Conference: Discretization in Geometry and Dynamics
In October 2015 the SFB TRR109 will hold an International Conference on Discretization in Geometry and Dynamics in Herrsching am Ammersee. During the five day conference, renowned guests will present talks on a wide spectrum of subjects related to the research themes of our Collaborative Research Centre. Furthermore there will be presentations of the advances made within our own research units and ample opportunity for scientific exchange and stimulating discussions in an informal atmosphere.
 Date: 05.10.  09.10.2015
 Type: Conference
 Location: Haus der bayerischen Landwirtschaft, Herrsching am Ammersee/ TU München
Eric Cances Ecole des Ponts, Paris Tech
Herbert Edelsbrunner IST Austria
Alexander Gaifullin Steklov Mathematical Institute, Moscow
Melvin Leok University of California, San Diego
Christian Lubich Universität Tübingen
Sheehan Olver University of Sydney
Tudor Ratiu EPFL Lausanne
Francisco Santos Universidad de Cantabria
J.M. SanzSerna Universidad Carlos III de Madrid
KarlTheodor Sturm Universität Bonn
Sergei Tabachnikov Pennsylvania State University
 Alexander Bobenko (TU Berlin)
 Folkmar Bornemann (TU München)
 Jürgen RichterGebert (TU München)
 Yuri Suris (TU Berlin)
 Günter Ziegler (FU Berlin)
The conference takes place at the Haus der bayerischen Landwirtschaft (HdbL) in Herrsching am Ammersee.
Website: www.hdblherrsching.de
Download: Program as PDF

Monday, 05.10.15 
from 11.00 
Registration 
12:00 – 13:30 
Lunch 
15:00 – 15:15 
Welcoming words – Alexander I. Bobenko 
15:15 – 16:15 
Melvin Leok: SpaceTime FiniteElement Exterior Calculus and Variational Discretizations of Gauge Field Theories 
16:15 – 16:45 
Coffee Break 
16:45 – 17:45 
Tudor Ratiu: Multisymplectic variational integrators for nonsmooth Lagrangian continuum mechanics 
17:50 – 18:10 
Simon Plazotta: Existence and longtime behaviour of solutions of gradient flows with time dependent perturbation 
18:30  19:30 
Dinner 

Tuesday, 06.10.15 
07:30  9:00 
Breakfast 
09:00 – 10:00 
J.M. SanzSerna: Symplectic RungeKutta methods in nonsymplectic applications 
10:00 – 10:30 
Massimo Fornasier: Discretization of evolutions of critical points and applications in fracture simulation 
10:30 – 11:00 
Coffee Break 
11:00 – 12:00 
Eric Cancès: Discretization of implicit solvent models for molecular dynamics and quantum chemistry 
12:00 – 13:30 
Lunch 
15:00 – 15:30 
Gero Friesecke: Xray imaging, discrete symmetries, and phase retrieval 
15:35 – 16:05 
Felix Günther: A report on the relation between discrete spinors and discrete holomorphicity 
16:05 – 16:30 
Coffee Break 
16:30 – 17:30 
Herbert Edelsbrunner: TDA with Bregman distances 
17:30 – 18:00 
Anton Nikitenko: The Expected Number of Critical Delaunay Simplices of a 3dimensional Poisson Point Process 
18:30  19:30 
Dinner 
20:00 
Meeting of the SFB Executive Board / Open scientific exchange 

Wednesday, 07.10.15 
07:30  9:00 
Breakfast 
09:00 – 10:00 
Sergei Tabachnikov: Iterating evolutes and involutes 
10:00 – 10:30 
Felix Knöppel: Complex line bundles over simplicial complexes 
10:30 – 11:00 
Coffee Break 
11:00 – 12:00 
KarlTheodor Sturm: SuperRicci Flows for Metric Measure Spaces 
12:00 – 13:30 
Lunch 
15:00 – 15:40 
Wolfgang Schief: Circle complexes and the discrete CKP equation 
15:40 – 16:00 
Moritz Firsching: Realizability and inscribability of simplicial polytopes 
16:00 – 16:30 
Coffee Break 
16:30 – 17:10 
Pavle Blagojevic: Equivariant problems of convex geometry 
17:15 – 17:45 
Lauri Loiskekoski: Separation in the graph of a simple polytope 
17:50 – 18:10 
Florian Pausinger: Approximation of intrinsic volumes 
18:30  19:30 
Dinner 
20:00 
SFB General Assembly 

Thursday, 08.10.15 
07:30  9:00 
Breakfast 
09:00 – 10:00 
Francisco Santos: Enumerating lattice 3polytopes 
10:00 – 10:30 
JeanPhilippe Labbé: Bounding the discrepancy of oddequal triangulations of the square 
10:30 – 11:00 
Coffee Break 
11:00 – 12:00 
Christian Lubich: Dynamical lowrank approximation 
12:00 – 13:30 
Lunch 
15:00 – 15:30 
Philipp Petersen: Anisotropic multiscale systems on bounded domains 
15:40 – 16:00 
