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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: 05.03.2024, 14:15 - 15:45
  • Type: Seminar
  • Location: TU Berlin, MA875 H-Cafe

Contact: Nina Smeenk

Room: MA875 (H-Cafe), TU Berlin

Time & Date: Tuesdays at 14:15

Talks

05.03.2024

  • 14:15 - 15:45 Discrete integrable systems, Niklas Affolter (TU Berlin)
    +
  • This will be a trial run of an introductory lecture to discrete integrable systems that I will give at IPAM. I'll give an introduction to 1D, 2D and 3D systems with geometric examples. The lecture is 75 minutes.

30.05.2023

  • 14:15 - 15:15 Projective matrix geometry, Niklas Affolter (TU Berlin)

16.05.2023

  • 14:15 - 15:15 Projective matrix geometry, Niklas Affolter (TU Berlin)

07.12.2022

  • 12:15 - 13:15 A new construction for discrete elastic curves, Jannik Steinmeier (TUM)
    +
  • Elastica have the property that they stay rigid under certain flows. Discrete Elastica that have previously been introduced also have this property. We introduce a notion of discrete elastica that are rigid under a double Bäcklund transformation, which can be seen as a discrete flow. For arc-length parametrized curves this notion coincides with the previous definition and the construction becomes very elegant. Unlike previous descriptions, our construction also allows for non arc-length parametrized curves.

23.11.2022

  • 12:15 - 13:15 The Gauss map of S-CMC surfaces of type I, Nina Smeenk (TU Berlin)
    +
  • S-isothermic surfaces in R^3 can be defined as Moutard nets in R^4,1 (Q-nets fulfilling the Moutard equation). In R^3 S-isothermic surfaces correspond to Koenigs nets with spheres at the vertices with the following property: spheres adjacent to a face have to have a common orthogonal circle. Further, along each of the two coordinate directions, the vertex spheres intersect in a constant angle (coming from constant Mobius scalar products). The simplest case are S-isothermic surfaces of ”type I touching”: adjacent vertex spheres touch. In this case, the orthogonal circle goes through these touching points and thus is tangential to the face (a face is given by the centers of vertex spheres). Discrete CMC surfaces can be defined using S-isothermic surfaces: An S-CMC surface is an S-isothermic surface such that its Christoffel dual is simultaneously a Dar- boux transformation, i.e., the side faces (f, f i , f i ∗ , f ∗ ) between an S-isothermic surface and its Christoffel dual are S-isothermic. The Gauss map of an S-CMC surface can be defined by the vectors connecting vertices, edges and faces of the primal and dual surfaces. For S-CMC surfaces of type I touching, it has been shown, that the Gauss map corresponds to an orthogonal ring pattern on the Sphere. I want to explain this construction and discuss the Gauss map of S-CMC surfaces of general type.

02.11.2022

  • 12:15 - 13:15 Discrete surfaces via binets: Geometry (Part II), Jan Techter (TU Berlin)
    +
  • In several classical examples discrete surfaces naturally arise as pairs consisting of combinatorially dual nets describing the "same" discrete surface. On the basis of this observation we introduce a discretization of parametrized surfaces via binets, which are maps from the vertices and faces of $\Z^2$ into $\R^3$. We take a closer look at discrete principal binets, which generalize the notions of circular and conical nets, and appear in examples such as orthogonal circle patterns, orthogonal ring patterns, and discrete confocal quadrics. Discrete principal binets admit a natural discrete Gauss map, a lift to Möbius geometry, Laguerre geometry, and Lie geometry. Moreover, we introduce discrete Koenigs binets in terms of equal Laplace invariants. They admit Christoffel duals and generalize the classical notion of "vertex based" Koenigs nets by Bobenko and Suris, and "face based" Koenigs nets by Doliwa. Together the notions of discrete principal binets and discrete Koenigs binets give rise to discrete isothermic binets, which turn out to coincide with discrete isothermic nets based on checkerboard patterns as introduced by Dellinger.

