Related papers: Enumerating Regular Objects associated with Suzuki…

We present an algorithm to compute the automorphism group of a Mori dream space. As an example calculation, we determine the automorphism groups of singular cubic surfaces with general parameters. The strategy is to study graded…

We construct a new class of affine complements ${\mathbb P}^M\setminus S$ with the trivial group of automorphisms, where $S\subset {\mathbb P}^M$ is a rational hypersurface, $M$ is odd and $M\geqslant 5$.

Following Penrose, we introduce a family of graph functions defined in terms of contractions of certain products of symmetric tensors along the edges of a graph. Special cases of these functions enumerate edge colorings and cycles of…

We characterize groups with Guoliang Yu's property A (i.e., exact groups) by the existence of a family of uniformly bounded representations which approximate the trivial representation.

In this paper we give a complete description of all possible automorphism groups of real $\mathbb{R}$-rational del Pezzo surfaces $X$ of degree $4$, using the description of $X$ as the blow-up of some smooth real quadric surface $Q$ in…

We show that amenability of a group acting by homeomorphisms can be deduced from a certain local property of the action and recurrency of the orbital Schreier graphs. This covers amenability of a wide class groups, the amenability of which…

In any category with a reasonable notion of cover, each object has a group of scissors automorphisms. We prove that under mild conditions, the homology of this group is independent of the object, and can be expressed in terms of the…

A simple surface amalgam is the union of a finite collection of surfaces with precisely one boundary component each and which have their boundary curves identified. We prove if two fundamental groups of simple surface amalgams act properly…

Let $S$ be a compact Riemann surface and $G$ a group of conformal automorphisms of $S$ with $S_0 = S/G$. $S$ is a finite regular branched cover of $S_0$. If $U$ denotes the unit disc, let $\Gamma$ and $\Gamma_0$ be the Fuchsian groups with…

Using suitable convex functions, we construct a new family of flat Minkowski planes whose automorphism groups are at least $3$-dimensional. These planes admit groups of automorphisms isomorphic to the direct product of $\mathbb{R}$ and the…

We classify rational surfaces for which the image of the automorphisms group in the group of linear transformations of the Picard group is the largest possible. This answers a question raised by Arthur Coble in 1928, and can be rephrased in…

This document is a practical guide to computations using an automatic structure for the mapping class group of a once-punctured, oriented surface $S$. We describe a quadratic time algorithm for the word problem in this group, which can be…

In this article we overview those aspects of the theory of affine semigroups and their algebras that have been relevant for our own research, and pose several open problems. Answers to these problems would contribute substantially to the…

Let $G_{n}$ be the dicyclic group of order $4n$. We observe that, up to isomorphisms, (i) for $n \geq 2$ even there is exactly one regular dessin d'enfant with automorphism group $G_{n}$, and (ii) for $n \geq 3$ odd there are exactly two of…

Let X be a smooth complex projective surface. We prove that for any sufficiently big m there exists a rational dominant map f from X into a complex rational ruled surface Y, such that f is generically finite of degree m and has monodromy…

We study quartic surfaces that admit a group of projective automorphisms isomorphic to icosahedron group.

We use intersections with horizontal manifolds to show that high-dimensional cycles in the Heisenberg group can be approximated efficiently by simplicial cycles. This lets us calculate all of the higher-order Dehn functions of the…

We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such…

We give a $q$-enumeration of circular Dyck paths, which is a superset of the classical Dyck paths enumerated by the Catalan numbers. These objects have recently been studied by Alexandersson and Panova. Furthermore, we show that this…

In this paper we investigate the $directed$ $normalizing$ $graph$ associated with a group $G$, defined as the simple directed graph whose vertices are the elements of $G$, with an arrow from $x$ to $y$ whenever the subgroup $\langle x…