TU Berlin Fakultät II
Institut für Mathematik
     

Arbeitsgruppe Geometrie

       

  

Geometry Group

Members

Projects


Lehre
Verlaufspläne:
  Bachelor
  Diplom
Vergangene Semester

Seminare

Images, Videos, and Games

Virtual Math Labs

Software

Contact



      

Student seminar Differential Geometry and Mathematical Physics (Summer 2019)

  • The available topics will be presented at the introductory meeting on Wednesday April 17 at 16:00 in MA 874/875.
  • The assignment of topics will be on Wednesday April 24 at 16:00 in MA 874/875.
  • Please send a mail with your name, student id and topic to knoeppel[at]math.

This is a block seminar. Each student has to give a 45 minute talk at the end of the semester. Each student has to attend at least 10 talks.

Topics

Alexander Bobenko

  • Flexible quadrileteral nets (B,M)
    • Ivan Izmestiev. Classification of flexible Kokotsakis polyhedra with quadrangular base. International Mathematics Research Notices. 2017. [link]
  • Miquel dynamics (B,M) ← Aldo Kiem
    • Sanjay Ramassamy. Miquel dynamics for circle patterns. arXiv:1709.05509 [math.DS]. [link]
    • Alexey Glutsyuk, Sanjay Ramassamy. A first integrability result for Miquel dynamics. arXiv:1801.01082 [math.DS]. [link]
  • Dimers and circle patterns (B,M)
    • Richard Kenyon, Wai Yeung Lam, Sanjay Ramassamy, Marianna Russkikh. Dimers and circle patterns. arXiv:1810.05616 [math-ph]. [link]

Ulrich Pinkall

  • Symmetric moving frames (B,M)
    • Etienne Corman, Keenan Crane. Symmetric Moving Frames. ACM Trans. Graph., Vol. 38, No. 4, Article 87. Publication date: 2019. [project page]
  • Real-time viscous thin films (B)
    • Orestis Vantzos, Saar Raz and Mirela Ben-Chen. Real-time Viscous Thin Films. ACM Transactions on Graphics 37(6), SIGGRAPH Asia 2018. [link]
  • Physical simulation of environmentally induced thin shell deformation (B,M) ← Kai Henning
    • Hsiao-yu Chen, Arnav Sastry, Wim M. van Rees, Etienne Vouga. Physical simulation of environmentally induced thin shell deformation. SIGGRAPH (ACM Transactions on Graphics), 2018. [link]
  • Fast winding numbers for soups and clouds (B,M)
    • Gavin Barill, Neil G. Dickson, Ryan Schmidt, David I.W. Levin, Alec Jacobsen. Fast winding numbers for soups and clouds. ACM Transactions on Graphics, Vol. 37, No. 4, Article 43. Publication date: August 2018. [link]
  • Canonical Möbius subdivision (B,M) ← Josef Pelz
    • Amir Vaxman, Christian Müller, Ofir Weber. Canonical Möbius subdivision. ACM Trans. Graph., Vol. 37, No. 6, Article 227. Publication date: November 2018.[link]

Boris Springborn

  • Simple closed curves on a hyperbolic torus with one cusp (B,M) ← Christopher Duncan
    • Greg McShane. A remarkable identity for lenghts of curves. PhD thesis, U Warwick, 1991. [link]
  • Flipping from one surface triangulation to another (algorithmically) (B,M) ← Luise Benke
    This is hidden in the following paper about much more complicated stuff:
    • Lee Mosher. Tiling the projective foliation space of a punctured surface. Trans. Amer. Math. Soc. 306 (1988), no. 1, 1-70. [link]
    The connectivity theorem for elementary moves is on p. 36, and the algorithmic proof begins on the bottom of p. 37 with the words:
    "Despite this plethora of proofs of the Connectivity Theorem, we wish to give a new proof, completely combinatorial in spirit, and quite elementary. Our proof has the advantage that it implicitly gives an algorithm for constructing a sequence of elementary moves ... "
  • Flipping from one 3-manifold (pseudo-)triangulation to another (B,M) ← Leon Ludwig
    • J. Hyam Rubinstein, Henry Segerman, Stephan Tillmann. Traversing three-manifold triangulations and spines. arXiv:1812.02806 [math.GT]. [link]
  • Configurations of non-intersecting straight lines in RP3 (B,M)
    • Julia Viro and Oleg Viro. Configurations of skew lines. arXiv:math/0611374 [math.GT]. [link]
  • Discrete harmonic maps (B,M) ← Jakob Wessel
    • Jonah Gaster, Brice Loustau, Léonard Monsaingeon. Computing discrete equivariant harmonic maps. arXiv:1810.11932 [math.GT]. [link]

