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Student Seminar Differential Geometry and Mathematical Physics (Winter 2019)

  • The available topics will be presented at the introductory meeting on Monday November 4 at 10:15 in MA 874/875.
  • The assignment of topics will take place on Monday November 11 at 14:15 in MA 874/875.

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.

Talks

Monday, 3 February
NameTitelZeit
Lev ChusovitinRigidity of polyhedra and circle polyhedra I12:00
Shana ChoukriRigidity of polyhedra and circle polyhedra II13:00
Niklas DenglerRigidity of polyhedra and circle polyhedra III14:00
Janosch HübnerComposition of binary quadratic forms15:00

Thursday, 6 February
NameTitelZeit
Saskia StrempelCentering Koebe polyhedra via Möbius transformations I12:00
Janna GolzeCentering Koebe polyhedra via Möbius transformations II13:00
Alireza SelahiSatz von Poncelet I14:00
Nina SmeenkSatz von Poncelet II15:00

Monday, 10 February
NameTitelZeit
Max RögerEuler equations on gl(3), cubic curves, and inscribed polygons12:00
Tim ZemlinDiscretization of the Euler top13:00
Nikolas DemmingContact Hamiltonian systems14:00
Arbi Moses BadlyanTime discretization of Lie-Poisson systems15:00
Stefanie SchindlerGeodesically convex gradient systems16:00

Tuesday, 11 February
NameTitelZeit
Miguel Medina GarciaDelaunay triangulations of points on circles10:00
Paulina JedrzejewskaA hyperbolic view of the seven circle theorem11:00
Leander BlumeOn unfoldings of stretched polyhedra12:00
Victor-Panos Rohde-GouromichosAffine Hopf fibrations13:00

Wednesday, 12 February
NameTitelZeit
Matthias ScheerCross ratio dynamics12:00
Niklas MartensenOn causality theory for spacetimes13:00
Robert TischerFlexible quadrilateral surfaces14:00
Stephan WormBonnet pairs and isothermic surfaces15:00

Thursday, 12 February
NameTitelZeit
Oliver GrossTBA12:00

All talks will take place at MA 874/875, all times s.t.

Topics

Boris Springborn

  • Rigidity of polyhedra and circle polyhedra (3 talks) ← Lev Chusovitin, Shana Choukri, Niklas Dengler
    • Herman Gluck. Almost all simply connected closed surfaces are rigid. [doi]
    • John C. Bowers, Philip L. Bowers, Kevin Pratt. Almost all circle polyhedra are rigid. [arxiv]
    • John C. Bowers, Philip L. Bowers, Kevin Pratt. Rigidity of Circle Polyhedra in the 2-Sphere and of Hyperideal Polyhedra in Hyperbolic 3-Space. [arxiv]
  • Centering Koebe polyhedra via Möbius transformations (1-2 talks) ← Saskia Strempel, Janna Golze
    • B. Springborn. A unique representation of polyhedral types. Centering via Möbius transformations. [doi] (B)
    • Zsolt Lángi. Centering Koebe polyhedra via Möbius transformations. [arxiv]
  • Composition of binary quadratic forms: Felix Klein's interpretation in terms of lattices and complex multiplication (1 talk) (M) ← Janosch Hübner
    • Felix Klein. Über die Komposition der binären quadratischen Formen (1893). In: Gesammelte mathematische Abhandlungen, Band 3, 283-286. [pdf]
    • Andreas Speiser. Über die Komposition der binären quadratischen Formen. In: H. Weber Festschrift (1912), 375-395. [pdf]

John Sullivan

  • Delaunay triangulations of points on circles (1 talk) ← Miguel Medina Garcia
    • Vincent Despré, Olivier Devillers, Hugo Parlier, Jean-Marc Schlenker. Delaunay Triangulations of Points on Circles. [arxiv]
  • A hyperbolic view of the seven circle theorem (1 talk) ← Paulina Jedrzejewska
    • Kostiantyn Drach, Richard Evan Schwartz. A Hyperbolic View of the Seven Circles Theorem. [arxiv]
  • On unfoldings of stretched polyhedra (1 talk) ← Leander Blume
    • Gözde Sert, Sergio Zamora. On Unfoldings of Stretched Polyhedra. [arxiv]
  • Affine Hopf fibrations (1 talk) (M) ← Victor-Panos Rohde-Gouromichos
    • V. Ovsienko, S. Tabachnikov. Affine Hopf fibrations. [arxiv]

Yuri Suris

  • Satz von Poncelet (2 talks) ← Alireza Selahi, Nina Smeenk
    • On the QRT map (chapter in Duistermaat)
    • Vladimir Dragovic, Milena Radnovic. Ellipsoidal billiards in pseudo-euclidean spaces and relativistic quadrics. [arxiv]
  • Euler equations on gl(3), cubic curves, and inscribed polygons (1 talk) ← Max Röger
    • Konstantin Aleshkin and Anton Izosimov. Euler equations on the general linear group, cubic curves, and inscribed hexagons. [pdf]
  • Discretization of the Euler top (1 talk) ← Tim Zemlin
    • Robert I. McLachlan, Klas Modin, Olivier Verdier. A minimal-variable symplectic integrator on spheres. [arxiv]
  • Contact Hamiltonian systems (1 talk) ← Nikolas Demming
    • Manuel Lainz Valcázar, Manuel de León. Contact Hamiltonian systems. [pdf]
  • Time discretization of Lie-Poisson systems ← Arbi Moses Badlyan

Alexander Bobenko

  • Cross ratio dynamics (1 talk) ← Matthias Scheer
    • Maxim Arnold, Dmitry Fuchs, Ivan Izmestiev, Serge Tabachnikov. Cross-ratio dynamics on ideal polygons. [arxiv]
  • Discrete mean curvature flows (1 talk) ← Daniel Krogmann
  • Flexible quadrilateral surfaces (2 talk) ← Robert Tischer
    • Ivan Izmestiev. Classification of flexible Kokotsakis polyhedra with quadrangular base. [arxiv] (M)
    • Wolfgang K. Schief, Alexander I. Bobenko and Tim Hoffmann. On the Integrability of Infinitesimal and Finite Deformations of Polyhedral Surfaces. [pdf]
  • Bonnet pairs and isothermic surfaces (1 talk) ← Stephan Worm
    • George Kamberov, Franz Pedit, Ulrich Pinkall. Bonnet pairs and isothermic surfaces. [arxiv]

Almost all topics are suitable to be turned into a Bachelor or Master thesis. The exceptional cases are indexed by (B), if recommended for Bachelor, and (M), if recommended for Master.

Responsible professors

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

Previous semester: Summer 2019


Felix Knoeppel . 16.01.2020.