Bernd Schulze

  • I am a Senior Lecturer in the Department of Mathematics and Statistics at Lancaster University.
  • Before coming here, I held postdoctoral positions at the Fields Institute, University of Toronto, (from 07.2011 to 12.2011) and at York University (from 01.2012 to 06.2012).
  • Prior to that (from 06.2009 to 06.2011), I worked as a postdoctoral fellow in the Discrete Geometry Group at the TU Berlin (and FU Berlin) under the direction of Günter M. Ziegler.
  • I studied mathematics and computer science at the FU Berlin and at Western Michigan University, and I did my Ph.D. in Toronto (York University, 05.2009) with Walter Whiteley.


  • 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

    Lancaster University

    Research

    Publications

    Talks and Presentations

    Teaching

    Miscellaneous


    Research interests

    Some nice examples:


    Publications

      Preprints/papers in preparation:

    1. Katie Clinch, Anthony Nixon, Bernd Schulze and Walter Whiteley, Pairing symmetries for projective and spherical frameworks, in preparation, 2018

    2. Derek Kitson, Anthony Nixon and Bernd Schulze, Rigidity of symmetric frameworks in normed spaces, submitted, 31 pages, 2018

    3. Bernd Schulze, Hattie Serocold and Louis Theran, Frameworks with coordinated edge motions, submitted, 2018

    4. Viktoria Kaszanitzky and Bernd Schulze, Sufficient connectivity conditions for rigidity of symmetric frameworks, submitted, 18 pages, 2018

    5. Viktoria Kaszanitzky, Csaba Kiraly and Bernd Schulze, Sufficient conditions for the global rigidity of periodic graphs, submitted, 13 pages, 2018

    6. Anthony Nixon, Bernd Schulze, Shin-ichi Tanigawa and Walter Whiteley, Rigidity of frameworks on expanding spheres, submitted, 22 pages, 2017

    7. Viktoria Kaszanitzky, Bernd Schulze and Shin-ichi Tanigawa, Global rigidity of periodic graphs under fixed lattice representations, submitted, 36 pages, 2016


    8. Papers published or accepted in refereed journals:

    9. 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, to appear, 31 pages, 2018

    10. Patrick Fowler, Simon Guest and Bernd Schulze, Mobility of symmetric block-and-hole polyhedra, International Journal of Solids and Structures, to appear, 12 pages, 2018

    11. Viktoria Kaszanitzky and Bernd Schulze, Characterizing minimally flat symmetric hypergraphs, Discrete Applied Mathematics 236, 256-269, 2018

    12. Stephen Power and Bernd Schulze, String-node nets and meshes, Discrete & Computational Geometry 59, 31-58, 2018

    13. Derek Kitson and Bernd Schulze, Motions of grid-like reflection frameworks, Journal of Symbolic Computation, 88, 47-66, 2018

    14. Viktoria Kaszanitzky and Bernd Schulze, Lifting symmetric pictures to polyhedral scenes, Ars Mathematica Contemporanea 13(1), 31-47, 2017

    15. 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

    16. 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

    17. Anthony Nixon and Bernd Schulze, Symmetry-forced rigidity of frameworks on surfaces, Geometriae Dedicata 182, No. 1, 163-201, 2016

    18. Derek Kitson and Bernd Schulze, Maxwell-Laman counts for bar-joint frameworks in normed spaces, Linear Algebra and its Applications 481, 313-329, 2015

    19. Bernd Schulze and Shin-ichi Tanigawa, Infinitesimal rigidity of symmetric bar-joint frameworks, SIAM Journal on Discrete Mathematics 29, No.3, 1259-1286, 2015

    20. Bernd Schulze and Shin-ichi Tanigawa, Linking rigid bodies symmetrically, European Journal of Combinatorics 42, 145-166, 2014

    21. Anthony Nixon, Bernd Schulze, Adnan Sljoka and Walter Whiteley, Symmetry adapted Assur decompositions , Symmetry 6 (3), 516-550, 2014

    22. 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

    23. 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

    24. Bernd Schulze and Walter Whiteley, Coning, symmetry, and spherical frameworks, Discrete & Computational Geometry 48, Issue 3, 622-657, 2012

    25. Bernd Schulze and Walter Whiteley, The orbit rigidity matrix of a symmetric framework, Discrete & Computational Geometry 46, Issue 3, 561-598, 2011

    26. Bernd Schulze, On the area discrepancy of triangulations of squares and trapezoids, The Electronic Journal of Combinatorics 18 (1), P137, 1-16, 2011

    27. Elissa Ross, Bernd Schulze, Walter Whiteley, Finite motions from periodic frameworks with added symmetry, International Journal of Solids and Structures 48, 1711-1729, 2011

    28. Bernd Schulze, Symmetric Laman theorems for the groups C_2 and C_s, The Electronic Journal of Combinatorics 17 (1), R154, 1-61, 2010

    29. Bernd Schulze, Symmetry as a sufficient condition for a finite flex, SIAM Journal on Discrete Mathematics 24, No. 4, 1291-1312, 2010

    30. 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

    31. Bernd Schulze, Symmetric versions of Laman's Theorem, Discrete & Computational Geometry 44, Issue 4, 946-972, 2010

    32. 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

    33. Bernd Schulze, Injective and non-injective realizations with symmetry, Contributions to Discrete Mathematics 5, No. 1, 59-89, 2010

    34. 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


    35. Papers published or accepted in refereed conference proceedings:

    36. Alyx, Burns, Bernd Schulze and Audrey St.John, Persistent multi-robot formations with redundancy, in Proceedings of the 13th International Symposium on Distributed Autonomous Robotic Systems (DARS 2016), Springer, 14 pages, 2018

    37. 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

    38. 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

    39. 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


    40. Book chapters:

    41. Bernd Schulze, Combinatorial rigidity of frameworks under symmetry, in Handbook of Geometric Constraint Systems Principles, Editors: Jessica Sidman, Meera Sitharam, Audrey St. John, CRC press (to appear in 2018)

    42. 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

    43. 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


    44. Ph.D. Thesis:

    45. 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


    Teaching

    At Lancaster University:

    At TU Berlin:

    At York University:

    At Western Michigan University:


    Together with Bruno Benedetti, I organized the Discrete Geometry Seminar at TU Berlin (and FU Berlin) from fall 2009 to summer 2011.


    Miscellaneous


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    last updated: August 2018