Aperiodic Order Research Group

Members

Current Members

Uwe Grimm
Ian Short
Ibai Aedo (from February 2019)
Thomas Bridge (from February 2019)
Yasushi Nagai (from April 2019)

Former Members

Lax Chan (2014 – 2018) — now at University of Nottingham, UK
Svenja Glied (May 2007 – January 2009) — now at Hannoversche Versicherungen, Hannover, Germany
Edmund Harriss (May – August 2009) — now at University of Arkansas, USA
Manuela Heuer (2006 – 2010) — now at Allianz AG, Germany
Christian Huck (May 2007 – January 2009) — now at University of Bielefeld, Germany
Bernd Sing (January – September 2007) — now at UWI, Cave Hill, Barbados

Recent and Forthcoming Visitors

Dan Rust (Bielefeld), 22 November 2018
Reem Yassawi (Lyon), 26–28 November 2018
Petra Staynova (Leeds), 22 January 2019
Stephen Power (Lancaster), 2 April 2019
Valerié Berthé (Paris-Diderot), 4 June 2019

Funding

Lyapunov Exponents and Spectral Properties of Aperiodic Structures
EPSRC Grant Reference EP/S010335/1, £348,847, April 2019 – March 2022
International Travel Grant
Royal Society, £880, 24 September – 2 October 2010
How do Shapes Fill Space?
EPSRC Partnerships for Public Engagement Grant EP/H004866/1, £20,043, May – November 2009
Combinatorics of Sequences and Tilings and its Applications
EPSRC Grant EP/D058465/1, £215,124, 1 October 2006 – 31 December 2009
Visiting Professorship Michael Baake
Leverhulme Trust, £25,340, starting 1 July 2008
IUCr Awards for young scientists
supporting the participation of Manuela Heuer and Svenja Glied at the 10th International Conference on Quasicrystals ICQ10 in Zürich, July 2008

Recent and Forthcoming Events

Aperiodic Order meets Number Theory
MATRIX, Creswick, Australia, 25 February – 1 March 2019
Organisers: Michael Baake, Michael Coons, Uwe Grimm, John A G Roberts, Reem Yassawi
Pattern Formation and Aperiodic Order
ICMS, Edinburgh, 4–8 June 2018
Organisers: Andrew Archer, Uwe Grimm, Alastair Rucklidge, Priya Subramanian
Workshop on Spectral Theory of Aperiodic Systems
Heinrich-Fabri-Institut, Blaubeuren, Germany, 21 – 27 June 2015
Organisers: Michael Baake, Franz Gähler, Uwe Grimm, Christian Huck
Mini-Workshop Dynamical versus Diffraction Spectra in the Theory of Quasicrystals
Mathematisches Forschungsinstitut Oberwolfach, Germany, 30 November – 6 December 2014
Organisers: Michael Baake, David Damanik, Uwe Grimm

Recent publications

Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction
Michael Baake, Natalie P. Frank, Uwe Grimm, E. Arthur Robinson jr., to appear in Studia Mathematica [arXiv:1706.03976]
Substitution-based structures with absolutely continuous spectrum
Lax Chan, Uwe Grimm and Ian Short, Indagationes Mathematicae 29 (2018) 1072-1086 [arXiv:1706.05289]
Spectral analysis of a family of binary inflation rules
Michael Baake, Uwe Grimm and Neil Mañibo, Letters in Mathematical Physics 108 (2018) 1783-1805 [arXiv:1709.09083]
Aperiodic Order. Volume 2: Crystallography and Almost Periodicity
Michael Baake and Uwe Grimm (Eds.), Encyclopedia of Mathematics and its Applications No. 166, Cambridge University Press, Cambridge (2017)
Discrete Tomography of Model Sets: Reconstruction and Uniqueness
Uwe Grimm, Peter Gritzmann and Christian Huck, in Aperiodic Order. Volume 2: Crystallography and Almost Periodicity, edited by Michael Baake and Uwe Grimm, Cambridge University Press (2017) pp. 39-71
Aperiodic order and spectral properties
Michael Baake, David Damanik and Uwe Grimm, Snapshots of modern mathematics from Oberwolfach 3/2017 [arXiv:1506.04978]
Substitution-based sequences with absolutely continuous diffraction
Lax Chan and Uwe Grimm, Journal of Physics: Conference Series 809 (2017) 012027 [arXiv:1611.05733]
Diffraction of a binary non-Pisot inflation tiling
Michael Baake and Uwe Grimm, Journal of Physics: Conference Series 809 (2017) 012026 [arXiv:1706.04448]
Aperiodic Order
Uwe Grimm, in Dynamical and Complex Systems, LTCC Advanced Mathematics Series volume 5, edited by Shaun Bullett, Tom Fearn and Frank Smith, World Scientific Publishing Europe, London (2017) pp. 41-80
Spectrum of a Rudin-Shapiro-like sequence
Lax Chan and Uwe Grimm, Advances in Applied Mathematics 87 (2017) 16-23 [arXiv:1611.04446]

