Analysis Research Group

Group Members

Core Faculty

• 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.

• 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.

Further 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. Collin sits in the Algebra and Combinatorics Research Group.

• 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.

• 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.

• Firdavs Rakhmonov

  My research primarily focuses on additive combinatorics, combinatorial number theory, discrete geometry, discrete Fourier analysis, fractal geometry, and geometric measure theory. Currently, I am investigating problems in vector spaces over finite fields and exploring analogous results in the continuous setting.

PhD Students

• Luke Derry

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

• Tianyi Feng

  I am interested in dimension theory, dynamical systems and their connections to fractal geometry.

• Ana de Orellana

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

• Saeed Shaabanian

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

• Yunlong Xu

• Lijian Yang

• 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

• Natalia Jurga (PDRA and Leverhulme Early Career Fellow, 2020-25)

• István Kolossváry (PDRA, 2019-2023)

• Alexia Yavicoli (Swiss International Fellow, 2011-13)

• Jonathan Hickman (PDRA, 2018-2019)

• Tom Kempton (PDRA, 2013-16)

• Xiong Jin (Newton International Fellow, 2011-13)

• Bernd Stratmann (Faculty, 1996-2010)

Recent PhD Students

• Raquel Couto (2024)

• Alex Rutar (2024)

• Shuqin Zhang (2023-2024)

• 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)