Bernd Schulze
Address: Department of Mathematics and Statistics Fylde College Lancaster University Lancaster LA1 4YF, United Kingdom Office: Fylde B11 Telephone: +44 (0) 1524 592173 E-Mail: b.schulze -at- lancaster.ac.uk |
Research interests
Some nice examples:
Publications
Bernd Schulze, Cameron Millar, Arek Mazurek and William Baker, States of self-stress in symmetric frameworks and applications, preprint, 2021
Cameron Millar, Arek Mazurek, Bernd Schulze and William Baker, Symmetry and the design of self-stressed structures, preprint, 2021
John Owen and Bernd Schulze, Mobility of geometric constraint systems with extrusion symmetry, preprint, 2021
Bernd Schulze, Shin-ichi Tanigawa and Louis Theran, Global rigidity of periodic frameworks, preprint, 2021
James Cruickshank, Eleftherios Kastis, Derek Kitson and Bernd Schulze, Braced triangulations and rigidity, submitted, 36 pages, 2021
Anthony Nixon, Bernd Schulze and Walter Whiteley, Rigidity through a projective lens, submitted, 110 pages, 2021
James Cruickshank and Bernd Schulze, Symmetric contact systems of segments, pseudotriangulations and inductive constructions for corresponding surface graphs, submitted, 37 pages, 2020
Bernd Schulze, Hattie Serocold and Louis Theran, Frameworks with coordinated edge motions, submitted, 16 pages, 2020
Viktoria Kaszanitzky and Bernd Schulze, Sufficient connectivity conditions for rigidity of symmetric frameworks, submitted, 18 pages, 2018
Viktoria Kaszanitzky, Csaba Kiraly and Bernd Schulze, Sufficient conditions for the global rigidity of periodic graphs, to appear in Discrete & Computational Geometry, 13 pages, 2021
Viktoria Kaszanitzky, Bernd Schulze and Shin-ichi Tanigawa, Global rigidity of periodic graphs under fixed lattice representations, Journal of Combinatorial Theory, Series B, 146, 176-218, 2021
Derek Kitson, Anthony Nixon and Bernd Schulze, Rigidity of symmetric frameworks in normed spaces, Linear Algebra and its Applications, 607, 231-285, 2020
Katie Clinch, Anthony Nixon, Bernd Schulze and Walter Whiteley, Pairing symmetries for Euclidean and spherical frameworks, Discrete & Computational Geometry, 64, 483-518, 2020
Yaser Eftekhari, Bill Jackson, Anthony Nixon, Bernd Schulze, Shin-ichi Tanigawa and Walter Whiteley, Point-hyperplane frameworks, slider joints, and rigidity preserving transformations, Journal of Combinatorial Theory, Series B, 135, 44-74, 2019
Anthony Nixon, Bernd Schulze, Shin-ichi Tanigawa and Walter Whiteley, Rigidity of frameworks on expanding spheres, SIAM Journal on Discrete Mathematics 32, Issue 4, 2591-2611, 2018
Patrick Fowler, Simon Guest and Bernd Schulze, Mobility of symmetric block-and-hole polyhedra, International Journal of Solids and Structures 150, 40-51, 2018
Viktoria Kaszanitzky and Bernd Schulze, Characterizing minimally flat symmetric hypergraphs, Discrete Applied Mathematics 236, 256-269, 2018
Stephen Power and Bernd Schulze, String-node nets and meshes, Discrete & Computational Geometry 59, 31-58, 2018
Derek Kitson and Bernd Schulze, Motions of grid-like reflection frameworks, Journal of Symbolic Computation, 88, 47-66, 2018
Viktoria Kaszanitzky and Bernd Schulze, Lifting symmetric pictures to polyhedral scenes, Ars Mathematica Contemporanea 13(1), 31-47, 2017
Derek Kitson and Bernd Schulze, Symmetric isostatic frameworks with l_1 or l_∞ distance constraints, The Electronic Journal of Combinatorics 23(4), P4.23, 1-23, 2016
