Mathematics, St Andrews
Tenure since 2014
Decision Problems in Groups of Homeomorphisms
Shayo's current research can be broadly described as decision problems in groups of homeomorphisms. In particular, he have been focused on some subgroups of the group of homeomorphisms of cantor space.
These are very large groups, and the research entails coming up with algorithms, terminating in a finite time, which decide when elements of these groups have specific properties. These questions, which are easy to solve for finite groups, become a lot more interesting for infinite groups, and often require a good understanding of the structure of the relevant group or of its action on the underlying space to yield nice and efficient solutions.
Thus far, Shayo has investigated successfully the conjugacy problem (deciding when two elements are conjugate) for a group V which lies in a family of these subgroups called the Higman-Thompson groups. Further effort yielded that the Higman-Thompson group all have infinitely many twisted-conjugacy classes. He is now currently working on the order problem (deciding when an element has finite order) in a different, but related subgroup -- the automorphism group of the Higman-Thompson groups.
Shayo is currently a PhD student at the university of St Andrews supervised by Dr Collin Bleak. His interests lie in geometric and combinatorial group theory. Prior to this he completed his undergraduate degree also at the University of St Andrews, throughout which time he attained the Dean's List. Shayo was also privileged to be awarded the Cormack Vacation Scholarship towards an undergraduate research in Solar theory project, supervised by Professor Allen Hood, on the emergence of flux tubes, and sunspot formation.
Shayo attended high school in Paisley at an institution which, coincidentally, is called St Andrews (Academy). While there he was a dux medalist (awarded to students who achieve five A's in their Scottish Highers) and achieved A's in all three advanced higher courses he took.
On a less mathematical note, completing war and peace is quite high on his list of literary achievements.