Wai Yeung Lam: Discrete minimal surfaces: critical points of the area functional from integrable systems 
16:00 – 16:30 
Coffee Break 
16:30 – 17:30 
Alexander Gaifullin: On the bellows conjecture in spaces of constant curvature 
17:35 – 18:05 
Nikolay Dimitrov: Discrete uniformization via hyperideal circle patterns 
18:30  19:30 
Dinner 
20:00 – 20:30 
Wolfgang Carl: On semidiscrete constant mean curvature surfaces and their associated families 
20:35 – 20:55 
Ulrike Bücking: Approximation of conformal mappings using conformally equivalent triangular lattices 

Friday, 09.10.15 
07:30  9:00 
Breakfast 
09:00 – 10:00 
Sheehan Olver: Practical infinitedimensional linear algebra 
10:00 – 10:30 
Matteo Petrera: Discrete pluriLagrangian systems 
10:30 – 11:00 
Coffee Break 
11:00 – 11:30 
Mats Vermeeren: Modified equations for variational integrators 
11:35 – 11:55 
Günter Rote: Optimal homotopic systems of paths 
12:00 – 13:30 
Lunch 
Departures 
Shuttle Bus to tube station Herrsching 
Invited Speakers
Implicit solvent models are empirical models which can easily be coupled to quantum or classical molecular models to take solvation effects into account. In this talk, I will present a new discretization method for simulating these models based on domain decomposition and boundary integral methods. This approach is extremely effective to simulate large biomolecules composed of thousands of atoms, and the potential energy surfaces computed with this discretization procedure are smooth, which is a critical property to perform geometry optimization and molecular dynamics simulations.
Affiliation: Ecole des Ponts, Paris Tech
The general pipeline for analyzing point data with persistent homology uses a notion of distance to convert the points into a filtration of complexes, it uses the homology functor to get a tower of vector spaces, and it finally converts the tower into bars or, equivalently, points in the birthdeath plane. In this talk, we will focus on the first step, arguing that the pipeline also works for Bregman divergences, which are generally not symmetric and do not satisfy the triangle inequality. Examples are the KullbackLeibler divergence commonly used for text and images, and the ItakuraSaito divergence preferred for sound data.
Affiliation: IST Austria
A flexible polyhedron in an $n$dimensional space of constant curvature is an $(n1)$dimensional closed polyhedral surface that can be deformed continuously so that every its face remains congruent to itself during the deformation, but the deformation is not induced by an ambient rotation of the space. Intuitively, one may think of a flexible polyhedron as of a polyhedral surface with faces made of some rigid material and with hinges at codimension~$2$ faces that allow dihedral angles to change continuously.
The bellows conjecture stated by Connelly in 1978 asserts that the volume of any flexible polyhedron in dimensions greater than or equal to~$3$ is constant during the flexion. (Originally this conjecture was stated for the threedimensional Euclidean space.)
The bellows conjecture was proved in Euclidean spaces of all dimensions (Sabitov for $n=3$, and the author for $n\ge 4$).
In the talk, we shall present the author's recent results on the bellows conjecture in nonEuclidean spaces. Namely, it turns out that the bellows conjecture is false in spheres of all dimensions and is true in odddimensional Lobachevsky spaces.
Affiliation: Steklov Mathematical Institute & Kharkevich Institute for Information Transmission Problems, Moscow
Many gauge field theories can be described using a multisymplectic Lagrangian formulation, where the Lagrangian density involves spacetime differential forms. While there has been prior work on finiteelement exterior calculus for spatial and tensor product spacetime domains, less has been done from the perspective of spacetime simplicial complexes. One critical aspect is that the Hodge star is now taken with respect to a pseudoRiemannian metric, and this is most naturally expressed in spacetime adapted coordinates, as opposed to the barycentric coordinates that Whitney forms are typically expressed in terms of.
