Analysis Research Group

Group Members

Staff

• Collin Bleak

  My research is in studying infinite groups of homeomorphisms via properties of their actions. In this study I employ tools from various fields including algebra, theoretical computer science, combinatorics, symbolic dynamical systems, and analysis.

• Spyridon Dimoudis

  I am interested in operator and spectral theory and their applications in mathematical quantum mechanics, specifically, in the analysis of non-self-adjoint Schrödinger, and related, operators.

• Kenneth Falconer

  My research centres around the geometry of fractals and multifractals, geometric measure theory, dimension theory, dynamical systems and probability. Specific topics include self-affine sets and measures, sections and projections of fractals, random fractals and stochastic processes, and applications of fractals to other areas.

• Jonathan Fraser (Head of Group)

  My research interests centre on fractal geometry and its connections with other areas of mathematics, such as: geometric measure theory, ergodic theory, Fourier analysis, and hyperbolic geometry. Particular topics include: self-affine sets, self-similar sets with overlaps, limit sets of Kleinian groups, and Fourier transforms of random measures associated with Brownian motion.

• Natalia Jurga

  My research interests lie in the interplay between dynamical systems, ergodic theory and fractal geometry. More specific topics include: dimension theory of dynamical systems, random matrix products, self-affine sets, transfer operator methods and thermodynamic formalism.

• István Kolossváry

  My current research interest is in fractal geometry and geometric measure theory, mainly concentrated around the dimension theory of self-affine sets and measures.

• Lars Olsen

  My research covers all aspects of fractal and multifractal geometry and geometric measure theory, including work on self-affine sets and measures, fractals defined by digits of numbers, typical structure of fractal sets and measures, etc.

• Liam Stuart

  I am interested in fractals and dimension theory, in particular limit sets of geometrically finite Kleinian groups and Julia sets of parabolic rational maps.

• Mike Todd

  I work in ergodic theory and dynamical systems, applying ideas from probability and thermodynamic formalism to study expansion and recurrence properties of, mostly, smooth low dimensional systems. Topics include Return Time Statistics, Extreme Value Theory, statistical stability, equilibrium states, phase transitions and transience.

PhD Students

• Amlan Banaji

  My main research interests relate to the geometry and dimension theory of fractal sets and measures. I have worked with fractals generated by conformal and non-conformal iterated function systems. Much of my research has been about interpolating between different notions of dimension. I am interested in finding connections between fractal geometry and other areas of mathematics.

• Raquel Couto

  I am broadly interested in dynamical systems and ergodic theory, more recently focusing on properties of chaotic systems through the study of dynamically defined stochastic processes.

• Alex Rutar

  I am generally interested in fractal geometry and dimension theory, with a particular interest in systems involving symbolic dynamics. This includes work in the dimension theory and multifractal analysis of overlapping self-similar and self-affine measures. I have also worked on classification results for dimension spectra.

• Liam Stuart

  I am interested in fractals and dimension theory, in particular limit sets of geometrically finite Kleinian groups and Julia sets of parabolic rational maps.

• Boyuan Zhao

  My interests in mathematics are generally in ergodic theory and chaotic dynamical systems, with possible applications to cryptography.

Recent Staff

• Stuart Burrell

• Jonathan Hickman

• Xiong Jin

• Tom Kempton

• Bernd Stratmann

• Alexia Yavicoli

Recent PhD Students

• Lawrence Lee (2021)

• Stuart Burrell (2020)

• Douglas Howroyd (2020)

• Nayab Khalid (2020)

• Han Yu (2019)

• James Hyde (2017)

• Vuksan Mijovic (2017)

• Sascha Troscheit (2017)

• Casey Donoven (2016)

• Abel Farkas (2015)

• Jonathan Fraser (2013)

• Graeme Boore (2011)

• Sara Munday (2011)

• Lining Liu (2010)

• Tony Samuel (2010)

• Martial Hille (2009)

• Jun Miao (2008)

• Nina Snigireva (2008)

• Ivan Werner (2004)

• Jiaxin Hu (2001)

• Kurt Falk (2000)

• Birger Lammering (2000)

• Julian Cole (1998)

• Mark Orzechowski (1997)

Recent Visitors

• Jian-Ci Xiao (2020-2021)

• Haipeng Chen (2019-2020)

• Pablo Shmerkin (2019-2020)

• Junda Zhang (2019-2020)

• Huaibin Li (2016-2017)

• Kathryn Hare (2013-2014)