Related papers: The Andreadakis Problem for the McCool groups

The McCool group has families of subgroups such as the ordinary pure braid group, the upper triangular McCool group and the partial inner automorphism group. The generalized Andreadakis conjecture holds for the ordinary pure braid group and…

Let $F\_n$ be the free group on $n$ generators. Consider the group $IA\_n$ of automorphisms of $F\_n$ acting trivially on its abelianization. There are two canonical filtrations on $IA\_n$: the first one is its lower central series…

Let $F\_n$ be the free group on $n$ generators. Consider the group $IA\_n$ of automorpisms of $F\_n$ acting trivially on its abelianization. There are two canonical filtrations on $IA\_n$: the first one is its lower central series…

In the degree-diameter problem for Abelian Cayley and circulant graphs of diameter 2 and arbitrary degree d there is a wide gap between the best lower and upper bounds valid for all d, being quadratic functions with leading coefficient 1/4…

We show that the argument of Alexander and McTague, that the bcc crystalline structure is favored in those crystallization processes where the first order character is not too pronounced, is not correct. We find that any solution that…

This note proves an upper bound for the fluctuations of a second-class particle in the totally asymmetric simple exclusion process. The proof needs a lower tail estimate for the last-passage growth model associated with the exclusion…

In this paper, I correct errors in my paper (Kodai Math. J. (2015)) about gamma filtrations for classifying spaces for abelian p-groups which are not elementary. We also extend Chetard's results for such 2-groups to p-groups for odd prime.

The outer automorphism group Out(G) of a group G acts on the set of conjugacy classes of elements of G. McCool proved that the stabilizer $Mc(c_1,...,c_n)$ of a finite set of conjugacy classes is finitely presented when G is free. More…

This paper considers the degree-diameter problem for undirected circulant graphs. The focus is on extremal graphs of given (small) degree and arbitrary diameter. The published literature only covers graphs of up to degree 7. The approach…

The paper studies analytic functors between presheaf categories. Generalising results of A. Joyal and of R. Hasegawa for analytic endofunctors on the category of sets, we give two characterisations of analytic functors between presheaf…

We show that the cuspidal component of the stable trace formula of a special odd orthogonal group over a number field, satisfies a weak form of beyond endoscopic decomposition. We also study the $r$-stable trace formula, when $r$ is the…

We establish a sharp lower-bound for the number of conjugacy classes $k(A_n)$ in the alternating group $A_n$, for $n \geq 3$. Namely, we show that $k\left(A_n\right) \geq \frac{k\left(A_7\right)}{\log_2\left|A_7\right|} \cdot…

This contribution is concerned with the effective viscosity problem, that is, the homogenization of the steady Stokes system with a random array of rigid particles, for which the main difficulty is the treatment of close particles. Standard…

The main aim of this paper is the investigation of the stability problem for ordinary delay differential equations. More precisely, we would like to study the following problem. Assume that for a continuous function a given delay…

This paper deals with a nonlinear degenerate parabolic equation of order $\alpha$ between 2 and 4 which is a kind of fractional version of the Thin Film Equation. Actually, this one corresponds to the limit value $\alpha=4$ while the Porous…

We use isoperimetric inequalities combined with a new technique to prove upper bounds for the site percolation threshold of plane graphs with given minimum degree conditions. In the process we prove tight new isoperimetric bounds for…

The paper investigates the stability properties of restrictions of irreducible representations of the symmetric group to the hyperoctahedral subgroup. A stability result is obtained, analogous to the classical Murnaghan theorem on the…

Let $G$ be a finite group and $P$ a Sylow $2$-subgroup of $G$. We obtain both asymptotic and explicit bounds for the number of odd-degree irreducible complex representations of $G$ in terms of the size of the abelianization of $P$. To do…

In this note we consider the coniveau filtration on the Grothendieck group of a regular separated noetherian scheme and its behavior with respect to the multiplication and the lambda ring structure. We show that a weak multiplicativity…

In this short note, we give a lower bound on the number of congruence classes of triangles in a small set of points in $\mathbb{F}_p^2$. More precisely, for $\mathcal{A}\subset \mathbb{F}_p^2$ with $|\mathcal{A}|\le p^{2/3}$, we prove that…