Patrick Fowler, Simon Guest and Bernd Schulze, Mobility of a class of perforated polyhedra, International Journal of Solids and Structures 85-86, 105-113, 2016
Anthony Nixon and Bernd Schulze, Symmetry-forced rigidity of frameworks on surfaces, Geometriae Dedicata 182, No. 1, 163-201, 2016
Derek Kitson and Bernd Schulze, Maxwell-Laman counts for bar-joint frameworks in normed spaces, Linear Algebra and its Applications 481, 313-329, 2015
Bernd Schulze and Shin-ichi Tanigawa, Infinitesimal rigidity of symmetric bar-joint frameworks, SIAM Journal on Discrete Mathematics 29, No.3, 1259-1286, 2015
Bernd Schulze and Shin-ichi Tanigawa, Linking rigid bodies symmetrically, European Journal of Combinatorics 42, 145-166, 2014
Anthony Nixon, Bernd Schulze, Adnan Sljoka and Walter Whiteley, Symmetry adapted Assur decompositions , Symmetry 6 (3), 516-550, 2014
Bernd Schulze, Patrick Fowler and Simon Guest, When is a symmetric body-hinge structure isostatic?, International Journal of Solids and Structures 51, 2157-2166, 2014
Bernd Schulze, Adnan Sljoka and Walter Whiteley, How does symmetry impact the flexibility of proteins?, Philosophical Transactions of the Royal Society A, Vol. 372, No. 2008, 2014
Bernd Schulze and Walter Whiteley, Coning, symmetry, and spherical frameworks, Discrete & Computational Geometry 48, Issue 3, 622-657, 2012
Bernd Schulze and Walter Whiteley, The orbit rigidity matrix of a symmetric framework, Discrete & Computational Geometry 46, Issue 3, 561-598, 2011
Bernd Schulze, On the area discrepancy of triangulations of squares and trapezoids, The Electronic Journal of Combinatorics 18 (1), P137, 1-16, 2011
Elissa Ross, Bernd Schulze, Walter Whiteley, Finite motions from periodic frameworks with added symmetry, International Journal of Solids and Structures 48, 1711-1729, 2011
Bernd Schulze, Symmetric Laman theorems for the groups C_2 and C_s, The Electronic Journal of Combinatorics 17 (1), R154, 1-61, 2010
Bernd Schulze, Symmetry as a sufficient condition for a finite flex, SIAM Journal on Discrete Mathematics 24, No. 4, 1291-1312, 2010
Simon Guest, Bernd Schulze and Walter Whiteley, When is a symmetric body-bar structure isostatic?, International Journal of Solids and Structures 47, 2745-2754, 2010
Bernd Schulze, Symmetric versions of
Laman's Theorem,
Discrete & Computational Geometry 44, Issue 4, 946-972, 2010
Bernd Schulze, Block-diagonalized rigidity matrices of symmetric frameworks and applications, Beiträge zur Algebra und Geometrie/Contributions to Algebra and Geometry 51, No. 2, 427-466, 2010
Bernd Schulze, Injective and non-injective realizations with symmetry, Contributions to Discrete Mathematics 5, No. 1, 59-89, 2010
Robert Connelly, Patrick Fowler, Simon Guest, Bernd Schulze and Walter Whiteley, When is a symmetric pin-jointed framework isostatic?, International Journal of Solids and Structures 46, 762-773, 2009
Bill Jackson, Viktoria Kaszanitzky and Bernd Schulze, Scene analysis and symmetry, Developments in Computer Science, Faculty of Informatics, ELTE, 4 pages, 2021
Alyx, Burns, Bernd Schulze and Audrey St.John, Persistent multi-robot formations with redundancy, in: Gross et al. (eds) Distributed Autonomous Robotic Systems, Springer Proceedings in Advanced Robotics, Vol 6. Springer, Cham, doi:10.1007/978-3-319-73008-0_10, 2018
Josep Porta, Lluis Ros, Bernd Schulze, Adnan Sljoka and Walter Whiteley, On the Symmetric Molecular Conjectures, Computational Kinematics, Mechanisms and Machine Science, Vol. 15, 175-184, 2014