Recent Presentations

3 – 6 October 2018
Joint Meeting of the Korean Mathematical Society and the German Mathematical Society, Seoul, Korea
Scaling behaviour of diffraction intensities
3 – 7 September 2018
Model Sets and Aperiodic Order, Durham, UK
Natural cut and project schemes
8 – 13 July 2018
Aperiodic 2018, Ames, Iowa
Diffraction of block substitution tilings

Public Dissemination

How do Shapes Fill Space?
EPSRC, 29 April 2010, Swindon
How do Shapes Fill Space?
Brighton Science Festival 2010, 27 February 2010
How do Shapes Fill Space?
Royal Society Summer Science Exhibition 2009, 30 June – 4 July, London
To repeat or not to repeat: The mathematics of quasicrystals (UG)
Denbigh School Science, Engineering & Mathematics Lecture Series, Milton Keynes, 5 February 2009
(postponed due to school closure as a result of heavy snow)
Forbidden Beauty — a story about symmetry & order in crystals (UG)
School Event, Milton Keynes Science Festival, Milton Keynes, 6 – 15 July 2007
Symmetry & Aperiodicity: The Forbidden Beauty of Quasicrystals (UG)
OU Festival of Research, Milton Keynes, 11 – 12 July 2007
Deformed model sets and distorted Penrose tilings (BS)
Evening Reception, Annual Presentations at the House of Commons, London, 19 March 2007
Aperiodicity & order — the forbidden beauty of quasicrystals (UG)
Café Scientifique, Cockermouth, 13 February 2007
Symmetry and (A)Periodicity (UG)
Christmas Lecture, Open University Region 05, Nottingham, 2 December 2006

Aperiodic Order at the Open University

Uwe Grimm has been active in this research area since he joined the Open University in December 2000. Supported by a research grant from the Engineering and Physical Sciences Research Council, a group of post-doctoral researchers, research students and visitors joined from October 2006.

From September 2007 until March 2008, Uwe Grimm spent six months as a Visiting Research Associate at the University of Tasmania in Hobart. In 2009/2010, Michael Baake will spend several months in the group as a Leverhulme Visiting Professor.

At the 10th International Conference on Aperiodic Crystals ICQ10 in Zürich 2008, the group contributed two talks (SG,UG) and two posters (MH,CH). Manuela Heuer's and Svenja Glied's participation were supported by IUCr Young Scientists awards, and Manuela Heuer won a prize for best student presentation for her poster Similar sublattices and coincidence rotations of the root lattice A4 and its dual.

The year 2009 turned out to be a busy year, with Uwe Grimm co-organising the exhibit How do shapes fill space? at the Royal Society Summer Science Exhibition 2009 as well as the 6th International Conference on Aperiodic Crystals Aperiodic'09 in Liverpool and a satellite workshop in Leicester, and presenting invited talks at meetings in Austria and France in July and October.

Group photo at ICQ10
Group photo at Aperiodic'09

Aperiodic'09 was the first major conference on aperiodic order in the UK and attracted about 110 participants from a range of disciplines including mathematics, physics, crystallography and materials science. The remit of the conference covers two broad areas of research, incommensurately modulated and composite crystals on the one hand, and quasicrystals on the other hand, sharing the property that they are aperiodically ordered solids.

A related EPSRC-supported workshop on Mathematical Aspects of Aperiodic Order was held in Leicester in the week preceding the conference, and attracted about 40 participants.

Highlights of the conference included a public lecture "Simple sets of shapes that tile the plane but cannot ever repeat" by Roger Penrose and a visit by Alan L. Mackay, bringing together two distinguished UK scientists who made seminal contributions to the subject.

