Kis-Sem: Keep it simple Seminar

This weekly seminar is intended for PhD Students and Postdocs to informally discuss topics in the field of Geometry and Mathematical Physics.

  • Last Occurrence: 08.09.2017, 14:00 - 15:00
  • Type: Seminar
  • Location: TU Berlin, MA875 H-Cafe

Contact: Thilo Rörig

Room: MA875 (H-Cafe)

Time: Tuesdays at 14:00, and Fridays at 14:00



  • 14:00 - 15:00 Discrete confocal quadrics: general parametrizations, Jan Techter 
  • Classical confocal coordinates can be characterized as factorizable orthogonal coordinates. This characterization is invariant under reparametrization along the coordinate lines. A discretization combining factorizability and a novel discrete orthogonality condition leads to discrete confocal coordinates which may be constructed geometrically via polarity with respect to a sequence of classical confocal quadrics.


  • 14:00 - 15:00 Pleating the hyperbolic plane, Lara Skuppin 
  • I will present a construction due to Thurston and followers on how to bend a plane in hyperbolic three-space along a lamination. This is in some sense inverse to taking the boundary of the convex hull in H^3 of a closed set X on the sphere at infinity. By the way: in the case where the set X consists of finitely many points, the latter construction yields an ideal hyperbolic polyhedron.


  • 14:00 - 15:00 Secondary Fans and Secondary Polyhedra of Punctured Riemann Surfaces, Robert Loewe 


  • 14:00 - 15:00 Ricci flow, Hanka Kourimska 


  • 14:00 - 15:00 Hyperbolic geodesics and tractrix metric, Niklas Affolter 


  • 14:00 - 15:00 Pluri-Lagrangian systems - discrete and smooth, Mats Vermeeren 


  • 14:00 - 15:00 On conformally equivalent triangle lattices, Ulrike Bücking 


  • 14:00 - 15:00 Phenomena of spin transformations with prescribed bi-normal, Christoph Seidel 


  • 14:00 - 15:00 A variational principle for isoradial graphs, Niklas Affolter 
  • I will repeat the basic idea of Rivin's theorem on prescribed dihedral angles and the discrete conformal theory. Then I want to show how these ideas can be reapplied to get to a variational principle for general isoradial graphs, and how consequently one can combine them to get a principle for flat isoradial graphs.


  • 14:00 - 15:00 Some aspects of integrability in the Six Vertex model, Ananth Sridhar 
  • I will review the basic correspondence between the Hamiltonian and the Lagrangian frameworkd and talk about some aspects of integrability in the Six Vertex model.


  • 14:00 - 15:00 Projective differential geometry, Thilo Roerig 
  • I will give a little introduction to *Projective differential geometry* and maybe give a nice description of the Lie quadric in Pluecker geometry.


  • 14:00 - 15:00 Pluri-Lagrangian systems and KdV hierarchy, Mats Vermeeren 
  • Today at 2pm I will talk about pluri-Lagrangian systems. The pluri-Lagrangian description of integrable systems is based on a variational principle and on the key fact that an integrable system is generally part of a family of compatible equations. It can be applied both in the continuous case (e.g. KdV hierarchy) and in the discrete case (e.g. quad equations).


  • 14:00 - 15:00 Knots, minimal surfaces, mapping class groups, Benedikt Kolben 
  • Today, the 14.3. at 2pm I would like to talk to you about knots, how one could go about trying to encode them in a finite symbol, what other sciences have to say, and some of the mathematics involved. I will assume that the tools used are far from common knowledge and begin with an introduction to mapping class groups, a key player in our mathematical set-up alongside orbifolds, after outlining the general idea of my approach to knot enumeration.


  • 14:00 - 15:00 Lagrange multipliers of a maximum entropy distribution, Niklas Affolter 
  • Last time Jan talked about the maximum entropy principle. In my talk today I want to show how the Lagrange multipliers involved can be seen as the critical points of a convex functional. We then want to apply this method to the Dimer model and see how far we can take it.


