Rigidity of periodic and symmetric structures in nature and engineering

• Dr Simon Guest, University of Cambridge, UK

Simon Guest holds the post of Reader in Structural Mechanics, working in the Structures Group of the Department of Engineering at the University of Cambridge.  He did his PhD with Sergio Pellegrino working on novel forms of deployable structures, and has retained an interest in structures that have unusual or unexpected properties.  Much of his work straddles the border between traditional structural mechanics, and the study of mechanisms.  A productive line of research has been an exploration of the effect of symmetry on structural properties, in collaboration with Patrick Fowler.  Simon first worked on the properties of repetitive structures with John Hutchinson, searching for ideal structural forms for shape-changing structures, and showed the interesting property that a repetitive structure, if stiff, must be overconstrained, and hence an apparently 'just' stiff repetitive structure must in fact be flexible.  This work has recently been reinterpreted in the study of zeolites.  He is currently exploring the extension of work on symmetry to include the space group symmetries appropriate for crystal structures.

• Professor Patrick Fowler, University of Sheffield, UK

Patrick Fowler is a Professor of Chemistry at the University of Sheffield, UK. He is interested in the theory, calculation and modelling of electric and magnetic molecular properties, and in applications of graph theory and other mathematical methods in chemistry and beyond, and with special reference to this meeting, applications of group theory to rigidity of engineered and other structures. Topics in chemistry on which he has published include theory and modelling of hydrogen bonding in weak complexes, properties of ions in solids, systematics of the fullerenes, and relations between aromaticity and molecular currents. He is a winner of Corday-Morgan and Tilden medals of the Royal Society of Chemistry and held a Royal Society/Wolfson Research Merit Award 2004-2009. 

• Professor Stephen Power, University of Lancaster, UK

Stephen Power is Professor of Mathematics in the Department of Mathematics and Statistics at Lancaster University, UK. He obtained his Bachelor of Science degree from Imperial College, in 1973, and his PhD and DPhil degrees from Edinburgh University, in 1976 and 1990. He has held postdoctoral positions at Dalhousie University and at the California Institute of Technology, and has held visiting professor positions at the Universities of Houston, Alabama, Indiana (Bloomington) and Waterloo. His research in Operator Theory and in Operator Algebras has appeared in two monographs in the Pitman Research Notes in Mathematics Series. His recent research concerns various aspects of the rigidity theory of finite and infinite bond-node frameworks, including bar-joint frameworks constrained to surfaces, the analysis of rigid unit modes (RUMs) in idealized crystal frameworks (New York J. Math, vol  17, 2011), and the theory of general infinite bar-joint frameworks.  

• Professor Mike Thorpe, Arizona State University, USA
• Audio recording (mp3)

In 2003, Michael Thorpe joined Arizona State University as Foundation Professor, and later became the Founding Director of the Center for Biological Physics. He previously had faculty appointments at Yale University and Michigan State University where he was University Distinguished Professor. His research interests are in the theory of disordered systems, with a special emphasis on properties that are determined by geometry and topology. He has a research background in condensed matter theory, and in recent years has developed the mathematical theory of flexibility and mobility for use in glassy networks, and also in crystalline materials with disorder, such as zeolites and manganites. His most recent work has been in biological physics. The flexible regions in proteins and protein complexes are determined from the x-ray crystallographic structure. These are used to determine dynamical pathways between different protein conformations using geometric simulation techniques. Proteins are stable enough to maintain a three-dimensional structure, but flexible enough for biological function. The aim of this research work is to find underlying principles and unifying concepts, to better understand the evolution and function of proteins and protein complexes. 

• Professor Walter Whiteley, York University Toronto, Canada
• Audio recording (mp3)

In the 1970's Walter Whiteley was a cofounder of the Structural Topology Research Group in Montreal, with Janos Baracs and Henry Crapo.  Using projective geometric and combinatorial methods, the group developed some key foundations for the current theory of infinitesimal and static rigidity of structures, and published the interdisciplinary journal Structural Topology.  Over the last 35 years, his research has ranged over theoretical and applied studies of the independence and rigidity of geometric constraints in the plane and in 3-space.  This work includes applications to: scene analysis (the space of liftings of a plane projection); the generic rigidity of structures in the plane and 3-space; the global rigidity of structures; predicting the flexibility and rigidity of protein structures from a single snap-shot; the decomposition and synthesis of linkages in mechanical engineering.  Recent work, with students and post-doctoral collaborators, has included studies of when symmetry adds flexibility compared with more generic structures; and when periodic structures when combined with added symmetry.  

Walter Whiteley is currently a Professor of Mathematics and Statistics at York University, as well as a member of the graduate programs in Mathematics, in Computer Science, in Education, and in Interdisciplinary Studies.     