28.10.2022

  • 12:15 - 13:15 Discrete surfaces via binets: Geometry, Jan Techter (TU Berlin)
    +
  • In several classical examples discrete surfaces naturally arise as pairs consisting of combinatorially dual nets describing the "same" discrete surface. On the basis of this observation we introduce a discretization of parametrized surfaces via binets, which are maps from the vertices and faces of $\Z^2$ into $\R^3$. We take a closer look at discrete principal binets, which generalize the notions of circular and conical nets, and appear in examples such as orthogonal circle patterns, orthogonal ring patterns, and discrete confocal quadrics. Discrete principal binets admit a natural discrete Gauss map, a lift to Möbius geometry, Laguerre geometry, and Lie geometry. Moreover, we introduce discrete Koenigs binets in terms of equal Laplace invariants. They admit Christoffel duals and generalize the classical notion of "vertex based" Koenigs nets by Bobenko and Suris, and "face based" Koenigs nets by Doliwa. Together the notions of discrete principal binets and discrete Koenigs binets give rise to discrete isothermic binets, which turn out to coincide with discrete isothermic nets based on checkerboard patterns as introduced by Dellinger.

08.12.2021

  • 14:15 - 15:15 Classification of untwisted weaving diagrams, Sonia Mahmoudi (Tohoku University)
    +
  • Weavings are historically well-known structures in materials science, and have more recently become a very active research topic in mathematics. This talk first attempts to present a formal mathematical definition of a weave, as a three-dimensional entangled network embedded into the thickened Euclidean plane. Next, we will introduce a method to classify untwisted weaving diagrams - which are weaves whose components are isotopic to straight lines - according to their number of crossings using topological and combinatorial arguments.

10.11.2021

  • 14:15 - 15:15 An introduction to counting closed geodesics on translation surfaces., Samantha Fairchild 
    +
  • We will introduce some history on billiard dynamics, which inspires the study of translation surfaces. A translation surface is a collection of polygons in the plane with parallel sides identified by translation to form a surface with a singular Euclidean structure. We will focus on two examples, the torus and a surface called the Golden L. With time we will also give probabilistic results on counting closed geodesics on these two surfaces.

27.10.2021

  • 14:15 - 15:15 Hyperbolic Dehn surgery and the volume of 3-torus knots, Max Krause 

20.10.2021

  • 14:15 - 15:15 Incidence theorems for Q-nets that are inscribed in quadrics, Alexander Fairley (TU Berlin)
    +
  • Many objects in DDG can be characterised as Q-nets that are inscribed in quadrics. For example, circular nets are Q-nets that are inscribed in the Möbius quadric of Möbius geometry. Another example, conical nets are Q-nets that are inscribed in the Blaschke quadric of Laguerre geometry. I will present incidence theorems concerning Q-nets that are inscribed in quadrics. I will explain applications to circular nets and also to conical nets. These applications are related to surfaces with principal curvature lines that are linear/circular/planar/spherical. This seminar talk will be an expanded version of my talk at the DGD Days in Landshut.

13.10.2021

  • 14:15 - 15:15 Computing hyperbolic structures on 3-manifolds, Fabian Bittl 

31.03.2020

  • 14:00 - 15:00 Integrability in octahedral lattices via diagrams, Niklas Affolter 

24.03.2020

  • 14:00 - 15:00 Concepts of integrability around discrete maps, Niklas Affolter 

24.02.2020

  • 12:00 - 13:00 Discrete confocal quadrics and checkerboard incircular nets, Jan Techter 

16.12.2019

  • 14:00 - 15:00 Hyperbolic complements of knots, Max Krause 

11.11.2019

  • 12:00 - 13:00 TBA, Yousuf Soliman (Caltech)

22.10.2019

  • 12:00 - 13:00 Isothermal constrained Willmore tori, Jonas Tervooren 

11.10.2019

  • 12:00 - 13:00 Structures in three-dimensional Euclidean space from hyperbolic tilings, Benedikt Kolbe 

30.08.2019

  • 12:00 - 13:00 Subdivision in the geometries of circles, spheres and lines, Niklas Affolter 

23.08.2019

  • 12:00 - 13:00 Discrete period matrices for branched coverings of the sphere and their convergence, Ulrike Bücking 

