We show that the variance of the number of simultaneous zeros ofm i.i.d. Gaussian random polynomials of degree N in an open set U ⊂ C with smooth boundary is asymptotic to N νmm Vol(∂U), where νmm is a universal constant depending only on the dimension m. We also give formulas for the variance of the volume of the set of simultaneous zeros in U of k < m random degree-N polynomials on C. Our res...

In this paper, we continue a study of simplicial commutative algebras with finite André-Quillen homology, that was begun in [19]. Here we restrict our focus to simplicial algebras having characteristic 2. Our aim is to find a generalization of the main theorem in [19]. In particular, we replace the finiteness condition on homotopy with a weaker condition expressed in terms of nilpotency for the...

Nilpotency for discrete groups can be defined in terms of central extensions. In this paper, the analogous definition for spaces is stated in terms of principal fibrations having infinite loop spaces as fibers, yielding a new invariant we compare with classical cocategory, but also with the more recent notion of homotopy nilpotency introduced by Biedermann and Dwyer. This allows us to character...

Let K be a field of positive characteristic p and KG the group algebra of a group G. It is known that if KG is Lie nilpotent then its upper (or lower) Lie nilpotency index is at most |G| + 1, where |G| is the order of the commutator subgroup. The class of groups G for which these indices are maximal or almost maximal have already been determined. Here we determine G for which upper (or lower) L...

Abstract Zero-divisor codes are constructed using group rings where their generators zero-divisors. Generally, zero-divisor can be equivalent despite associated groups non-isomorphic, leading to the proposed conjecture “Every dihedral code has an form of cyclic code”. This paper is devoted study equivalence in $$F_2G$$ <mml:ms...

Numerous scientific texts insist on safe topical application of specific herbal products like those containing Boswellia oleogumresin, but adverse effects arising during clinical trials of herbal medicines give the opportunity to clarify the blind spots in the area of drug safety. A 36-year-old woman without allergic background had two burn wounds because of hot oil. Her hand's wound w...

We prove that the existence of a homogeneous invariant of degree n for a representation of a semi-simple Lie group guarantees the existence of non-trivial solutions of D α = 0: these correspond to the maximum value of the square of the invariant divided by the norm of the representation to the n th power.

We study orbifold Gromov–Witten invariants of the r -th root stack X D , with a pair mid-ages when is sufficiently large. prove that genus g k / and 1 ? are polynomials in i -coefficients degree bounded by 2 . Moreover, zero independent choice mid-ages. As an application, we obtain identity for relative theory which can be viewed as modified version usual loop axiom.