Andrew Sale

I have two principal strands of research. One involves Max Dehn's conjugacy problem, looking for ways to use the geometry of groups to understand more about the nature of conjugacy in infinite groups. In a different direction I have been investigating the properties of outer automorphism groups of graph products, such as right-angled Artin groups. I also have a couple of papers on wreath products, for example, with Ben Hayes, we showed that the wreath product of two sofic groups is sofic.

Scroll down, or click for: Preprints, Publications, Thesis.

Preprints:

• On virtual indicability and property (T) for outer automorphism groups of RAAGs,
  arXiv


• Outer automorphism groups of graph products: subgroups and quotients, with Tim Susse
  arXiv, to appear in Pacific Journal of Mathematics.

Publications:

• Calculating the virtual cohomological dimension of the automorphism group of a RAAG, with Matt Day and Ric Wade
  arXiv, Bulletin of the LMS (2020).


• The outer automorphism group of a RACG is either large or virtually abelian, with Tim Susse
  arXiv, MathSciNet, Transactions of the AMS (2019).


• Metric approximations of wreath products, with Ben Hayes
  arXiv, MathSciNet, Annales de l'Institut Fourier (2018).


• Vastness properties of automorphism groups of RAAGs, with Vincent Guirardel
  arXiv, MathSciNet, Journal of Topology (2018).


• Permute and conjugate: the conjugacy problem in relatively hyperbolic groups, with Yago Antolín
  arXiv, MathSciNet, Bulletin of the LMS (2016).


• Conjugacy length in group extensions,
  arXiv, MathSciNet, Communications in Algebra (2016).


• The geometry of the conjugacy problem in lamplighter groups,
  arXiv, MathSciNet, Algebra and Computer Science, AMS Contemporary Math (2016).


• The geometry of the conjugacy problem in wreath products and free solvable groups,
  arXiv, MathSciNet, Journal of Group Theory (2015).


• Palindromic width of wreath products, metabelian groups, and max-n solvable groups, with Tim Riley
  arXiv, MathSciNet, Groups Complexity Cryptology (2015).


• Metric behaviour of the Magnus embedding,
  arXiv, MathSciNet, Geometriae Dedicata (2015).


• Bounded Conjugators For Real Hyperbolic and Unipotent Elements in Semisimple Lie Groups,
  arXiv, MathSciNet, Journal of Lie Theory (2014).

Thesis

My DPhil thesis, supervised by Cornelia Drutu, is available here.

The Length of Conjugators in Solvable Groups and Lattices of Semisimple Lie Groups, University of Oxford, Dec 2012.

Other papers:

• The wreath product of two sofic groups is sofic, with Ben Hayes
  arXiv.
  

  This paper was the initial version of what later became Metric approximations of wreath products (2018; arXiv link). It is notably shorter at 8 pages, and much of the technical details required for generalising the result are not needed here. Any reader interested only in the result for sofic groups may find it easier to start here.



• Short conjugators in solvable groups,
  arXiv.
  

All results in this paper were either generalised in the sequel Conjugacy length in group extensions (2016; arXiv link), or can be found in The geometry of the conjugacy problem in lamplighter groups (2016; arXiv link).

---