Related papers: Relation between the two geometric Satake equivale…
Working in the framework of nilpotent geometry, we give a unified scheme for the equivalence problem of geometric structures which extends and integrates the earlier works by Cartan, Singer-Sternberg, Tanaka, and Morimoto. By giving a new…
For Schroedinger operators with long-range magnetic vector potentials and short-range electric scalar potentials in an exterior domain $\Omega$ in ${\bf R}^n$ with $n \geq 2$, we show that there is a one-to-one correspondence between the…
Let $k$ be an algebraically closed field of characteristic $p$. Denote by $W(k)$ the ring of Witt vectors of $k$. Let $F$ denote a totally ramified finite extension of $W(k)[1/p]$ and $\mathcal{O}$ the its ring of integers. For a connected…
Given Z-graded rings A and B, we study when the categories gr-A and gr-B are equivalent. We relate the Morita-type results of Ahn-Marki and del Rio to the twisting systems introduced by Zhang. Using Z-algebras, we obtain a simple proof of…
We show that one can construct two equivalent gauge theories from a linking theory and give a general construction principle for linking theories which we use to construct a linking theory that proves the equivalence of General Relativity…
The appearance of two geometries in one and the same gravitational theory is familiar. Usually, as in the Brans-Dicke theory or in string theory, these are conformally related Riemannian geometries. Is this the most general relation between…
We prove a result comparing the rationality of some elementary algebraic cycles introduced by Alexander Vishik, defined on orthogonal grassmannians, with the rationality of some algebraic cycles defined on fiber products of the…
The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach.
In this article, we develop the theory of stratified perverse Nori motives to prove a refinement of the geometric Satake equivalence of Mirkovi\'c-Vilonen, for which we call the Nori motivic Satake equivalence, in contrast to the "Tate…
We examine the relation between supersymmetric lattice gauge theories constructed by the link approach and by orbifolding and show that they are equivalent. We discuss the number of preserved supersymmetries.
We review the status of recent investigations on validating the gauge-gravity duality conjecture through numerical simulations of strongly coupled maximally supersymmetric thermal gauge theories. In the simplest setting, the gauge-gravity…
This article proves, in the case of split groups over arbitrary fields, that all fibers of convolution morphisms attached to parahoric affine flag varieties are paved by products of affine lines and affine lines minus a point. This applies…
In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.
We study some aspects of linearized gravity as gauge theory, with massive deformation. Recently it has been shown that there are two distinct solutions, which represent physical massive gravity. The purpose of the present work is to show…
Let $G$ be a generically reductive group over a smooth projective curve $X$ over a finite field. For any finite set $I$, we show that nearby cycles commute with proper direct image from stacks of shtukas to $X^I$. This generalizes some…
Sagnac effect has been studied in terms of Gyroscopic system in both Lorentz frame as well as flat Einstein frame. The Einstein equivalence principle has been used to determine the phase shift due to pseudo force in the transformation from…
Only very recently a trigonometric proof of the Pythagoras theorem was given by Zimba \cite{1}, many authors thought this was not possible. In this note we give other trigonometric proofs of Pythagoras theorem by establishing,…
A description of how a theory of gravity can be considered as a gauge theory (in the sense of Trautman) of the Poincare' group is given. As a result, it is shown that a gauge theory of this kind is consistent with the Equivalence Principle…
We prove that if two Calabi-Yau invertible pencils have the same dual weights, then they share a common factor in their zeta functions. By using Dwork cohomology, we demonstrate that this common factor is related to a hypergeometric…
Geometric vertex algebras are a simplified version of Huang's geometric vertex operator algebras. We give a self-contained account of the equivalence of geometric vertex algebras with Z-graded vertex algebras.