  • 14:00 - 15:00 Plausible inference and the maximum entropy principle, part2, Jan Techter 


  • 13:00 - 14:00 Plausible inference and the maximum entropy principle, Jan Techter 
  • Plausible reasoning is a generalization of deductive reasoning. The main ingredient is Cox's theorem, which states that under certain assumptions of consistency and qualitative correspondence to common(?) sense, plausible inference is governed by the laws of probability theory. Anyway, if you want to reason plausibly you still need some prior probabilities to start with representing your state of knowledge. One possible approach is the maximum entropy principle. It is based on Shannon's finding that (again) given some sensible requirements there is a unique measure for uncertainty of probability distributions. As an application we will derive the Boltzmann/Gibbs distribution of statistical mechanics.


  • 14:30 - 15:30 Smooth polyhedral surfaces, Felix Günther 


  • 15:15 - 15:45 Crystalline structures from hyperbolic tilings, Benedikt Kolben 
  • The EPINET project enumerates crystalline frameworks that arise as structures derived from hyperbolic tilings. Using combinatorial tiling theory by Dress and Delaney, the 3-dimensional structures arising through this process can be ordered by complexity. The aim is to ultimately construct and classify all possible three-dimensional structures that arise in this way. This approach was recently expanded to include regular examples of so-called free tilings, which are tilings that include unbounded tiles and resulted in many novel 3-dimensional structures that also contained separate but interwoven nets. The goal of this work is to construct three-dimensional nets and weavings from hyperbolic tilings that arise by further generalizing the above approach to incorporate irregular tilings with two distinct edges. These tilings are projected onto some prominent examples of triply periodic minimal surfaces such as the P, D, G and H surface. Using this process, we can systematically construct increasingly complicated 3-dimensional structures. While this work has ties to areas as diverse as the mesoscale structure of soft matter or knot theory, before looking at the arising three-dimensional structures, the first step of the problem is to find a way to order, by complexity, all subsymmetries of an asymmetric patch of the minimal surface that represent the same group of symmetries.
  • 16:00 - 16:30 Ricci Flow III: On the topological condition for existence of a circle packing metric with constant Gaussian curvature, Hana Kourimska 
  • In the earlier KisSem talks we have briefly seen that an existence of a circle packing metric with constant Gaussian curvature is equivalent to a certain topological condition, developed by Thurston. The goal of today's talk will be to understand this condition.
  • 16:45 - 17:15 Conjugate Silhouette nets, Thilo Roerig 
  • We will study Laplace transformations of surfaces with conjugate parametrization and show, that degenerate Laplace transformations are characteristic for projective translational surfaces.


  • 14:30 - 15:30 Infinitesimal deformations of discrete surfaces, Wai-Yeung Lam 


  • 14:15 - 15:15 Ricci flow, part 2, Hana Kourimska 
  • After the introduction to the smooth and discrete Ricci flow of a few weeks ago, I will look deeper into the properties of the first of the discrete Ricci flows based on a weighted triangulation. I will discuss some parts of the proof of convergence of this Ricci flow to a metric of constant curvature and the existence and uniqueness of such metric.


  • 14:00 - 15:00 Envelope and orthogonal trajectories of a family of circles, Jan Techter 
  • We will discuss the elementary problem of finding the two envelope curves and all orthogonal trajectories of a one-parameter family of circles in the plane. The latter case is governed by a Riccati equation, which describes the infinitesimal motion of a Möbius transformation. We will also consider a possible discretization using the local symmetry, which leads to similar equations.


  • 14:00 - 15:00 Projective model of Möbius geometry, Thilo Roerig 


  • 12:00 - 13:00 Variational Methods for Discrete Surface Parameterization. Applications and Implementation., Stefan Sechelmann 


  • 13:00 - 14:00 Ricci flow, part 1, Hana Kourimska 
  • Introduced in the 1980's by Richard Hamilton, the Ricci flow is one of the most useful tools nowadays to study the properties of Riemann manifolds, in particular in dimension three, and it has played an essential role in proving Thurston's geometrization conjecture, thus classifying all closed 3-manifolds. I will start the talk by mentioning the role of the smooth Ricci flow in the modern mathematics and then explaining its behaviour, concentrating on manifolds of dimension 2 - surfaces. We will encounter and discuss different discretizations of the flow, depending on the choice of discretization of the metric and the Gaussian curvature.