Patrick Fowler, Simon Guest and Bernd Schulze, Mobility of symmetry-regular bar-and-joint frameworks, Fields Institute Communications, Vol. 70 (Rigidity and Symmetry), 117-130, 2014
Bernd Schulze, Adnan Sljoka and Walter Whiteley, Protein flexibility of dimers: do symmetric motions play a role in allosteric interactions?, AIP Conference Proceedings of AMMCS 2011, Vol. 1368, doi:10.1063/1.3663478, 135-138, 2011
Bernd Schulze, Combinatorial rigidity of frameworks under symmetry, in Handbook of Geometric Constraint Systems Principles, Editors: Jessica Sidman, Meera Sitharam, Audrey St. John, Chapman and Hall/CRC, 2018
Bernd Schulze and Walter Whiteley, Rigidity and Scene Analysis, in Handbook of Discrete and Computational Geometry, Third Edition, Editors: Csaba D. Toth, Joseph O'Rourke, Jacob E. Goodman, Chapman and Hall/CRC, 2017
Bernd Schulze and Walter Whiteley, Rigidity of Symmetric Frameworks, in Handbook of Discrete and Computational Geometry, Third Edition, Editors: Csaba D. Toth, Joseph O'Rourke, Jacob E. Goodman, Chapman and Hall/CRC, 2017
Bernd Schulze, Combinatorial
and Geometric Rigidity with Symmetry Constraints,
York University,
Toronto, ON, Canada, May 2009
Advisor: Prof.
Walter Whiteley
The thesis was awarded the York
University Dissertation Prize 2010 (for best thesis of the year across all disciplines).
Selection of invited talks
Global rigidity of periodic body-bar frameworks, Workshop on Progress and Open Problems in Rigidity Theory, Fields Institute, Toronto, ON, Canada, February 2021
Frameworks with coordinated constraints and a union of matroids, Virtual seminar on algebraic matroids, rigidity theory, distance geometry, and geometric constraint systems, online seminar, November 2020
Periodic rigidity, Workshop on Rigidity and flexibility of microstructures, American Institute of Mathematics (AIM), San Jose, CA, USA, November 2019
Rigidity of periodic structures: Recent progress and open questions, BIRS Workshop on Soft Packings, Nested Clusters, and Condensed Matter, Casa Matematica Oaxaca (CMO), Oaxaca, Mexico, September 2019
Pairing symmetry groups for spherical and Euclidean frameworks, SIAM Conference on Applied Algebraic Geometry (Session on Algebraic geometry and combinatorics of jammed sructures), Universitaet Bern, Bern, Switzerland, July 2019
Group pairings with equivalent rigidity properties for bar-joint and point-hyperplane frameworks, Workshop on Geometric constraint systems: rigidity, flexibility and applications, Lancaster University, Lancaster, UK, June 2019
Rigidity of bar-joint frameworks with coordinated constraint relaxations, Mathematics Seminar, NUI Galway, Galway, Ireland, February 2019
Frameworks with coordinated edge motions, Workshop on Rigidity and Flexibility of Geometric Structures, Erwin Schroedinger International Institute For Mathematics and Physics, Vienna, Austria, September 2018
Scene analysis and parallel drawing, Automatic Control and Systems Engineering Seminar, University of Sheffield, Sheffield, UK, Aril 2018
Rigidity and global rigidity of graphs, Pure Mathematics Seminar, University of Plymouth, Plymouth, UK, March 2018
Global rigidity of periodic graphs, Workshop on Distance Geometry: Inverse problems between geometry and optimization, Physikzentrum, Bad Honnef, Germany, November 2017
Global rigidity of periodic frameworks, Cornell Conference on Rigidity: Stability of Structures, Large and Small, Cornell University, Ithaca, NY, USA, July 2017
