We bound the nuclear dimension of crossed products associated to some partial actions finite groups or Z on dimensional locally compact Hausdorff second countable spaces. Our results apply globalizable actions, group minimal automorphisms, and automorphisms acting zero-dimensional spaces, a class one containing 1-dimensional CW complexes. This extends work global systems by Hirshberg Wu.

For mixing Zd-actions generated by commuting automorphisms of a compact abelian group, we investigate the directional uniformity of the rate of periodic point distribution and mixing. When each of these automorphisms has finite entropy, it is shown that directional mixing and directional convergence of the uniform measure supported on periodic points to Haar measure occurs at a uniform rate ind...

We study the structure of length four polynomial automorphisms of R[X, Y ] when R is a UFD. The results from this study are used to prove that if SLm(R[X1, X2, . . . , Xn]) = Em(R[X1, X2, . . . , Xn]) for all n, m ≥ 0 then all length four polynomial automorphisms of R[X, Y ] that are conjugates are stably tame.

We prove that the isomorphism problem for finitely generated fully residually free groups (or F-groups for short) is decidable. We also show that each F-group G has a decomposition that is invariant under automorphisms of G, and obtain a structure theorem for the group of outer automorphisms Out(G).

We discuss central automorphisms of partial linear spaces, particularly those with three points per line. When these automorphisms have order two and their products are restricted to have odd order, we are in the situation of Glauberman's Z∗-theorem. This sheds light on the structure of various coordinatizing loops, particularly Bol and Moufang loops.

We discuss the group of automorphisms of a general MR-algebra. We develop several functors between implication algebras and cubic algebras. These allow us to generalize the notion of inner automorphism. We then show that this group is always isomorphic to the group of inner automorphisms of a filter algebra.

We study whether the basin of attraction of a sequence of automorphisms of Ck is biholomorphic to Ck. In particular we show that given any sequence of automorphisms with the same attracting fixed point, the basin is biholomorphic to Ck if every map is iterated sufficiently many times. We also construct Fatou-Bieberbach domains in C2 whose boundaries are 4-

We present a systematic, rigorous construction of all 70 strongly rational, holomorphic vertex operator algebras $V$ central charge 24 with non-zero weight-one space $V_1$ as cyclic orbifold constructions associated the Niemeier lattice $V_N$ and certain 226 short automorphisms in $\operatorname{Aut}(V_N)$. show that up to algebraic conjugacy these are exactly generalised deep holes, introduced...

Consider cotangent bundles of exotic spheres, with their canonical symplectic structure. They admit automorphisms which preserve the part at infinity of one fibre, and which are analogous to the square of a Dehn twist. Pursuing that analogy, we show that they have infinite order up to isotopy (inside the group of all automorphisms with the same behaviour).

We present a new method to obtain cyclic subcodes of algebraic geometric codes using their automorphisms. Automorphisms of algebraic geometric codes from F. K. Schmidt curves are proposed. We present an application of this method in designing frequency hopping sequences for spread spectrum systems. Algebraic geometric codes can provide sequences longer (better randomness) than the ones from Ree...