Analysis

Analysis

Analysis is an extremely broad mathematical discipline. In Glasgow, research in analysis encompasses partial differential equations, harmonic analysis, complex analysis and operator algebras. The group currently consists of three members of academic staff. More information about our research interests can be found through the links below and information about postdocs, research students, grants and collaborators through the links on the right.

Staff

Dr Christian Voigt  Senior lecturer

Noncommutative geometry; K-theory; Quantum groups

Member of other research groups: Geometry and Topology, Algebra
Research students: Jamie Antoun, Andrew Monk, Samuel Evington

  • Personal Website
  • Publications

    • Dr Stephen J Watson  Lecturer

    The application of new mathematical ideas and new computational paradigms to material science, with an emphasis on self-assembling nano-materials; analysis and numerical analysis of partial differential equations arising in Continuum Physics; Material Science and Geometry.

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems

  • Publications

    • Dr Stuart White  Professor of Mathematics

    C* and von Neumann algebras; rigidity and similarity properties of operator algebras

    Member of other research groups: Geometry and Topology, Algebra
    Research student: Samuel Evington

  • Personal Website
  • Publications

    • Dr Mike Whittaker  Lecturer

    Operator algebras, topological dynamical systems, and noncommutative geometry.

    Member of other research groups: Geometry and Topology, Algebra
    Research students: Dimitrios Gerontogiannis , Mustafa Ozkaraca, Jamie Antoun
    Postgraduate opportunities: Aperiodic substitution tilings and their C*-algebras., Operator algebras associated to self-similar actions.

  • Personal Website
  • Publications

    • Dr Joachim Zacharias  Reader

    C*-algebras, their classification and amenability properties; special examples of C*-algebras; K-theory and non commutative topology, noncommutative dynamical systems, geometric group theory with applications to C*-algebras.

    Member of other research groups: Integrable Systems and Mathematical Physics, Geometry and Topology, Algebra
    Research staff: Joan Bosa
    Research students: Luke Hamblin, Dimitrios Gerontogiannis

  • Personal Website
  • Publications


    • Postgraduates


    Postgraduate opportunities

    Operator algebras associated to self-similar actions. (PhD)

    Supervisors: Mike Whittaker
    Relevant research groups: Geometry and Topology, Analysis, Algebra

    This project will focus on self-similar groups and their operator algebras. The primary aim will be to examine a new class of groups that act self-similarly on the path space of a graph and to study the noncommutative geometry of a natural class of operator algebras associated to these self-similar groups. 

    Self-similar groups are an important and active new area of group theory. The most famous example is the Grigorchuk group, which was the first known example of a group with intermediate growth. This makes investigating C*-algebras associated to them particularly interesting. In particular, these groups are often defined by their action on a graph, and the associated C*-algebra encodes both the group and path space of the graph in a single algebraic object, as well as the interaction between them. 

     

    Aperiodic substitution tilings and their C*-algebras. (PhD)

    Supervisors: Mike Whittaker
    Relevant research groups: Geometry and Topology, Analysis

    A tiling is a collection of subsets of the plane, called tiles, for which any intersection of the interiors of two distinct tiles is empty and whose union is all of the plane. A tiling said to be aperiodic if it lacks translational periodicity. The most common method of producing aperiodic tilings is to use a substitution rule; a method for breaking each tile into smaller pieces, each of which is a scaled down copy of one of the original tiles, and then expanding so that each tile is congruent to one of the original tiles.
     
    This project will focus on a natural class of operator algebras associated with an aperiodic substitution tiling. These algebras were first considered by Kellendonk and reflect the symmetries of a tiling in an algebraic object that allows up to consider invariants in a noncommutative framework. A key area of study are spectral triples associated with aperiodic tilings, which allow us to think of tilings as noncommutative geometric objects.