Related papers: Hilbert-Kunz multiplicities and the F-signature
We use the results of our paper "p-Fractals and power series--I" (Journal of Algebra 280, 2004, pp. 505--536) to prove the rationality of the Hilbert-Kunz series of a large family of power series, including those of the form \sum_i…
This is a survey article on the invariant rings of Hopf actions
This paper continues the work which attempts to understand the general properties of the graded algebras associated with Hecke symmetries without a restriction on the parameter q of the Hecke relation imposed in earlier results.
The more recent paper "Generic strange duality for K3 surfaces" by the authors contains stronger results.
A few remarks on hep-ph/9612213 are given.
This paper concerns the question of whether a more direct limit can be used to obtain the limit Hilbert-Kunz multiplicity, a possible candidate for a characteristic zero Hilbert-Kunz multiplicity. The main goal is to establish an…
This is a survey article on classical groups (over arbitrary division rings) and their geometries.
This is an expository article for the Encyclopedia of Mathematical Physics on the subject in the title.
In this note we first give a new bound on $e_{HK}(\sim)$ the Hilbert-Kunz multiplicity of invariant rings, by the help of the Noether's bound. Then, we simplify, extend and present applications of the reciprocity formulae due to L. Smith.…
In this survey, we give a short overview of the recent progress on the multidimensional L2 conjecture. It can also serve as an introduction to the subject.
Boltzmann's work, ``Ueber die sogenannte H-Curve," discusses his demonstration of the essential characteristics of the H-curve in a clear, concise, and precise style, showcasing his efforts to persuade his peers. To make these findings more…
This is a survey paper of the theory of crystal bases, global bases and the cluster algebra structure on the quantum coordinate rings.
We present results on the Watanabe-Yoshida conjecture for the Hilbert-Kunz multiplicity of a local ring of positive characteristic. By improving on a "volume estimate" giving a lower bound for Hilbert-Kunz multiplicity, we obtain the…
Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.
This is a survey of results, both classical and recent, on behaviour of plurisubharmonic functions near their $-\infty$-points, together with the related topics for positive closed currents.
This is a survey on stated skein algebras and their representations.
We give a closed-form formula for the Hilbert function of the tangent cone at the identity of a Schubert variety X in the Grassmannian in both group theoretic and combinatorial terms. We also give a formula for the multiplicity of X at the…
The article provides a brief survey of the mathematics of some of the newly being developed so called "hybrid" (also called "multi-physics" or "multi-wave") imaging techniques.
Elementary review article on quantum cryptography.
This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular we tried to extend this concept and prove some theorems.