• Professor Nicolas Triantafyllidis, Laboratoire de Mecanique des Solides & Departement de Mecanique, USA
• Audio recording (mp3)

Professor Triantafyllidis has obtained his PhD in engineering from Brown University in the US in 1980. The same year he joined the faculty of the Aerospace Department at the University of Michigan in Ann Arbor, starting as an Assistant Professor and ending up as a Full Professor. In 2009 he joined the Solid Mechanics Laboratory and the Mechanics Department at the Ecole Polytechnique in Palaiseau, France. His research focuses on stability in solids and structures, structural mechanics and nonlinear continuum mechanics. Over the years he has worked in sheet metal forming problems, large flexible space structures, composites and cellular materials, the geomechanics of the earth’s crust, the thermo-mechanical stability of shape memory crystals and on coupled thermo-mechanical/electro-magnetic problems in mechanics. He has developed and taught a number of graduate and undergraduate courses in solid mechanics. He has graduated fifteen PhD students, who subsequently became University faculty or joined government and industrial research institutions. He has collaborated extensively with researchers on both sides of the Atlantic and has strong service record in his community. He is a fellow of the ASME (American Society of Mechanical Engineers) and was recently honored with the Koiter Medal of the ASME and the Doisteau-Blutet Prize of the French Academy of Sciences. 

• Professor Michael O'Keeffe, Arizona State University, USA

Michael O'Keeffe was born in Bury St Edmunds. He read Chemistry at the University of Bristol (BSc 1954, PhD 1958, DSc 1976). Since 1963 he has been at Arizona State University where he currently Research Professor and Regents' Professor Emeritus. He has published widely on diffusion and conduction in solids, and on theoretical and experimental studies of inorganic crystal chemistry. His recent interests are focused particularly on the design and synthesis of microporous crystals and on the mathematical aspects of the periodic graphs (nets) that describe their underlying topology.  He is number 3 on the global list of chemists whose work has had the highest impact (citations per paper) in the decade 2000-2010. 

• Dr Vanessa Robins, The Australian National University, Australia
• Audio recording (mp3)

Vanessa Robins completed her BSc(Hons) degree in Mathematics at the Australian National University in 1994 and received her PhD degree  in Applied Mathematics from the University of Colorado, Boulder in   2000.  She has been a research fellow in the Department of Applied Mathematics at the Australian National University since 2000.  Her research interests are in computational topology and geometry, and the enumeration and properties of periodic nets.  She works on mathematical foundations, algorithms and scientific applications in  these fields.  She is currently living in Port Moresby with her husband and two daughters, and is a visiting fellow at the University of Papua New Guinea. 

• Mr Colby Dawson, Arizona State University, USA
• Audio recording (mp3)

• Professor Stephen Power, University of Lancaster, UK
• Audio recording (mp3)

Stephen Power is Professor of Mathematics in the Department of Mathematics and Statistics at Lancaster University, UK. He obtained his Bachelor of Science degree from Imperial College, in 1973, and his PhD and DPhil degrees from Edinburgh University, in 1976 and 1990. He has held postdoctoral positions at Dalhousie University and at the California Institute of Technology, and has held visiting professor positions at the Universities of Houston, Alabama, Indiana (Bloomington) and Waterloo. His research in Operator Theory and in Operator Algebras has appeared in two monographs in the Pitman Research Notes in Mathematics Series. His recent research concerns various aspects of the rigidity theory of finite and infinite bond-node frameworks, including bar-joint frameworks constrained to surfaces, the analysis of rigid unit modes (RUMs) in idealized crystal frameworks (New York J. Math, vol  17, 2011), and the theory of general infinite bar-joint frameworks.  

• Dr Elissa Ross, York University, Canada
• Audio recording (mp3)

Elissa Ross is currently a postdoctoral fellow at York University. She completed her PhD in 2011 under the supervision of Professor Walter Whiteley, and was a postdoctoral fellow at the Fields Institute (Toronto) in connection with their thematic program on Discrete Geometry. Her research is concerned with the rigidity of periodic structures. 

