Geometry of Smooth and Discrete Surfaces

on the occasion of Ulrich Pinkall’s 60th birthday

Geometry of smooth and discrete surfaces is an actively developing research area in mathematics. The aim of this workshop is to discuss recent developments in this area. The workshop is open to everyone interested in the field and will also be broadcast live to the Zentrum Mathematik at the TU München, Seminarroom 02.06.011

  • Date: 10.03.2015
  • Type: Workshop
  • Location: Technische Universität Berlin, Department of Mathematics, Straße des 17. Juni 136, 10623 Berlin

Organizers


Alexander Bobenko (TU Berlin) 
Peter Schröder (Caltech)

 

Speakers


Alexander Bobenko (TU Berlin)

Keenan Crane (Columbia U)

Franz Pedit (U of Massachusetts)

Peter Schröder (Caltech)

Max Wardetzky (U Göttingen)

 

Program


Timetable Tuesday, 10 March 2015
Starting time: s.t. Speaker Title
09:30 - 10:00 Registration
10:00 - 10:50 Alexander Bobenko What one can build from circles
11:00 - 11:50 Franz Pedit Integrable Surface Geometry for non-Abelian Topology
12:00 - 12:20 Coffee break
12:20 - 13:10 Max Wardetzky Variational Convergence of Minimal Surfaces
13:20 - 14:50 Lunch break
14:50 - 15:40 Keenan Crane Spin Transformations and Geometry Processing
15:50 - 16:10 Coffee break
16:10 - 17:00 Peter Schröder Close-to-Conformal Deformations of Volumes
All talks will take place in room MA 041 (ground floor of the Dept. of Mathematics)

Please pre-register with your name and affiliation by sending an e-mail to Pia Janik at janik@math.tu-berlin.de

The workshop posters:
Icon A4 Workshop Poster (14.0 MB)
Icon A3 Workshop Poster (24.6 MB)
 

Abstracts


What one can build from circles (Alexander Bobenko)

We discuss some geometric constructions of curves and surfaces based on circle patterns. In particular a construction of confocal conics will be presented (joint work with A. Akopyan).

Spin Transformations and Geometry Processing (Keenan Crane)

Explicit representations of surfaces (e.g., triangle meshes) are increasingly important in science and industry. How should we work with these surfaces in practice? And how can we understand them in terms of continuous differential geometry? This talk explores a viewpoint where triangle meshes in R^3 are naturally interpreted as conformally immersed surfaces. This representation allows one to manipulate the extrinsic curvature of a surface by solving linear-elliptic problems, lending itself naturally to efficient algorithms for geometry processing. It will also touch on applications to constrained Willmore flow, isometric embedding, and the relationship to discrete conformal equivalence.

Integrable Surface Geometry for non-Abelian Topology (Franz Pedit)

We will discuss recent advances in the theory of constant mean curvature surfaces with non-abelian fundamental groups. Our approach, extending the classical "finite gap integration", makes use of the Riemann-Hilbert correspondence between local systems and representation varieties via holomorphic bundles. Computer experiments and visualization support and guide the theoretical investigations.

Close-to-Conformal Deformations of Volumes (Peter Schröder)

Conformal deformations are infinitesimal scale-rotations, which can be parameterized by quaternions. The condition that a volumetric deformation is conformal becomes a linear condition on the quaternion and we can measure the deviation of a given deformation from conformality with a quadratic, convex Dirichlet energy. Applied to tetrahedral meshes this allows us to find deformations close to conformal by finding the principal eigenvector of a (quaternionic) Laplace matrix. The resulting algorithms can be implemented with highly optimized standard linear algebra libraries and yield deformations comparable in quality to far more expensive approaches. Joint work with Albert Chern and Ulrich Pinkall.

Variational Convergence of Minimal Surfaces (Max Wardetzky)

While discrete minimal surfaces are perhaps one of the most widely studied examples of discrete surfaces in DDG, their convergence to smooth minimal surfaces has only been proven for special cases, such as for disk-like and cylinder-like topologies. Using tools from variational analysis, I will present a convergence result for triangulated area-minimizing surfaces that deals with the general case of arbitrary topology.

 

Travel Information


TU Berlin Campus Map

Icon Map of TU Berlin Campus (1.8 MB)

How to get to the Department of Mathematics at TU Berlin, Straße des 17. Juni 136, 10623 Berlin
 

By car

Exit the A 100 at the Kaiserdamm exit and drive along Kaiserdamm street (it later changes its name into Bismarckstraße) for approximately 2 km in the direction of Ernst-Reuter-Platz. At the roundabout, take the second exit onto Straße des 17. Juni. After a few metres you will see the Department of Mathematics on the left-hand side.

By train

If you arrive by train, please get off at central train station Hauptbahnhof and take the S5, S7 or S75 interurban train „S-Bahn“ from there in the direction of Spandau (S5), Wannsee/Potsdam (S7) or Westkreuz (S75), getting off at Zoologischer Garten station. From there take the underground U2 in the direction of Ruhleben/Theodor-Heuss-Platz for one stop and get off at Ernst-Reuter-Platz. Exit the underground station in the direction of „Technische Universität“ and cross the street „Straße des 17. Juni“ at the traffic light. Turn right after crossing: After a few metres you will see the Department of Mathematics on the left-hand side. The journey takes about 20 minutes.

For public transportation please buy a ticket with travel zones AB (single ticket = EURO 2,70). If you take a taxi from Hauptbahnhof, you will arrive at the Department of Mathematics in about 10 minutes; costs for a taxi will be around EURO 12.

By plane to Tegel airport

From Tegel airport take Expressbus X9 in the direction of Zoologischer Garten and get off at the Ernst-Reuter-Platz stop. Cross the street „Hardenberstraße“ at the traffic light behind the bus, continue past the underground station and cross the street „Straße des 17. Juni“ at the next traffic light. Turn right after crossing: After a few metres you will see the Department of Mathematics on the left-hand side. The journey takes about 20 minutes.

For public transportation you will need a ticket with travel zones AB (single ticket = EURO 2,70). If you take a taxi from Tegel airport, you will be at the Department of Mathematics in 15-20 minutes; costs for a taxi will be around EURO 20.

By plane to Schönefeld airport

From Schönefeld airport please walk to Schönefeld train station (about 6 minutes). From there take the Airport-Express RE7 or RB14 in the direction of Bad Belzig/Dessau (RE7) or in the direction of Nauen (RB14) and get off at Zoologischer Garten station. Here, take the underground U2 for one stop in the direction of Ruhleben/Theodor-Heuss-Platz and get off at Ernst-Reuter-Platz. Exit the underground station in the direction of „Technische Universität“ and cross the street „Straße des 17. Juni“ at the traffic light. Turn right after crossing: After a few metres you will see the Department of Mathematics on the left-hand side. The journey takes about 50 minutes.

For public transportation you will need a ticket with travel zones ABC (single ticket = EURO 3,30). If you take a taxi from Schönefeld airport, you will get to the Department of Mathematics within 40-45 minutes; costs for a taxi will be around EURO 43.

For detailed timetables please consult the homepage of our local public transportation system (English available): http://www.bvg.de/