02.08.2019

  • 12:00 - 13:00 The Multivariable Alexander Polynomial for Periodic Links, Max Krause 

19.07.2019

  • 12:00 - 13:00 Elementary divisors and the classification of pencils of quadrics, Jan Techter 

05.07.2019

  • 12:00 - 13:00 On asymptotic, characteristic, circular and curvature lines on quadrics, Jan Techter 

21.06.2019

  • 12:00 - 13:00 Carnot's Theorem and Quadrics, Alexander Fairley 
    +
  • Carnot's theorem is a classical theorem that was published by Lazare Carnot in "Géométrie de position" (1803). For any triangle, Carnot's theorem is about algebraic curves that transversally intersect the edges of the triangle. After sketching a proof of Carnot's theorem, I will explain how Carnot's theorem can be used to describe quadrics that are tangent to the edges/faces of triangles/tetrahedra. I will also explain a connection to Segre's theorem, which is an elegant theorem about non-degenerate conics in finite projective planes.

14.06.2019

  • 12:00 - 13:00 On Bubble Rings and Ink Chandeliers, Marcel Padilla 
    +
  • Vorticity in a fluid tends to roll up into so called vortex filaments which have been used to run smoke simulations. We will expand the filament theory to include viscosity and buoyancy along with a few more tricks to reproduce low Reynolds number flows.

11.06.2019

  • 14:00 - 15:00 Existence of piecewise linear metrics with constant discrete Gaussian curvature, part 2, Hana Kourimska 

07.06.2019

  • 12:00 - 13:00 Discretization via loop groups and Discrete mean curvature coordinates, Alexander Preis 

03.06.2019

  • 12:00 - 13:00 Existence of piecewise linear metrics with constant discrete Gaussian curvature, part 1, Hana Kourimska 

17.05.2019

  • 12:00 - 13:00 The Loewner energy of curves and loops, Yizheng Yuan 
    +
  • Consider a simply connected planar domain D with two marked boundary points a,b. There are many simple curves in D that go from a to b, the simplest being the hyperbolic geodesic. We introduce an energy functional of such curves which measures how much a curve deviates from the hyperbolic geodesic. This notion can also be used to define an energy of simple loops in the extended complex plane.

10.05.2019

  • 12:00 - 13:00 Stretch deformations of complete finite area hyperbolic surfaces, Lara Skuppin 

16.04.2019

  • 14:00 - 15:00 Babich Bobenko tori and why they can not be embedded, part 2, Jonas Tervooren 

12.04.2019

  • 12:00 - 13:00 Babich Bobenko tori and why they can not be embedded, Jonas Tervooren 
    +
  • 1993 Mikhail V. Babich and Alexander I. Bobenko constructed Willmore tori with umbilic lines using theta functions and eliptic integrals. Considering the usual $R^3$ as union of two hyperbolic half spaces that touch at their ideal boundary plane, the restriction of these tori to the half spaces have constant mean curvature with respect to the hyperbolic metric. I will give a short introduction to conformal geometry from a Riemannian perspective and then introduce a special sphere congruence in order to proof that the Babich Bobenko tori can not be embedded. ( theta functions and eliptic integrals will not appear in the talk).

01.03.2019

  • 12:00 - 13:00 Discrete Uniformization for surfaces of hyperbolic type with boundary, Isabella Retter 

22.02.2019

  • 12:00 - 13:00 Discrete integrable systems and Mobius geometry, Niklas Affolter 

01.02.2019

  • 12:00 - 13:00 Computational problems from a geometric perspective, Albert Chern 

18.01.2019

  • 12:00 - 13:00 Riemannian approach to Teichmüller theory, Christoph Seidel 

07.12.2018

  • 12:00 - 13:00 Periodic knot theory and colored link invariants, Max Krause 
    +
  • What happens to knots if we leave the well-known realms of $R^3$ and consider entanglements in other 3-manifolds? In my talk I will give a brief overview of knot theory and then look at what happens if we take a slightly more complicated base space, the solid torus, for knot theory, and how we can generalize well-known invariants of standard knot theory to this setting.

