Arbeitsgruppe Geometrie

Studierendenseminar der AG Geometrie und Mathematische Physik (Winter 2015)

• Es fehlen noch Unterschriften (Nötig, falls ihr euch das Seminar als Studienleistung anrechnen lassen möchtet).
• Zur Erinnerung: Bitte schickt mir eine Mail (an knoeppel@math.tu-berlin.de) mit euren Daten, d.h.
  • Name,
  • Matrikelnummer,
  • Studiengang,
  • Thema,
  • Professor.
• Die Einführungsveranstaltung mit Präsentation findet am 28.10.15 um 14 Uhr im MA 874/875 statt.
• Die Vergabe der Themen findet am 04.11.15 um 14 Uhr im MA 874/875 statt.

Themen

Alexander Bobenko

• Discrete parameterized surfaces (André Greiner-Petter)
  • Tim Hoffmann, Andrew O. Sageman-Furnas, Max Wardetzky, A discrete parametrized surface theory in R³. arXiv:1412.7293 [math.DG] [online]
  
  
• Discrete parameterized surfaces: constant mean curvature (Akraam Alraai)
  • Tim Hoffmann, Andrew O. Sageman-Furnas, Max Wardetzky, A discrete parametrized surface theory in R³. arXiv:1412.7293 [math.DG] [online]
  
  
• Isothermic Triangulated Surfaces (Yve Mehlan)
  • Wai Yeung Lam, Ulrich Pinkall, Isothermic Triangulated Surfaces. arXiv:1501.02587 [math.DG] [online]
  
  
• Discrete minimal surfaces (Viktoria Schwarzott)
  • Wai Yeung Lam, Discrete minimal surfaces: critical points of the area functional from integrable systems. arXiv:1510.08788 [math.DG] [online].
  
  
• Tutte's theorem (Felix Prause)
  • Gortler, Steven J.; Gotsman, Craig; Thurston, Dylan, Discrete one-forms on meshes and applications to 3D mesh parameterization. Computer Aided Geometric Design 23 (2): 83-112 [online]
  
  
• Applications of Tutte's theorem in geometry processing and computer graphics (Marcel Padilla)
  • Noam Aigerman, Yaron Lipman, Orbifold Tutte Embeddings. ACM SIGGRAPH Asia 2015 [online]
  
  

Boris Springborn

• Löwner's differential equation for slit domains (Nimrod Knoller)
  • Goluzin, G. M., Geometric theory of functions of a complex variable. Translations of Mathematical Monographs, Vol. 26 American Mathematical Society, Providence, R.I. 1969
  • Golusin, G. M., Geometrische Funktionentheorie. Hochschulbücher für Mathematik, Bd. 31. VEB Deutscher Verlag der Wissenschaften, Berlin, 1957
  
  
• Tilt formulas and horospherical Delaunay triangulations (Paula Rockmann)
  • Weeks, Jeffrey R., Convex hulls and isometries of cusped hyperbolic 3-manifolds. Topology Appl. 52 (1993), no. 2, 127-149. [doi]
  • Sakuma, Makoto; Weeks, Jeffrey R., The generalized tilt formula. Geom. Dedicata 55 (1995), no. 2, 115-123. [doi]
  
  
• Holomorphic vector fields and quadratic differentials on planar triangulations (Philipp Ripplinger)
  • Wai Yeung Lam, Ulrich Pinkall, Holomorphic vector fields and quadratic differentials on planar triangulations. arXiv:1506.08099 [math.CV]. [online]
  
  
• Discrete conformal equivalence in 3D is the same as Möbius equivalence (David Reich)
  

John Sullivan

• Lebesgue universal covering problem (José Mandujano)
  • John C. Baez, Karine Bagdasaryan, Philip Gibbs, The Lebesgue Universal Covering Problem. arXiv:1502.01251 [math.MG] [online]
  
  
• Minimum solid angle in a tetrahedron (Peter Seikowski)
  • Arseniy Akopyan, Roman Karasev, Bounding minimal solid angles of polytopes. arXiv:arXiv:1505.05263 [math.MG] [online]
  
