Related papers: Lattices in function fields and applications
Geometric structures on manifolds became popular when Thurston used them in his work on the geometrization conjecture. They were studied by many people and they play an important role in higher Teichm\"uller theory. Geometric structures on…
We consider various inequalities for polynomials, with an emphasis on the most fundamental inequalities of approximation theory. In the sequel a key role is played by the generalized Minkowski functional \alpha(K,x), already being used by…
In this project we initiate an investigation of the applicability of Quasi-Monte Carlo methods to lattice field theories in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an…
Let $X$ be an $n$-dimensional manifold and $V_1,\ldots,V_n\subset C^\infty(X,\mathbb R)$ finite-dimensional vector spaces. For systems of equations $\{f_i = a_i\colon\: f_i\in V_i,\:a_i \in\mathbb R,\:i=1,\ldots,n\}$ we discover a…
The lattice size of a lattice polygon $P$ was introduced and studied by Schicho, and by Castryck and Cools in relation to the problem of bounding the total degree and the bi-degree of the defining equation of an algebraic curve. In this…
We review results on several interesting phenomena in warped compactifications of M theory, as presented at Strings 2000. The behavior of gauge fields in dimensional reduction from $d+1$ to $d$ dimensions in various backgrounds is explained…
We combine functional analytic and geometric viewpoints on approximate Birkhoff and isosceles orthogonality in generalized Minkowski spaces which are finite-dimensional vector spaces equipped with a gauge. This is the first approach to…
We study fixed points of a function arising in a representation theory of the Drinfeld modules by the bounded linear operators on a Hilbert space. We prove that such points correspond to number fields of the class number one. As an…
Coincidence Site Lattices (CSLs) are a well established tool in the theory of grain boundaries. For several lattices up to dimension $d=4$, the CSLs are known explicitly as well as their indices and multiplicity functions. Many of them…
Fourier transforms of Lorentz invariant functions in Minkowski space, with support on both the timelike and the spacelike domains are performed by means of direct integration. The cases of 1+1 and 1+2 dimensions are worked out in detail,…
We construct convergent and divergent lattices in negative curvature and give a precise asymptotic description of the behavior of their counting function.
The communications and interrelations between different locations on the Earth's surface have far-reaching implications for both social and natural systems. Effective spatial analytics ideally require a spatial representation, where…
It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…
The Minkowski problem in convex geometry concerns showing that a given Borel measure on the unit sphere is, up to perhaps a constant, some type of surface area measure of a convex body. Two types of Minkowski problems in particular are an…
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…
In connection with an unsolved problem of Bang (1951) we give a lower bound for the sum of the base volumes of cylinders covering a d-dimensional convex body in terms of the relevant basic measures of the given convex body. As an…
The author defines and analyzes the $1/k$ length spectra, $L_{1/k}(M)$, whose union, over all $k\in \NN$ is the classical length spectrum. These new length spectra are shown to converge in the sense that $\lim_{i\to\infty} L_{1/k}(M_i)…
With the help of the recently introduced parametric geometry of numbers by W. M. Schmidt and L. Summerer, we prove a strong version of a conjecture of Schmidt concerning the successive minima of a lattice.
Support material for lectures at the May '25 Galileo Galilei Institute school on asymptotic sym- metries and flat holography. Contains an introduction to Noether theorem for gauge theories and gravity, covariant phase space formalism,…
We consider feasibility and constrained optimization problems defined over smooth and/or strongly convex sets. These notions mirror their popular function counterparts but are much less explored in the first-order optimization literature.…