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Dr Dan Rust

Dan Rust

Profile summary

  • Central Academic Staff
  • Lecturer in Applied Mathematics
  • Faculty of Science, Technology, Engineering & Mathematics
  • School of Mathematics & Statistics
  • dan.rust

Professional biography

I am a Lecturer of Applied Mathematics at the Open University. After receiving an MMath from Manchester University in 2012, IÌýobtained myÌýPhD from the University of Leicester in 2016 under the supervision of Alex Clark. I then undertook a 4 year position in Bielefeld Unviersity as a postdoctoral researcher as a member of the Aperiodic Order group of Michael Baake. I joined the Open University from there in May 2020.

I am the student research experience coordinatorÌýfor the School of Mathematics & Statistics. For more information about these schemes and how to apply, see or contact me directly by email.

Research interests

My research is focused on symbolic dynamics, as well as the topology, dynamics and spectral theory ofÌýaperiodic tilings and quasicrystals. Specific topics include:

  • The representation of tiling spaces as inverse limits of branched manifolds and their ÄŒech cohomology

  • The dynamics of tilings and bi-infinite sequences - especially those arising from substitutions, S-adic systems andÌýrandom substitutions, as well asÌýcut and project sets

  • Applications of aperiodic order to other areas of mathematics - specifically the study of combinatorial game theory, dimension groups and Diophantine approximation

I also have interests in general topological dynamics and algebraic topology as a whole. I have a particular fondness for the applications of algebraic topology to knot theory andÌýbraids.

The above image is a Barge Diamond complex which was automatically generated by the program Grout.

Grout

Developed by myself and , Grout is a free user-friendly program for Windows and Mac which can calculate various topological and combinatorial properties of symbolic substitutions.
For an explanation of the computations that Grout performs, we have provided documentation on theÌý.
You can download Grout ´Ú°ù´Ç³¾Ìý.

Teaching interests

I amÌýinvolved in the production andÌýpresentation of several undergraduate and postgraduate modules in Mathematics, including MST124 - Essential Mathematics 1,ÌýMST326 -ÌýMathematical Methods and Fluid Mechanics, MST374 - Computational Applied Mathematics,ÌýM823Ìý-ÌýAnalytic Number Theory IÌýandÌýM840Ìý- Dissertation in Mathematics (Topic: Aperiodic Tilings and Symbolic Dynamics).

Publications

(2024-09)
Fokkink, Robbert; Rust, Dan and Salo, Ville
Indagationes Mathematicae, 35(5) (pp. 931-958)

(2024-04)
Moat, Richard J; Clarke, Daniel John; Carter, Francesca; Rust, Dan and Jowers, Iestyn
Applied Materials Today, 37, Article 102127

(2024)
Fokkink, Robbert and Rust, Dan
International Journal of Game Theory, 53 (pp. 1099-1117)

(2023-10)
Mañibo, Neil; Rust, Dan and Walton, James J.
Bulletin of the London Mathematical Society, 55(5) (pp. 2425-2445)

(2023-01)
Gohlke, P.; Mitchell, A.; Rust, D. and Samuel, T.
Annales Henri Poincaré, 24(1) (pp. 277-323)

(2022-11-28)
Miro, Eden; Rust, Dan; Sadun, Lorenzo and Tadeo, Gwendolyn S.
Israel Journal of Mathematics(2022)

(2020-11)
Rust, Dan
Monatshefte für Mathematik, 193 (pp. 683-704)

(2019-09)
Gohlke, Philipp; Rust, Dan and Spindeler, Timo
Discrete & Continuous Dynamical Systems - A, 39(9) (pp. 5085-5103)

(2018-08)
Rust, Dan and Spindeler, Timo
Indagationes Mathematicae, 29(4) (pp. 1131-1155)

(2018-05)
Maloney, Gregory R. and Rust, Dan
Ergodic Theory and Dynamical Systems, 38(3) (pp. 1086-1117)

(2017-01-27)
Balchin, Scott and Rust, Dan
Journal of Integer Sequences, 20, Article 17.4.1

(2016)
Rust, Dan
Topology and its Applications, 205 (pp. 58-81)