Global rigidity of periodic frameworks with fixed lattice representations, Egervary Seminar , ELTE, Budapest, Hungary, November 2016
Rigidity preserving transformations, Geometric Rigidity Workshop , Lancaster University, Lancaster, UK, June 2016
Characterizing minimally flat symmetric hypergraphs, Rigidity Workshop , Hausdorff Research Institute For Mathematics, Bonn, Germany, October 2015
Rigidity of frameworks on spheres with variable radii, Workshop on Advances in Combinatorial and Geometric Rigidity, Banff International Research Station (BIRS), Banff, AB, Canada, July 2015
Lifting symmetric pictures to polyhedral scenes, Workshop on Geometric Rigidity, Lancaster University , Lancaster, UK, June 2015
Rigidity of frameworks on expanding spheres, Combinatorics Seminar, Queen Mary University of London, London, UK, February 2015
Combinatorial characterisations of rigid frameworks, LMS workshop on Applied Algebraic Topology, Queen Mary University of London, London, UK, January 2015
Rigidity and flexibility of symmetric structures, Graduiertenkolleg: Experimentelle und konstruktive Algebra , RWTH Aachen, Aachen, Germany, December 2014
Frameworks and linkages with symmetry, Workshop on configuration spaces of linkages, American Institute of Mathematics (AIM), Palo Alto, CA, USA, November 2014
Rigidity, symmetry and applications, Discrete Optimization and Algorithms Research Seminar, RIMS, Kyoto University, Kyoto, Japan, September 2013
On the Symmetric Molecular Conjectures, 6th International workshop on Computational Kinematics , Resid�ncia d'Investigadors , Barcelona, Spain, May 2013
Generic rigidity with symmetry, Workshop on Geometric and Topological Graph Theory , University of Bristol , Bristol, UK, April 2013
On equidissections of squares and other polygons, Combinatorics Seminar , University of Bristol , Bristol, UK, November 2012
On the area discrepancy of triangulations of squares and trapezoids, Pure Mathematics Seminar , Lancaster University , Lancaster, UK, October 2012
How does symmetry impact the flexibility of proteins?, Workshop on Rigidity of periodic and symmetric structures in nature and engineering , The Kavli Royal Society International Centre , Buckinghamshire, UK, February 2012
Finite motions from periodic frameworks with added symmetry, CMS Winter Meeting (Special Session on Discrete Geometry), Toronto, ON, Canada, December 2011
Symmetric versions of Laman's Theorem, Western Michigan University Colloquium, Western Michigan University, Kalamazoo, MI, USA, November 2011
Counts for predicting symmetric motions in frameworks with applications to protein flexibility, Workshop on Rigidity and Symmetry, Fields Institute, Toronto, ON, Canada, October 2011
Protein flexibility of dimers: do symmetric motions play a role in allosteric interactions?, Applied Mathematics, Modeling and Computational Science Conference (AMMCS) 2011, Wilfried Laurier University, Waterloo, ON, Canada, July 2011
Finite motions from periodic frameworks with added symmetry, Workshop on Topological and Geometric Combinatorics, Mathematisches Forschungsinstitut Oberwolfach (MFO), Oberwolfach, Germany, February 2011
Detecting mechanisms in symmetric structures via orbit counts, LMS Workshop: Rigidity of Frameworks and Applications, Lancaster University, Lancaster, UK, July 2010
The orbit rigidity matrix of a symmetric framework, Graduiertenkolleg: Methods for Discrete Structures, FU Berlin, Berlin, Germany, February 2010