• Professor Alphose Zingoni, University of Cape Town, South Africa
• Audio recording (mp3)

Alphose Zingoni is Professor of Structural Engineering & Mechanics, and Head of the Department of Civil Engineering at the University of Cape Town. He earned an MSc degree in structural engineering (with Distinction) from Imperial College London in 1988, and a PhD on shells of revolution (also from Imperial College) in 1992. Between 1992 and 1994, he was a Research Fellow of the Royal Commission for the Exhibition of 1851, studying various problems in structural engineering using group theory. His main research interests are shell analysis and development of group-theoretic formulations for problems in structural mechanics. He has authored two books and over 100 peer-reviewed scientific articles in these areas, edited the Proceedings of four international conferences in the more recent past, and guest-edited five special issues for international journals. He currently serves on the editorial boards of 5 international journals, and has served on the advisory boards of numerous international conferences. He is a Fellow of the Institution of Structural Engineers (London), a Fellow of the International Association for Bridge & Structural Engineering (Zurich), a Fellow of the South African Academy of Engineering, and a Member of the Academy of Science of South Africa.  

• Professor Ciprian Borcea, Rider University, USA
• Audio recording (mp3)

Ciprian Borcea received his PhD from the University of Bucharest, Romania, with a thesis on "Deformations of complex structures". After a membership at the Institute for Advanced Study in 1989-1990, he joined Rider University, Lawrenceville, NJ, where he is currently Professor of Mathematics.

His contributions to algebraic and analytic geometry relate to moduli spaces, K3 surfaces, homogeneous spaces, Calabi-Yau manifolds and constructions of mirror families. An expanding interest in the role of algebraic geometry for studies of articulated systems developed through investigations of polygon spaces, linkages, robot arms, hinge structures and periodic frameworks. In collaboration with Professor Ileana Streinu, he has generated new geometrical and combinatorial approaches for problems pertaining to rigidity and flexibility. 

• Dr Simon Guest, University of Cambridge, UK
• Audio recording (mp3)

Simon Guest holds the post of Reader in Structural Mechanics, working in the Structures Group of the Department of Engineering at the University of Cambridge.  He did his PhD with Sergio Pellegrino working on novel forms of deployable structures, and has retained an interest in structures that have unusual or unexpected properties.  Much of his work straddles the border between traditional structural mechanics, and the study of mechanisms.  A productive line of research has been an exploration of the effect of symmetry on structural properties, in collaboration with Patrick Fowler.  Simon first worked on the properties of repetitive structures with John Hutchinson, searching for ideal structural forms for shape-changing structures, and showed the interesting property that a repetitive structure, if stiff, must be overconstrained, and hence an apparently 'just' stiff repetitive structure must in fact be flexible.  This work has recently been reinterpreted in the study of zeolites.  He is currently exploring the extension of work on symmetry to include the space group symmetries appropriate for crystal structures. 

• Professor Hellmuth Stachel, Technische Universität Wien, Austria
• Audio recording (mp3)

Professor Stachel was born in Graz, Austria. In 1965 he graduated with a secondary school teacher accreditation in “Mathematics‘” and “Descriptive Geometry” from the University of Technology (TU) Graz.  He finished his my PhD in Mathematics in 1969 at the University Graz.

His academic career started 1967 with the position of an assistant at the Institute of Geometry, TU Graz.  He habilitated there in geometry 1971. In 1976 he became an associate professor at TU Graz. 1978 he was appointed as full professor for Applied Geometry at the Institute for Mathematics and Applied Geometry, University for Mining in Leoben. From 1980 onwards, he was full professor for Geometry at the Vienna University of Technology.  He retired from this position at the end of September 2011.

In August 1984 he was visiting professor at South China Institute for Technology in Guangzhou/PR China, in October 1989 visiting professor at the Tongji University in Shanghai/PR China. 1991 he was elected to a corresponding member of the Austrian Academy of Sciences. 2010 he received an honorary doctorate from the University of Technology in Dresden/Germany. 

• Dr Bernd Schulze, York University, Canada
• Audio recording (mp3)

After studying mathematics and computer science at the Free University Berlin (Germany) and at Western Michigan University (USA), Dr Bernd Schulze pursued his PhD in mathematics at York University (Canada) under the direction of Professor Walter Whiteley. As a PhD student he focused his research studies on problems in rigidity theory and its applications. In particular, he investigated the impact of symmetry on the rigidity properties of bar-and-joint frameworks and other geometric constraint systems. His doctoral thesis is entitled ‘Combinatorial and Geometric Rigidity with Symmetry Constraints'. After his graduation in May 2009, he worked as a postdoctoral fellow in the Discrete Geometry Group at the Berlin Institute of Technology (Germany) under the direction of Professor Guenter M Ziegler for two years. During this time he continued his research in the areas of rigidity and symmetry, and he also extended his research activities to various other aspects of discrete and computational geometry. In particular, he studied diverse problems related to triangulations of polygons and polytopes. In July 2011 he moved back to Canada to work as a postdoctoral fellow at the Fields Institute in Toronto for the duration of the Thematic Program on Discrete Geometry and Applications. Currently he is still in Toronto, working as a postdoctoral fellow at York University.