04.12.2018

  • 14:00 - 15:00 On the projective geometry of inscribed conics, Alexander Fairley 

30.11.2018

  • 12:00 - 13:00 Simulating Hurricanes on Bunnies, Point Vortex Dynamics on Closed Surfaces, Marcel Padilla 
    +
  • If we get lazy and track fluid motion just as a set of points representing the whirls of the fluid we end up with point vortex dynamics. The main question now becomes: "how do these point vortices move by the whirls they induce?" In my talk I will explain this for planar, spherical and bunny shaped planets. This will also be a gentle introduction into fluid dynamics.

16.11.2018

  • 12:00 - 13:00 Laguerre Geometry in Space Forms, Carl Lutz 

09.11.2018

  • 12:00 - 13:00 Contact Hamiltonian dynamics, Mats Vermeeren 
    +
  • Contact Hamiltonian dynamics is a generalization of canonical Hamiltonian dynamics, where the underlying geometry is not symplectic but has a contact structure. This has several physical applications, including mechanical systems with friction. I will give a short introduction to contact geometry, explain the contact Hamiltonian formalism and discuss the corresponding variational principle.

02.11.2018

  • 12:00 - 13:00 Curved Folding, Leonardo Alese (TU Graz)

26.10.2018

  • 12:00 - 13:00 The evolution of random simplicial complexes, Andrew Newman 
    +
  • In 2003, Linial and Meshulam introduced their model of random simplicial complexes generalizing the Erdős--Rényi random graph model to higher dimensions. In this talk I will discuss the evolution of the homology groups of random simplicial complexes in the Linial--Meshulam model. Along the way, we will see how the story in d ≥ 2 dimensions parallels the story in the random graph setting, but with some unexpected differences.

20.07.2018

  • 12:00 - 13:00 Moduli spaces of Feynman diagrams, Marko Berghoff (HU Berlin)

19.07.2018

  • 12:00 - 13:00 Feynman diagrams, Ananth Sridhar 

17.07.2018

  • 13:30 - 14:00 Introduction to the talk "Polytopal surfaces in Fuchsian manifolds", Roman Prosanov 

13.07.2018

  • 12:00 - 13:00 Gauge Theory, Ananth Sridhar 

10.07.2018

  • 14:00 - 15:00 Connections on principle bundles, Hanka Kourimska 

06.07.2018

  • 12:00 - 13:00 Principle Bundles, Alxander Preis 

26.06.2018

  • 13:30 - 14:00 Introduction to the talk "Constraint-based Point Set Denoising" , Martin Skrodzki 

22.06.2018

  • 12:00 - 13:00 Inversions in Lie geometry, Thilo Rörig 

19.06.2018

  • 14:00 - 15:00 The Fundamental theorem of (non-abelian) calculus, Alexander Preis 

08.06.2018

  • 12:00 - 13:00 Fock-Goncharov coordinates on the module space of framed convex projective structures of a surface, Robert Löwe 

01.06.2018

  • 12:00 - 13:00 Schwarzian derivative, Ulrike Bücking 

11.05.2018

  • 12:30 - 13:30 Discrete Bonnet Pairs, Andrew Sageman-Furnas 

27.04.2018

  • 12:00 - 13:00 Quadratic differentials, part 2, Jonas Tervooren 

20.04.2018

  • 12:00 - 13:00 Quadratic differentials, part 1, Jonas Tervooren 

13.04.2018

  • 12:00 - 13:00 Laguerre geometry and the checkerboard incircle incidence theorem, Jan Techter 

03.04.2018

  • 14:00 - 15:00 Immersions, regular homotopies, rimmed surfaces and spin structures of surfaces, Albert Chern 

27.03.2018

  • 14:00 - 15:00 Hirota's bilinear method, Mats Vermeeren 

23.03.2018

  • 14:00 - 15:00 Parallelogram maps, Ananth Sridhar 

16.03.2018

  • 13:00 - 14:00 Introduction to Teichmüller Theory, Lara Skuppin 

27.02.2018

  • 14:00 - 15:00 Variational principles for discrete conformal maps and Ronkin's functions, Ulrike Bücking 