IUCr Congress Madrid 2011

Two trips to Japan (ICQ11 Sapporo and RIMS workshop, Kyoto) and Korea (KIAS workshop) were highlights in 2010. The visit to Korea was supported by a Royal Society International Travel Grant. Uwe's talk Some comments on a hexagonal monotile at the Korea Institute of Advanced Study was videotaped; the recording can be viewed here.

The year 2011 started with an Oberwolfach workshop in January. With Marjorie Senechal, Uwe co-chaired a microsymposium What is order, and how can one describe it (What kinds of matter diffract?) at the International Congress of Crystallography in Madrid in August. At the congress, Uwe was elected to the Commission on Aperiodic Crystals of the International Union of Crystallography. In September and October, invitations to workshops at BIRS in Banff and at the Fields Institute in Toronto meant two visits to Canada.

IUCr Congress Madrid 2011

Activities in 2012 included presenting a talk at the workshop Periodic orbits in dynamical systems at the Erwin Schrödinger International Institute for Mathematical Physics in Vienna in May, organising a session on Geometric complexity in aperiodic order at Mathematics of Distances and Applications in Varna in July and — last but not least — the 7th International Conference on Aperiodic Crystals Aperiodic 2012 in Cairns in September.

SIAM Conference 2013, Phildelphia

In 2013 Uwe presented a talk at the workshop SubTile 2013 at the CIRM in January, an invited topical talk at the German Physical Society (DPG) Spring Meeting in Regensburg in March and an invited talk at the SIAM Conference on Mathematical Aspects of Materials Science in Philadelphia in June. At the 12th International Conference on Quasicrystals ICQ12 in Kraków in September, Uwe will gave an invited tutorial. Also, with Michael Baake he finally completed the first volume of their book series on Aperiodic Order, which was available from late August.

Aperiodic Order. Volume 1:
A Mathematical Invitation
MFO 2014

In 2014, Uwe presented a couple of invited talks at the AMS Spring Eastern Sectional Meeting, and an invited talk at the 23rd Congress and General Assembly of the International Union of Crystallography in Montréal, where Uwe was elected Chair of the IUCr Commission on Aperiodic Crystals. A highlight was the Mini-Workshop Dynamical versus Diffraction Spectra in the Theory of Quasicrystals at the Mathematisches Forschungsinstitut Oberwolfach (left), which was co-organised by Uwe.

2015 saw a visit to the Heinrich-Fabri Institut in Blaubeuren, where Uwe co-organised a Workshop on Spectral Theory of Aperiodic Systems (right), one of the first meetings that Uwe's PhD student Lax Chan (supervised jointly with Ian Short) attended. Uwe also presented invited talks in Leicester, Trondheim, Oberwolfach and Paris, and was a member of the International Program Committee of Aperiodic 2015 in Prague.

Blaubeuren 2015

The year 2016 brought along a number of workshops and conferences, starting with Dynamical systems for aperiodicity in Lyon in January and a Lorentz Center workshop on Combining Aperiodic Order with Structural Disorder in May/June. Uwe presented talks at the SIAM Conference on Mathematical Aspects of Materials Science in Philadelphia in May and at the 13th International Conference on Quasicrystals ICQ13 in Kathmandu in September. On the right you can see him explaining correlations between two points.

ICQ13

2017 was a very busy year with travel to Australia, Germany, USA, India and France. Uwe presented talks at the SIAM Conference on Applications of Dynamical Systems in Snowbird in May, a Lorentz Center workshop on Aperiodic Patterns in Crystals, Numbers and Symbols in June, a Workshop on Aperiodicity and Hierarchical Structures in Tilings in Lyon in September and at the CIRM workshop on Tilings and Recurrence in Luminy in December. In addition, Uwe was a co-organiser of The 29th international conference on Formal Power Series and Algebraic Combinatorics FPSAC 2017 in London in July and a member of the international program committee for the XXIV Congress and General Assembly of the International Union of Crystallography in Hyderabad in August, and attended an Oberwolfach workshop on Spectral Structures and Topological Methods in Mathematical Quasicrystals in October. At the end of the year, volume 2 of the Aperiodic Order book series appeared in print.

Aperiodic Order. Volume 2:
Crystallography and Almost Periodicity

Photos from the 2009 exhibit How do shapes fill space?

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