  • 12:00 - 13:00 Super-Nets, Thilo Roerig 


  • 13:00 - 14:00 Teichmüller maps, part 2, Lara Skuppin  


  • 13:00 - 14:00 Teichmüller maps, part 1, Lara Skuppin 
  • In this talk, I will present an introduction to extremal quasiconformal mappings (in the continuous theory). We will start with the definition of quasiconformal mappings and review the Grötzsch problem of finding an extremal quasiconformal mapping between two rectangles. In order to proceed to a more general case, we will then discuss holomorphic quadratic differentials and Teichmüller maps, which are very special quasiconformal maps: Namely, these can be described by a pair of holomorphic quadratic differentials that locally yield conformal coordinates in which the map is just an affine stretch. Our goal is to explain Teichmüller's theorem, which asserts that given two Riemann surfaces of the same (finite, non-exceptional) type, Teichmuller maps are the unique extremal quasiconformal mappings in each homotopy class.


  • 13:00 - 14:00 The dimer model, Niklas Affolter 
  • We introduce the dimer model, a topic in statistical physics. It deals with perfect matchings in graphs, where the probability of picking a matching comes from the sum of the involved edge-energies. There are some surprising geometric results including the occurence of a familiar function... This will be an introductory talk, presenting the definitions, some results and details on how to count perfect matchings with determinants.


  • 12:00 - 13:00 Discrete Confocal Quadrics as orthogonal Koenigs nets, Jan Techter 
  • We introduce discrete confocal quadrics as separable solutions of the discrete Euler-Darboux equation. They are discrete Koenigs nets, and up to component-wise rescaling, satisfy a new discrete orthogonality condition involving a combinatorically dual net. We also show that discrete confocal conics derived from incenters of incircular-nets belong to the same class of orthogonal Koenigs nets.


  • 13:00 - 14:00 Rigidity theory, Wai-Yeung Lam 
  • Basic introduction to rigidity theory for discrete surfaces.


  • 13:00 - 14:00 Minimal surfaces from discrete harmonic functions, Wai-Yeung Lam 
  • We introduce discrete harmonic functions in the sense of the cotangent Laplacian. We show that given a discrete harmonic function on a planar triangular mesh, there is a family of discrete surfaces sharing properties analogous to smooth minimal surfaces. Certain discrete minimal surfaces, including those from Schramm?s orthogonal circle patterns, are in addition critical points of the total area.


  • 11:00 - 12:00 On a discretization of confocal quadrics, part 2, Jan Techter 
  • discrete part: discrete Euler-Darboux equation and discrete confocal quadrics up to component-wise scaling


  • 11:00 - 12:00 On a discretization of confocal quadrics, part 1, Jan Techter 
  • smooth part: confocal quadrics and the Euler-Darboux equation


  • 11:00 - 12:00 Zero-sum problems in abelian groups, Florian Frick 


  • 11:00 - 12:00 On connections between electric networks, discrete harmonic functions, extremal length and random walks III, Ulrike Bücking 


  • 11:00 - 12:00 On connections between electric networks, discrete harmonic functions, extremal length and random walks II, Ulrike Bücking 


  • 11:00 - 12:00 On connections between electric networks, discrete harmonic functions, extremal length and random walks, Ulrike Bücking 


  • 11:00 - 12:00 Inscribed cyclic polygons, Hanna Kourimska und Lara Skuppin 


  • 11:00 - 12:00 Poncelet's Porism, Ulrike Bücking 


  • 11:00 - 12:00 Euclidean plane geometry via geometric algebra, Charles Gunn 


  • 11:00 - 12:00 Lexell's Theorem in the hyperbolic plane, Christoph Seidel 


  • 10:15 - 11:15 Nets with unique nodes and spherical geometry, Thilo Rörig 


  • 09:45 - 11:00 Discrete line congruences on triangulated surfaces, Jan Techter 


  • 10:15 - 11:15 Isothermic triangulated surfaces, Wayne Lam 


  • 10:15 - 11:15 Nerve complexes of arcs in $\mathbb{S}^1$, Florian Frick 


  • 16:15 - 17:15 Constrained Willmore Minimizers - Theory and Experiments, Lynn Heller (Uni Tuebingen)