We introduce a novel characterization of Whitney forms and their Hodge dual with respect to a pseudoRiemannian metric that is independent of the choice of coordinates, and then apply it to a variational discretization of the covariant formulation of Maxwell's equations. Since the Lagrangian density for this is expressed in terms of the exterior derivative of the fourpotential, the use of finitedimensional function spaces that respects the de Rham cohomology results in a discretization that inherits the gauge symmetries of the continuous problem. This yields a variational discretization that exhibits a discrete Noether's theorem.
Affiliation: University of California, San Diego
This talk reviews differential equations on manifolds of matrices or tensors of low rank. They serve to approximate, in a lowrank format, large timedependent matrices and tensors that are either given explicitly via their increments or are unknown solutions of highdimensional differential equations, such as multiparticle timedependent Schr\"odinger equations. Suitable numerical integrators are based on splitting the projector onto the tangent space of the lowrank manifold at the current approximation. In contrast to all standard integrators, these projectorsplitting methods are robust with respect to the presence of small singular values in the lowrank approximation. This robustness relies on geometric properties of the lowrank manifolds.
The talk is based on work done intermittently over the last decade with Othmar Koch, Achim Nonnenmacher, Ivan Oseledets, Bart Vandereycken, Emil Kieri and Hanna Walach.
Affiliation: Universität Tübingen
We describe a framework for applying linear algebra routines directly to infinitedimensional linear equations without discretization, which can be used to solve linear ordinary differential equations with general boundary condition and singular integral equations. The algorithm achieves O(n) complexity, where n is the number of degrees of freedom required to achieve a desired accuracy, which is determined adaptively. We include an example arising from Riemann–Hilbert problems, where direct discretization of the operator naturally leads to singular or extremely badly conditioned systems, whereas solving in infinitedimensions without discretization is successful.
Affiliation: University of Sydney
This talk presents a framework for the theory of multisymplectic variational integrators for nonsmooth continuum mechanics with constraints. Typical problems are the impact of an elastic body on a rigid surface or the collision of two elastic bodies. The integrators are obtained by combining, at the continuous and discrete levels, the variational multisymplectic formulation of nonsmooth continuum mechanics with the generalized Lagrange multiplier approach for optimization problems with nonsmooth constraints. These integrators verify a spacetime multisymplectic formula that generalizes the symplectic property of time integrators. In addition, they preserve the energy during the impact. In presence of symmetry, a discrete version of Noether's theorem is verified. All these properties are inherited from the variational character of the integrator. Numerical illustrations are presented.
Affiliation: EPFL Lausanne
A lattice 3polytope is a polytope $P$ with integer vertices. We call size of $P$ the number of lattice points it contains, and width of P the minimum, over all integer linear functionals $f$, of the length of the interval $f(P)$. For example, $P$ has width one if it is contained between two consecutive parallel lattice planes.
We are interested in the classification of lattice 3polytopes modulo affine integer isomorphism. Lattice 3polytopes of size four (that is, “empty lattice tetrahedra”) are classified since long, and they are known to have width one. However, there are infinitely many of them, which implies that there are also infinitely many 3polytopes of any given size greater than four. However, we show that all but finitely many of them have width one, which suggests the possibility of completely classifying those of width larger than one. In this talk we report on an algorithm to do this.
For sizes five and six our methods are quite adhoc, combining geometric and oriented matroid techniques with a detailed case study of the possible configurations that arise. Starting with size seven we use a more structured approach, based on the proof that every lattice 3polytope of width larger than one falls into one of the following three categories:
a) It projects orthogonally to one of a list of five particular $2$polytopes of sizes four to six. We call $3$polytopes of this type spiked, and they can be described explicitly, for each size.
b) Except for three of its lattice points, $P$ is contained in a rational parallelepiped of width one with respect to every facet. We call these polytopes boxed. They have size at most 10 and we have completely enumerated them with the help of computer (there are 23 of size 7, seven of size 8, and only one of sizes 9 and 10).
c) It has (at least) two vertices $u$ and $v$ whose removal still has width larger than one. Polytopes of this type can be all obtained ``gluing'' smaller polytopes of width larger than one.
