision III+$\text{I}_0^{*\text{ns}}$. We construct the four possible crepant resolutions of such a…
Straightedge and compass construction problems are one of the oldest and most challenging problems in elementary mathematics. The central challenge, for a human or for a computer program, in solving construction problems is a huge search…
I review some marginal deformations of SU(2) and SL(2,R) Wess-Zumino-Witten models, which are relevant for the investigation of the moduli space of NS5/F1 brane configurations. Particular emphasis is given to the asymmetric deformations,…
The class number divisibility problem for number fields is one of the classical problems in algebraic number theory, which originated from Gauss' class number conjectures. The relation between the points on an elliptic curve and class…
We study the Hermitian hull of a particular family of generalized Reed-Solomon codes. The problem of computing the dimension of the hull is translated to a counting problem in a lattice. By solving this problem, we provide explicit formulas…
This essay contains three parts. The first part of essay focuses on the hypothesis of the functional semantic constructions (FSC-Hypothesis). This hypothesis explains that a language, a number, a money are the functional semantic…
The JCMT Gould Belt Survey was one of the first Legacy Surveys with the James Clerk Maxwell Telescope in Hawaii, mapping 47 square degrees of nearby (< 500 pc) molecular clouds in both dust continuum emission at 850 $\mu$m and 450 $\mu$m,…
It is known that all modular forms on $SL_2(Z)$ can be expressed as a rational function in $\eta(z)$, $\eta(2z)$ and $\eta(4z)$. By using a theorem by Gordon, Hughes, and Newman, and calculating the order of vanishing, we can compute the…
This note covers two parts. The first one provides an errata to the paper "Numerical and analytical modeling of busbar systems". We mainly give the correction for three equations affected by a typographical mistake. Despite the corrections…
This thesis pertains to the study of elliptic and parabolic partial differential equations on "thin" structures. The first main objective is to establish the strong and weak low-dimensional counterparts of the parabolic Neumann problem. The…
We construct some new Integrable Systems (IS) both classical and quantum associated with elliptic algebras. Our constructions are partly based on the algebraic integrability mechanism given by the existence of commuting families in skew…
In this review the foundations of Geometric Quantization are explained and discussed. In particular, we want to clarify the mathematical aspects related to the geometrical structures involved in this theory: complex line bundles, hermitian…
In this short paper we propose four conjectures in synthetic geometry that generalize Erdos-Mordell Theorem, and three conjectures in number theory that generalize Fermat Numbers.
Expressions are given for the elliptic genera of the Kazama-Suzuki models associated with hermitian symmetric spaces when the problems of field identifications are absent. We use the models' known Coulomb gas descriptions.
A construction of integration, function calculus, and exterior calculus is made, allowing for integration of unital magma valued functions against (compactified) unital magma valued measures over arbitrary topological spaces. The Riemann…