  • 16:15 - 17:15 Geometric invariant theory of the space - a modern approach to solid geometry (with a much simpler proof of the Kepler's conjecture as an exemplary application), Wu-Yi Hsiang (UC Berkeley/Hong Kong University)


  • 14:00 - 15:00 Zyklidische und hyperbolische Netze, Emanuel Huhnen-Venedey 
  • Eine stückweise glatte Diskretisierung orthogonaler und asymptotischer Netze in der diskreten Differenzialgeometrie.


  • 14:00 - 15:00 Zyklidische und hyperbolische Netze, Emanuel Huhnen-Venedey 
  • Eine stückweise glatte Diskretisierung orthogonaler und asymptotischer Netze in der diskreten Differenzialgeometrie.


  • 14:00 - 15:00 Thickening Dubins Paths, Thomas El Khatib 


  • 14:00 - 15:00 Tverberg's Theorem strikes back, Florian Frick 


  • 12:00 - 13:00 Quasi-conformal distortion, Lara Skuppin 


  • 12:00 - 13:00 Generalized isoradial circle patterns, Jan Techter 


  • 10:15 - 12:00 Elastic curves and knots, Thomas El Khatib 


  • 10:15 - 12:00 Splitting Separatrices in Dynamical Systems, Marina Gonchenko 


  • 10:15 - 12:00 Hyperbolic Delaunay Triangulations, Thilo Rörig 


  • 10:15 - 12:00 Teichmüller spaces, Lara Skuppin 


  • 10:15 - 12:00 Teichmüller spaces, Lara Skuppin 


  • 10:15 - 12:00 Statistical Mechanics, Andrew Kels 


  • 10:15 - 12:00 Subdivision of Koenigs nets, Stefan Sechelmann 


  • 10:15 - 12:00 Troyanov Theorem on Riemann surfaces and polyhedral metrics, Micheal Joos 


  • 10:15 - 12:00 Canonical immersions of complex tori, Andre Heydt 


  • 10:15 - 12:00 From Maxwell's equations to Hamiltonian Flows on Phase Space, Christian Lessig 


  • 10:15 - 12:00 Triangulations with valence bounds, Florian Frick 


  • 10:15 - 12:00 Theorem on circles and lines - old and new, Arseniy Akopyan 


  • 10:15 - 12:00 Symmetries on Riemann surfaces, Isabella Thiessen 


  • 10:15 - 12:00 Darboux transforms of plane curves, Thilo Rörig 


  • 10:00 - 12:00 Direction fields, Felix Knöppel 


  • 10:00 - 12:00 Nets on surfaces, Thilo Rörig 


  • 10:00 - 12:00 Axis of motions in different geometries/ Discussion: Hopf fibration, Charles Gunn 


  • 10:00 - 12:00 Smooth vector fields on discrete surfaces, Felix Knöppel 


  • 10:00 - 12:00 Axes of motions via geometric algebra in different metrics, Charles Gunn 


  • 10:00 - 12:00 Axes of hyperbolic motions, Thilo Rörig 


  • 10:00 - 12:00 From Hyperboloid to Poincare model via Klein model, Thilo Rörig 


  • 10:00 - 12:00 A game on graphs, Felix Günther 


  • 10:00 - 12:00 Curvature line and asymptotic line parametrizations in Lie and Pluecker Geometry, Emanuel Huhnen-Venedey 


  • 10:00 - 12:00 Homology theories, Stefan Born 


  • 10:00 - 12:00 , Nikolay Dimitrov 


  • 10:00 - 12:00 3D- and 4D-consistency, quad equations, Bäcklund transformations and consistency, Bianchi permutability, Raphael Boll 


  • 10:00 - 12:00 Discrete and smooth KdV-equations, Bäcklund transformations, quad equations, 3D-consistency, Raphael Boll 


  • 10:00 - 12:00 Cosine-law for spherical triangles and dynamical systems, Matteo Petrera 


  • 10:00 - 12:00 Schläfli principle, David Chubelaschwili