Symmetric versions of Laman's Theorem, Workshop on Rigidity and Volume Inequalities, ELTE, Budapest, Hungary, July 2009
Characterizations of symmetric generically isostatic graphs, Discrete Geometry Seminar, TU Berlin, Berlin, Germany, June 2009
Symmetry as a sufficient condition for a finite flex, AMS Spring Eastern Section Meeting (Special Session on Discrete Geometry and Combinatorics), Worcester Polytechnic Institute, Worcester, MA, USA, April 2009
Symmetric versions of Laman's Theorem, Discrete Geometry and Combinatorics Seminar, Cornell University, Ithaca, NY, USA, March 2009
Symmetry as a sufficient condition for a finite flex, Workshop on Discrete Differential Geometry, Mathematisches Forschungsinstitut Oberwolfach (MFO), Oberwolfach, Germany, January 2009
Symmetry as a sufficient condition for a finite flex, Discrete Geometry Meeting, Fields Institute, Toronto, ON, Canada, November 2008
Rigidity of frameworks with symmetry constraints, Workshop on Recent Progress in Rigidity Theory, Banff International Research Station (BIRS), Banff, AB, Canada, July 2008
Rigidity of symmetric frameworks, Workshop on Rigidity and Polyhedral Combinatorics, American Institute of Mathematics (AIM), Palo Alto, CA, USA, December 2007
Teaching
Lent Term 2021: Instructor for MATH 327 (Combinatorics)
Michaelmas Term 2020: Instructor for MATH 101 (Calculus)
Michaelmas Term 2020: Instructor for MATH 271 (Minor Course in Mathematics)
Lent Term 2020: Instructor for MATH 327 (Combinatorics)
Michaelmas Term 2019: Instructor for MATH 101 (Calculus)
Lent Term 2019: Instructor for MATH 240 (Project skills: project 1: Matchings in bipartite graphs; project 2: Hamiltonian graphs and the TSP)
Michaelmas Term 2018: Instructor for MATH 327 (Combinatorics)
Michaelmas Term 2018: Instructor for MATH 101 (Calculus)
Michaelmas Term 2017: Instructor for MATH 390 (Project Skills: Vector Calculus)
Michaelmas Term 2017: Instructor for MATH 327 (Combinatorics)
Michaelmas Term 2017: Instructor for MATH 101 (Calculus)
Lent Term 2017: Instructor for MATH 327 (Combinatorics)
Lent Term 2016: Instructor for MATH 327 (Combinatorics)
Lent Term 2016: Instructor for MATH 113 (Geometry and Calculus)
Lent Term 2015: Instructor for MATH 113 (Geometry and Calculus)
Michaelmas Term 2014: Instructor for MATH 327 (Combinatorics)
Lent Term 2014: Instructor for MATH 113 (Geometry and Calculus)
Michaelmas Term 2013: Instructor for MATH 327 (Combinatorics) (this is a new course I designed in summer 2013)
Lent Term 2013: Instructor for MATH 113 (Geometry and Calculus)
Michaelmas Term 2012: Instructor for MATH 142 (Determinants, Vectors and Further Complex Numbers)
Michaelmas Term 2012: Instructor for MATH 390 (Project Skills: Spherical Geometry and Map Projections)
Winter 2010: Instructor for Discrete Geometry II (with Günter M. Ziegler)
Summer 2010: Instructor for Lineare Algebra II (with Günter M. Ziegler)
Winter 2012: Instructor for MATH 1025 (Applied Linear Algebra)
Winter 2008: Instructor for MATH 2320 (Discrete Mathematical Structures)
Winter 2009: Tutorials for MATH 3050 (Introduction to Geometries)
Fall 2008: Tutorials for MATH 3050 (Introduction to Geometries)
Winter 2002: Tutorials for MATH 1160 (Finite Mathematics and Applications)
Fall 2001: Instructor for GERMAN 100
Miscellaneous
Miscellaneous links (various mathematical links, group photos of some workshops I attended, my Erdös number, etc.)
last updated: July 2021