The complete classification of boxed and spiked $3$polytopes allows for a computational enumeration of all lattice $3$polytopes of width larger than one up to any given size. We have completed this enumeration up to size nine. In particular, this implies the complete classification of ``distinctpairsum'' (or dps, for short) $3$polytopes, which have size at most eight, and allows us to answer certain questions by Reznick on dps polytopes.
This is joint work with Monica Blanco.
Affiliation: Universidad de Cantabria
The class of symplectic RungeKutta methods, which has attracted much attention in the last twenty five years, coincides with the class of RungeKutta methods that exactly preserve quadratic integrals of motion. In this talk I shall survey a number of applications where symplectic RungeKutta schemes are useful due to the quadratic conservation property while the preservation of the symplectic structure plays no role. In particular I shall discuss the integration of adjoint problems, and of optimal control problems.
Affiliation: Universidad Carlos III de Madrid
We study heat equation and optimal transports on timedependent metric measure spaces with particular emphasis on mmspaces which evolve as superRicci flows. A timedependent family of Riemannian manifolds is a superRicci flow if $2 \mathrm{Ric} + \partial_t g \ge 0$. This includes all static manifolds of nonnegative Ricci curvature as well as all solutions to the Ricci flow equation.
We characterize superRicci flows of metric measure spaces in terms of coupling properties of (backward) Brownian motions, gradient estimates for the (forward) heat equation, as well as dynamical convexity of the Boltzmann entropy on the Wasserstein space. And we prove stability and compactness of superRicci flows under measured GromovHausdorff limits.
Affiliation: Universität Bonn
The evolute of a plane curve is the envelope of its normals; the involute is a converse construction: the evolute of an involute is the given curve. These classical notions have been studied since 17th century.
In this talk I shall discuss iterations of these two constructions, in the continuous and the discrete settings. In the latter case, one deals with polygons, and one considers two discrete analogs of the normals: the bisectors of the angles, and the perpendicular bisectors of the sides. The dynamics of these two systems are very different. Our study relies heavily on computer experiments, and some observations still remain mysterious.
This is a joint work in progress with M. Arnold, D. Fuchs, I. Izmestiev, and E. Tsukerman.
Affiliation: Pennsylvania State University
SFB Members and Guest Professors
In this talk we discuss several problems from convex geometry, like Tverberg type coincidence problems, GrünbaumHadwigerRamos hyperplane mass partition problem and Nandakumar \& RamanaRao problem with a view towards embeddability and periodic billiard trajectories problems. Using the configuration space / test map ansatz we construct a bridge that connects the convex geometry problems with particular problems from (equivariant) topology. Advanced machinery of equivariant obstruction theory is used efficiently in addressing these problems.
This talk is based on the joint work with Florian Frick, Albert Haase, and Günter M. Ziegler
Two triangle meshes are conformally equivalent if their edge lengths are related by scale factors associated to the vertices. Such a pair can be considered as preimage and image of a discrete conformal map.
In this talk we consider the approximation of a given smooth conformal map $f$ by such discrete conformal maps $f^\eps$ defined on triangular lattices. In particular, let $T$ be an infinite triangulation of the plane with congruent strictly acute triangles. We scale this triangular lattice by $\eps>0$ and approximate a compact subset of the domain of $f$ with a portion of it. For $\eps$ small enough we prove that there exists a conformally equivalent triangle mesh whose scale factors are given by $\logf'$ on the boundary. Furthermore we show that the corresponding discrete conformal (piecewise linear) maps $f^\eps$ converge to $f$ uniformly in $C^1$ with error of order $\eps$.
Surfaces with constant mean curvature or constant Gauss curvature have been of interest in differential geometry for a long time. The modern viewpoint is to associate these special geometries with the theory of integrable systems, in particular discrete ones. An essential feature of this approach is that surfaces with constant curvature come with oneparameter associated families.
In this talk we investigate semidiscrete surfaces with constant mean curvature, where the notion of curvature comes from a recently developed curvature theory for quadrilateral meshes equipped with unit normal vectors. In case of vanishing mean curvature, associated families are defined via a Weierstrass representation, otherwise by a Lax pair representation.