  
• Complexity measures for 3-manifolds (Corrie Barthelheimer)
  • Jae Choon Cha, Complexities of 3-manifolds from triangulations, Heegaard splittings, and surgery presentations. arXiv:1506.00757 [math.GT] [online]
  
  
• Fáry/Milnor for C¹ limits (Dennis Choy)
  • Henryk Gerlach, Philipp Reiter, Heiko von der Mosel, The elastic trefoil is the twice covered circle. arXiv:1510.06171 [math.DG] [online]
  (Here we're talking about the Appendix of that paper. Of course the rest of the paper could be a topic for a more ambitious and analytic project.)
  
  
• Fullerenes / Shapes of Polyhedra (Viktoria Langer, Juliane Pawlitzki)
  • Victor M. Buchstaber, Nickolai Erokhovets, Construction of fullerenes. arXiv:1510.02948 [math.CO] [online]
  • Richard Evan Schwartz, Notes on Shapes of Polyhedra. arXiv:1506.07252 [math.GT] [online]
  • William P. Thurston, Shapes of polyhedra and triangulations of the sphere. arXiv:math/9801088 [math.GT] [online]
  (This of course could easily be split into several seminar topics. A master's thesis might want to combine and compare the papers.)
  
  
• Scribability of polytopes (Julia)
  • Hao Chen, Arnau Padrol, Scribability problems for polytopes. arXiv:1508.03537 [math.MG] [online]
  (On Monday, Nov 2 at 2 pm, Arnau Padrol talks about scribability problems on polytopes at Graduiertenkolleg: Methods for Discrete Structures of FU Berlin.)
  
  

Yuri Suris

• Why isothermic surfaces are called isothermic? (Laura Schumacher)
  • Darboux, Gaston, Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitésimal. Gauthier-Villars 1887-96 [excerpt]
  
  
• Elliptic curves and geometry (Luise Benke)
  • Dimitri Zvonkine, Courbes Elliptiques dans la Géométrie Elémentaire. Quadrature, 1997, no. 27, 5-13 [online]
  
  
• Poisson reduction on the space of polygons (Alejandro Torres Orjuela)
  • Ian Marschall, Poisson reduction on the space of polygons. International Mathematics Research Notices, Vol. 2015, No. 18, pp. 8925-8958, [online]
  
  
• Generalization of Kahan's integrator for polynomial vector fields of degree > 2 (Rico)
  • Elena Celledoni, Robert I. McLachlan, David I. McLaren, Brynjulf Owren, G. R. W. Quispel, Discretization of polynomial vector fields by polarization. [online]
  
  
• Commuting exterior billiards (Alexej Jordan)
  • Serge Tabachnikov, Commuting dual billiard maps. Geometriae Dedicata 53: 57-68, 1994. [online]
  
  
• Functions whose poisson brackets are constant (Stefanie Schindler)
  

Die Vorträge dauern 45 Minuten mit anschließenden Fragen. Bitte besprechen Sie Ihr Thema und den Inhalt nach der Vergabe mit dem jeweiligen verantwortlichen Dozenten (siehe unten). Für die erfolgreiche Teilnahme am Seminar ist die Anwesenheit bei mindestens 10 Studierendenvorträgen erforderlich.

Termine

Montag, der 1. Februar

Mittwoch, der 3. Februar

Donnerstag, der 4. Februar

Montag, der 8. Februar

Mittwoch, der 10. Februar

Donnerstag, der 11. Februar

Freitag, der 12. Februar

Alle Vorträge finden im Raum MA 874/875 statt und können auf deutsch oder englisch gehalten werden. Alle Zeiten sind in 's.t.' angegeben.

Verantwortliche Dozenten

• Prof. Dr. Alexander Bobenko (bobenko@math.tu-berlin.de)
• Prof. Dr. Boris Springborn (springb@math.tu-berlin.de)
• Prof. Dr. John Sullivan (sullivan@math.tu-berlin.de)
• Prof. Dr. Yuri Suris (suris@math.tu-berlin.de)

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

Vorheriges Semester: Sommer 2015