Related papers: On the conjugacy classes of monomial birational ma…

We classify conjugacy classes of involutions in the isometry groups of nondegenerate, symmetric bilinear forms over the field of two elements. The new component of this work focuses on the case of an orthogonal form on an even dimensional…

Let G be a simple algebraic group over an algebraically closed field k. We classify the spherical conjugacy classes of G.

We give an effective solution of the conjugacy problem for two by two matrices over the polynomial ring in one variable over a finite field.

We explore the relations among quadratic modules, 2-crossed modules, crossed squares and simplicial groups with Moore complex of length 2.

We classify the conjugacy classes of minimally ramified nonabelian subgroups of order 8 in the Nottingham group $N(F_4)$. We then use finite automata to give explicit descriptions of representatives for each of these conjugacy classes.

This paper considers a simple geometric construction, called the Pentagram map. The pentagram map, performed on N-gons, gives rise to a birational mapping on the space of all N-gons. This paper finds what conjecturally are all the…

Using generating functions, we enumerate regular semisimple conjugacy classes in the finite classical groups. For the general linear, unitary, and symplectic groups this gives a different approach to known results; for the special…

We describe the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in terms of the extended Dynkin diagram of the simply connected cover, together with…

Motivated by the study of the Kahan--Hirota--Kimura discretisation of the Euler top, we characterise the growth and integrability properties of a collection of elements in the Cremona group of a complex projective 3-space using techniques…

In this article we show that there are homeomorphisms of plane continua whose conjugacy class is residual and have the shadowing property.

We study finite non-linearizable subgroups of the plane Cremona group which potentially could be stably linearizable.

The classifying spaces of cobordisms of singular maps have two fairly different constructions. We expose a homotopy theoretical connection between them. As a corollary we show that the classifying spaces in some cases have a simple product…

We study automorphism groups of real del Pezzo surfaces, concentrating on finite groups acting minimally on them. As a result, we obtain a vast part of classification of finite subgroups in the real plane Cremona group.

We prove that every topological conjugation between two germs of singular holomorphic curves in the complex plane is homotopic to another conjugation which extends homeomorphically to the exceptional divisors of their minimal…

We describe birational representations of discrete groups generated by involutions, having their origin in the theory of exactly solvable vertex-models in lattice statistical mechanics. These involutions correspond respectively to two kinds…

In this article, we study the properties of conjugacies between polynomial basins. For any conjugacy, there is a quasiconformal conjugacy in the same homotopy class minimizing the dilatation. We compute the precise value of the minimal…

In the paper, I considered construction of algebra of fractions of algebra with conjugation. I also considered algebra of polynomials and algebra of rational mappings over algebra with conjugation.

Given an almost complex manifold (M, J), we study complex connections with trivial holonomy and such that the corresponding torsion is either of type (2,0) or of type (1,1) with respect to J. Such connections arise naturally when…

This paper is, essentially, a survey related to the problem of understanding the combinatorics of the action of the monoidal category of finite dimensional modules over a simple finite dimensional Lie algebra on various categories of Lie…

In this article we consider a restricted orbital counting problem for the action of certain discrete groups on suitable spaces. In particular, we present asymptotics for counting those points in an orbit restricted to a single conjugacy…