In this talk I will present a discrete version of the classical uniformization theorem based on the theory of hyperideal circle patterns. It applies to surfaces represented as finite branched covers over the Riemann sphere as well as to compact polyhedral surfaces with nonpositive cone singularities. The former include all Riemann surfaces represented as smooth algebraic curves, and more generally, any closed Riemann surface with a choice of a meromorphic function on it. The latter include any closed Riemann surface with a choice of a quadratic differential on it. We show that for such surfaces discrete uniformization via hyperideal circle patterns always exists and is unique (up to isometry). We also propose a numerical algorithm, utilizing convex optimization, that constructs the desired discrete uniformization.
The classification of polytopes has been studied since antiquity. Since the 1980s, no significant progress has been made in the classification of simplicial polytopes with few vertices in low dimensions. Recently we were able to enumerate all simplicial $4$polytopes with $10$ vertices and neighbourly simplicial $d$polytopes with $n$ vertices for the pairs $(d,k)$=$(4,11),(5,10),(6,11)$ and $(7,11)$. We also decided for almost all enumerated polytopes, whether they can be realized with all vertices on the unit sphere. We will indicate how these results were obtained using optimization techniques and outline possible future applications.
We present a novel constructive approach to define time evolution of critical points of an energy functional. Differently from other more established approaches based on viscosity approximations in infinite dimension, our procedure is prone to efficient and consistent numerical implementations, and allows for an existence proof under very general assumptions. We consider in particular rather nonsmooth and nonconvex energy functionals, provided the domain of the energy is finite dimensional. Nevertheless, in the infinite dimensional case study of a cohesive fracture model, we prove a consistency theorem of a discretetocontinuum limit. We show that a quasistatic evolution can be indeed recovered as limit of evolutions of critical points of fi nite dimensional discretizations of the energy, constructed according to our scheme. To illustrate the results, we show several numerical experiments. These agree with the crack initiation criterion, which states that a fracture appears only when the stress overcomes a certain threshold, depending on the material.
I discuss the role of continuous and discrete symmetries in classical and novel (G.F., James, Juestel, arXiv:1506.04240)
Xray methods for atomic structure determination.
Socalled spin holomorphic functions on rhombic quadgraphs played a keyrole in Chelkak's and Smirnov's proof of the universality of the Ising model. These functions are in onetoone correspondence to real spinors on a double cover of the medial graph, that satisfy the propagation equation introduced by Mercat. It turns out that spin holomorphic functions cannot be defined on a larger class of quadgraphs, but discrete spinors and the discrete propagation equation can be defined on general discrete Riemann surfaces. Still, decompositions into parallelograms play a special role, as did rhombic decompositions in the work of Mercat. The aim of this talk is to motivate the propagation equation as a discrete holomorphicity condition and to sketch how this discrete holomorphicity on the medial graph is related to the established linear theory of discrete Riemann surfaces. Some possible directions for future research will be also mentioned.
In last years we successfully applied line bundle theory to problems in computer graphics. This talk is about the discrete theory behind it. This includes classification theorems, a discrete PoincaréHopf index theorem and a generalization of the wellknown cotanLaplace operator to discrete hermitian line bundles with curvature.
The objective of the project is to study the discrepancy problem for dissections of a square into an odd number of triangles. First, we will use a slightly more general version of Monsky’s result allowing the use of gap theorems in real algebraic geometry to prove a doubly exponential lower bound on the discrepancy. We give some examples of dissections showing the computational diversity of dissections and some dissections of particular interests. In particular, we will see that non facetoface dissection achieve better discrepancies for dissection using 7 triangles and 8 vertices. We will finish by providing a candidate family which seems to provide a better upper bound for the discrepancy.
We consider a discrete surface as an arbitrary cell decomposition of a surface. We define two types of discrete minimal surfaces and show that they are conjugate to each other. By triangulating their Gauss maps, these discrete minimal surfaces correspond to harmonic functions on planar meshes with respect to the cotangent Laplacian. They generalize earlier notions of discrete minimal surfaces as quad meshes: circular minimal and conical minimal.
In addition, the associated family of certain minimal surfaces, including those from discrete isothermic nets and Schramm's orthogonal circle patterns, are shown to be critical points of the area functional.
Separation in graphs is related to graphs being expanders. A conjecture by Kalai generalizes the planar separation theorem to simple polytopes. It states that the graph of a simple dpolytope can be separated to two roughly equal parts by removing O(n^((d2)/(d1))) vertices. We provide a counterexample to this conjecture. This is joint work with Günter Ziegler.