02.02.2018

  • 11:00 - 12:00 cotan weights, Niklas Affolter 

26.01.2018

  • 13:00 - 14:00 Comparing polyhedral surfaces - a metric defined via cotan weights and edge flips, Isabella Retter 

23.01.2018

  • 13:30 - 14:00 Introduction to the talk "Euler-Arnold theory for SPDEs", Alexander Schmeding 

19.01.2018

  • 13:00 - 14:00 A parametrized surface theory for non-planar quad meshes in $\mathbb{R}^3$, Andrew Sageman-Furnas 

16.01.2018

  • 13:30 - 14:00 Introduction to the talk "Quanta of Discrete Spacetime", Alex Goeßmann 

12.01.2018

  • 12:00 - 13:00 The star-triangle move on integrable circle patterns, Niklas Affolter 

08.12.2017

  • 12:15 - 13:15 Anti-de Sitter space, smooth CMC surfaces in AdS, Alexander Preis 

01.12.2017

  • 12:00 - 13:00 Loop group description of CMC surfaces in the Anti-de Sitter space, Alexander Preis 

24.11.2017

  • 11:30 - 12:30 Projective varieties, Marta Panizzut 

17.11.2017

  • 12:00 - 13:00 Fluid dynamics and prequantum bundle, part 3, Albert Chern 

14.11.2017

  • 14:00 - 15:00 Fluid dynamics and prequantum bundle, part 2, Albert Chern 

10.11.2017

  • 12:00 - 13:00 Fluid dynamics and prequantum bundle, part 1, Albert Chern 

07.11.2017

  • 14:00 - 15:00 Characterising symmetric tetrahedra, Hana Kourimska 

03.11.2017

  • 12:00 - 13:00 Toric Geometry, Lars Kastner 

24.10.2017

  • 12:00 - 13:00 The sphere as a ruled surface, Jan Techter 

20.10.2017

  • 11:15 - 12:15 Isothermic channel surfaces, Jonas Tervooren 

17.10.2017

  • 14:00 - 15:00 Embedding the real projective space into the complex projective space, Jan Techter 

08.09.2017

  • 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.

28.07.2017

  • 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.

25.07.2017

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

04.07.2017

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

16.06.2017

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

13.06.2017

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

25.04.2017

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

07.04.2017

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

04.04.2017

  • 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.

31.03.2017

  • 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.

28.03.2017

  • 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.

17.03.2017

  • 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).

14.03.2017

  • 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.

10.03.2017

  • 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.

07.03.2017

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

03.03.2017

  • 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.

30.11.2016

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

27.07.2016

  • 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.

22.06.2016

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

01.06.2016

  • 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.

25.05.2016

  • 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.

04.05.2016

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

22.04.2016

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

20.04.2016

  • 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.

15.04.2016

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

30.03.2016

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

23.03.2016

  • 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.

16.03.2016

  • 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.

11.03.2016

  • 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.

09.03.2016

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

02.03.2016

  • 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.

04.12.2015

  • 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

27.11.2015

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

26.06.2015

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

12.06.2015

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

05.06.2015

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

29.05.2015

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

27.02.2015

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

20.02.2015

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

23.01.2015

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

16.01.2015

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

05.11.2014

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

29.10.2014

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

22.10.2014

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

15.10.2014

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

18.06.2014

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

28.05.2014

  • 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)

02.04.2014

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

26.03.2014

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

19.03.2014

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

26.02.2014

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

31.01.2014

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

17.01.2014

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

06.12.2013

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

22.11.2013

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

15.11.2013

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

08.11.2013

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

01.11.2013

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

25.10.2013

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

18.10.2013

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

21.06.2013

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

14.06.2013

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

31.05.2013

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

24.05.2013

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

17.05.2013

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

03.05.2013

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

26.04.2013

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

19.04.2013

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

12.04.2013

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

15.03.2013

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

08.03.2013

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

01.03.2013

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

22.02.2013

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

15.02.2013

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

08.02.2013

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

01.02.2013

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

18.01.2013

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

07.12.2012

  • 10:00 - 12:00 , Nikolay Dimitrov 

30.11.2012

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

23.11.2012

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

16.11.2012

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

09.11.2012

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