Bernd Schulze I am currently a postdoctoral fellow in the Department of Mathematics and Statistics at York University Previously I worked as a postdoctoral fellow at the Fields Institute for Research in Mathematical Sciences for the duration of the Thematic Program on Discrete Geometry and Applications From June 2009 till June 2011 I worked as a postdoctoral fellow in the Discrete Geometry Group at the FU Berlin under the direction of Prof. Guenter M. Ziegler Current Address: Department of Mathematics and Statistics York University 4700 Keele Street Toronto, ON, M3J 1P3 Canada Office: Ross S618 Telephone: +1 (416) 736-2100 - 66672 E-Mail: bschulze -at- mathstat.yorku.ca

Research

Publications

Talks and Presentations

Teaching

CV (March 2012)

DiscreGeom Seminar

• Discrete geometry, rigidity theory, symmetry, triangulations, polytope theory, graph theory, matroids, combinatorics, algebraic methods, representation theory, computational geometry, interdisciplinarity
• I am currently particularly interested in the rigidity and flexibility of symmetric framework systems as well as in `equal-area-triangulation problems'.

Published or accepted in refereed journals:

• Coning, symmetry, and spherical frameworks
  with Walter Whiteley
  To appear in Discrete & Computational Geometry, 2012

• The orbit rigidity matrix of a symmetric framework
  with Walter Whiteley
  Discrete & Computational Geometry 46, Issue 3, 561-598, 2011

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

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

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

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

• When is a symmetric body-bar structure isostatic?
  with Simon Guest and Walter Whiteley
  International Journal of Solids and Structures 47, 2745-2754, 2010

• Symmetric versions of Laman's Theorem
  Discrete & Computational Geometry 44, Issue 4, 946-972, 2010
  

• Block-diagonalized rigidity matrices of symmetric frameworks and applications
  Contributions to Algebra and Geometry 51, No. 2, 427-466, 2010

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

• When is a symmetric pin-jointed framework isostatic?
  with Robert Connelly, Patrick Fowler, Simon Guest, and Walter Whiteley
  International Journal of Solids and Structures 46, 762-773, 2009

Published or accepted in refereed conference proceedings:

• Mobility of symmetry-regular bar-and-joint frameworks
  with Patrick Fowler and Simon Guest
  To appear in The Fields Institute Conference Proceedings (workshops on rigidity and symmetry), 2012

• Protein flexibility of dimers: do symmetric motions play a role in allosteric interactions?
  with Adnan Sljoka and Walter Whiteley
  AIP Conference Proceedings of AMMCS 2011, Vol. 1368, doi:10.1063/1.3663478, 135-138, 2011

Submitted to refereed journals:

• How does symmetry impact the flexibility of proteins?
  with Adnan Sljoka and Walter Whiteley
  Submitted, 2012

Ph.D. Thesis:

• Combinatorial and Geometric Rigidity with Symmetry Constraints
  York University, Toronto, ON, Canada, May 2009
  Advisor: Prof. Walter Whiteley
  Committee: Prof. Asia Ivic Weiss, Prof. Mike Zabrocki, and Prof. Meera Sitharam
  The thesis was awarded the York University Dissertation Prize 2010

• 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, U.K., February 2012

• Finite motions from periodic frameworks with added symmetry
  CMS Winter Meeting (Special Session on Discrete Geometry)
  Toronto, ON, December 2011

• Symmetric versions of Laman's Theorem
  Western Michigan University Colloquium
  Western Michigan University, Kalamazoo, 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
  London Mathematical Society 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

• A symmetry-adapted version of Maxwell's rule for rigidity of frameworks
  Geometry Seminar
  York University, Toronto, ON, Canada, November 2006

• A proof of Alexandrov's Theorem using static rigidity
  Geometry Seminar
  York University, Toronto, ON, Canada, December 2005

• Infinite families of nontrivial trivalent graphs which are not Tait colorable
  Graph Theory Seminar
  Western Michigan University, Kalamazoo, MI, USA, March 2003

• Colorings and orientations of graphs
  Graph Theory Seminar
  FU Berlin, Berlin, Germany, November 2000

At TU Berlin:

• Winter 2010: Co-Instructor for Discrete Geometry II (with Guenter M. Ziegler)

• Summer 2010: Co-Instructor for Lineare Algebra II (with Guenter M. Ziegler)

At York University:

• 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)

• MATH LAB

At Western Michigan University:

• Winter 2002: Tutorials for MATH 1160 (Finite Mathematics and Applications)

• Fall 2001: Instructor for GERMAN 100

last updated: March 20, 2012