Related papers: Gorenstein property for phylogenetic trivalent tre…
In this paper, we show that the Gorenstein global dimension of trivial ring extensions is often infinite. Also we study the transfer of Gorenstein properties between a ring and its trivial ring extensions. We conclude with an example…
We obtain analogues of classical results on automorphism groups of holomorphic fiber bundles, in the setting of group schemes. Also, we establish a lifting property of the connected automorphism group, for torsors under abelian varieties.…
The existence of the Gorenstein projective precovers over arbitrary rings is an open question. It is known that if the ring has finite Gorenstein global dimension, then every module has a Gorenstein projective precover. We prove here a…
The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we…
We provide a fundamental result for bucket increasing trees, which gives a complete characterization of all families of bucket increasing trees that can be generated by a tree evolution process. We also provide several equivalent…
In previous work, the authors introduced the ozone group of an associative algebra as the subgroup of automorphisms which fix the center pointwise. The authors studied PI skew polynomial algebras, using the ozone group to understand their…
Polystability of (twisted) Stokes representations (i.e. wild monodromy representations) will be characterised, in terms of the corresponding differential Galois group (generalising the Zariski closure of the monodromy group in the tame…
In this paper we develop Host--Kra and inverse Gowers theory for abelian groups of bounded exponent. We show that the Host--Kra factors $Z^{\leq k}(\mathrm{X})$ associated with actions of such groups admit extensions with the structure of…
We introduce families of two-parameter multivariate polynomials indexed by pairs of partitions $v,w$ -- biaxial double $(\beta,q)$-Grothendieck polynomials -- which specialize at $q=0$ and $v=1$ to double $\beta$-Grothendieck polynomials…
We develop the Dirac-Schwinger-Zwanziger (DSZ) quantization of classical abelian gauge theories with general duality structure on oriented Lorentzian four-manifolds $(M,g)$ of arbitrary topology, obtaining, as a result, the…
The higher connectivity at infinity for mapping class groups of surfaces with boundary components and punctures is understood with the exceptions of the mapping class groups for the closed surfaces of genus 3 and 4. In this paper we prove a…
The purpose of this paper is to exhibit infinite families of conjugate projective curves in a number field whose complement have the same abelian fundamental group, but are non-homeomorphic. In particular, for any $d>3$ we find Zariski…
We describe Galois connections which arise between two kinds of combinatorial structures, both of which generalize trees with labelled leaves, and then apply those connections to a family of polytopes. The graphs we study can be imbued with…
In this paper, we examine the relation between certain subclasses of the classes of Gorenstein projective, Gorenstein flat and Gorenstein injective modules over a group algebra, which consist of the cofibrant, cofibrant-flat and fibrant…
We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval…
In this second paper, we look at the following question: are the properties of the trees associated to the tilings $\{p,4\}$ and $\{p$+$2,3\}$ of the hyperbolic plane still true if we consider a finitely generated tree by the same rules but…
A group $G$ has property $R_\infty$ if for every $\phi\in Aut(G)$, there are an infinite number of $\phi$-twisted conjugacy classes of elements in $G$. In this note, we determine the $R_\infty$-property for $G=\pi_1(M)$ for all geometric…
We consider a multitype Galton-Watson process that allows for the mutation and reversion of individual types in discrete and continuous time. In this setting, we explicitly compute the time evolution of quantities such as the mean and…
We study, using the language of log schemes, the problem of extending biextensions of smooth commutative group schemes by the multiplicative group. This was first considered by Grothendieck in SGA 7. We show that this problem admits a…
Masbaum and Vaintrob's "Pfaffian matrix tree theorem" implies that counting spanning trees of a 3-uniform hypergraph (abbreviated to 3-graph) can be done in polynomial time for a class of "3-Pfaffian" 3-graphs, comparable to and related to…