John Sullivan

  • Descartes circle theorem, Steiner porism, and spherical designs (B,M) ← José Mandujano
    • Richard Evan Schwartz, Serge Tabachnikov. Descartes circle theorem, Steiner porism, and spherical designs. arXiv:1811.08030 [math.MG]. [link]
  • Delaunay triangulation of points on circles (B)
    • Vincent Despré, Olivier Devillers, Hugo Parlier, Jean-Marc Schlenker. Delaunay triangulation of points on circles. arXiv:1803.11436 [cs.CG]. [link]
  • Torsion of locally convex curves (B) ← Julian Marx
    • Mohammad Ghomi. Torsion of locally convex curves. arXiv:1704.00081 [math.DG]. [link]
  • The length, width, and inradius of space curves (B,M) ← Dennis Choy
    • Mohammad Ghomi. The length, width, and inradius of space curves. arXiv:1605.01144 [math.DG]. [link]

Yuri Suris

  • The Symmetric Representation of the Generalized Rigid Body Equations and Symplectic Reduction (B,M) ← Gentaro Masuda
    • Tomoki Ohsawa. The Symmetric Representation of the Generalized Rigid Body Equations and Symplectic Reduction. arXiv:1811.03184 [math-ph]. [link]
  • Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature (B,M)
    • Krishan Rajaratnam, Raymond G. McLenaghan and Carlos Valero. Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature. arXiv:1607.00712[link]
  • Classification of the orthogonal separable webs for the Hamilton-Jacobi and Laplace-Beltrami equations on 3-dimensional hyperbolic and de Sitter spaces (B,M)
    • Carlos Valero, Raymond G. McLenaghan. Classification of the orthogonal separable webs for the Hamilton-Jacobi and Laplace-Beltrami equations on 3-dimensional hyperbolic and de Sitter spaces. Journal of Mathematical Physics 60, 033501 (2019). [link]
  • Canonical Melnikov theory for diffeomorphisms (B,M)
    • H.E. Lomeli, J.D. Meiss, R. Ramirez-Ros. Canonical Melnikov theory for diffeomorphisms. arXiv:0706.2515 [nlin.CD]. [link] [doi]
  • Interpolating vector fields for near identity maps and averaging (B,M)
    • V. Gelfreich, A. Vieiro. Interpolating vector fields for near identity maps and averaging. arXiv:1711.01983. [link] [iop]
  • Geometry of Discrete-Time Spin Systems (B,M) ← Julien Grubisic
    • Robert I. McLachlan, Klas Modin, Olivier Verdier. Geometry of Discrete-Time Spin Systems. arXiv:1505.04035 [math-ph]. [link] [doi]
  • ADMM and Accelerated ADMM as Continuous Dynamical Systems ← Duc Nguyen
  • Algebraic entropy of birational maps with invariant curves ← Jana Larisch
  • Time discretization of Lie-Poisson systems ← Arbi Moses Badlyan

Responsible professors

Assistent: Felix Knöppel (knoeppel@math.tu-berlin.de)

Previous semester: Winter 2018


Felix Knoeppel . 16.05.2019.