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.

• Dmytro Karvatskyi (Visiting)

  My research is devoted to the study of sets having a complicated local structure, such as fractals, Cantorvals, fat Cantor sets, etc. Such sets naturally appear in various branches of mathematics. In particular, they are attractors for some iterated function systems.

• 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.

• 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

• 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.

• Luke Derry

  I am interested in C*-algebras, curvature measures, and multifractal analysis.

• Ana de Orellana

  My research interests revolve around the connections between geometric measure theory, dimension theory, and Fourier analysis.

• Alex Rutar

  I am primarily interested in fractal geometry and dynamical systems, including (but not limited to) the geometry of self-similar and self-affine sets and associated invariant measures, multifractal analysis, and general dimension theory and dimension interpolation.

• Saeed Shaabanian

  My tendency is Dynamical systems and Ergodic Theory, also I researched into the relation between ergodic theory and operator algebra.

• Shuqin Zhang (Visiting)

  My research interests relate to multifractal geometry, in particular in-homogeneous self-similar measures.

• Boyuan Zhao

  My interests in mathematics are generally in ergodic theory, symbolic dynamics, and low-dimensional interval maps with possible applications to cryptography.

Recent Staff

• Liam Stuart

• Stuart Burrell

• Jonathan Hickman

• Xiong Jin

• Tom Kempton

• István Kolossváry

• Bernd Stratmann

• Alexia Yavicoli

Recent PhD Students

• Amlan Banaji (2023)

• Liam Stuart (2022)

• 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

• Aleksi Pyörälä (2022)

• 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)