Mapping every simplex in the Delaunay triangulation of a discrete point set to the radius of the smallest empty circumsphere gives a generalized discrete Morse function. Assuming the points are chosen by a Poisson point process in R^2 or in R^3, we determine the expected number of critical simplices as well as of intervals in the generalized discrete gradient.
Given a smooth body M ⊂ Rn and a certain digital approximation of it, we are interested in multigrid convergent digital algorithms to compute the intrinsic volumes of M using only measurements taken from its digital approximations. In this short talk we aim to motivate our problem and present our main results. The crucial idea behind our novel algorithms is to link the recent theory of persistent homology to the theory of intrinsic volumes via the Crofton formula from integral geometry.
This is joint work with Herbert Edelsbrunner.
Driven by an overwhelming amount of applications numerical approximation of partial differential equations was established as one of the core areas in applied mathematics.
During the last decades a trend for the solution of PDEs emerged, that focuses on employing systems from applied harmonic analysis for the adaptive solution of these equations. Most notably wavelet systems have been used and lead for instance to provably optimal solvers for elliptic PDEs. Inspired by this success story also other systems with various advantages in different directions should be employed in various discretization problems. For instance, ridgelets where recently successfully used in the discretization of linear transport equations.
Another famous system is that of shearlets, which admits optimal representations of functions that have singularities along smooth curves. However, in order to apply these methods in adaptive discretization algorithms it is necessary to have a system on a bounded domain or even a manifold. To apply standard algorithms this system should yields a frame, should be capable of incorporating boundary conditions, and should characterize Sobolev spaces.
Although there have been first approaches to construct shearlet systems for the solution of PDEs on bounded domains they fail to satisfy all the desiderata above.
In this talk we will introduce a novel shearlet system that meets all the requirements mentioned above and admits optimal approximation rates for functions with discontinuities along curves.
I will present an overview of the results achieved in the framework of the project B07. In particular, I will focus on the notion of discrete pluriLagrangian systems, thus promoting them as integrable discrete variational systems. Concrete results will be presented for systems in dimension 1,2 and 3.
We deal with the analysis of a class of evolution equations with timedependent perturbations in the framework of a general metric space and with the asymptotic behavior of solutions to these evolution equations.
We generalize several results on the metric formulation, which extends the notion of curves of steepest descent for autonomous gradient flows in metric spaces and prove the existence of such solutions for the related nonautonomous initial value problem by means of a variational approximation scheme by time discretization. Additionally, we show the exponential contractivity property of convex gradient flows and the related asymptotic behavior of the corresponding solutions. As a particular application, we use the previous results to show the existence of curves of steepest descent for the FokkerPlanck equation in the Wasserstein space. In the last part, we analyze the nonautonomous FokkerPlanck equation with timedependent quadratic potential energies. We explicitly compute the solutions for this evolution equation and show that in the longtime behavior solutions behave asymptotically like a shifted and dilated Maxwellian distribution or respectively in the nonlinear case like a shifted and dilated Barenblatt solution. At last, we show that in the highfrequency limit the solution curves will converges to a solution curve related to an average.
We study the design and optimization of polyhedral patterns, which are patterns of planar polygonal faces on freeform surfaces. Working with polyhedral patterns is desirable in architectural geometry and industrial design. However, the classical tiling patterns on the plane must take on various shapes in order to faithfully and feasibly approximate curved surfaces. We define and analyze the deformations these tiles must undertake to account for curvature, and discover the symmetries that remain invariant under such deformations. We propose a novel method to regularize polyhedral patterns while maintaining these symmetries into a plethora of aesthetic and feasible patterns. Finally, we raise the question of faithful approx imations of smooth surfaces by polyhedral surfaces.
For a plane graph G with k special "terminal" vertices, we want to embed a specified system of noncrossing paths between terminal vertices. The cyclic order of the paths around each terminal is prescribed, thus specifying the homotopy type of the system of paths. Each path has its own cost function, as a mapping from the edges to the reals, and we want to minimize the overall cost of all paths. This problem arises in the choice of reparametrizations for the numeric solution of RiemannHilbert problems.
We solve the problem for k=2 terminals (with many parallel paths between them) in polynomial time by a linearprogramming formulation.
In the spirit of Klein's Erlangen Program, we present various aspects of the geometric and algebraic structure of fundamental line complexes and the underlying privileged discrete integrable system for the minors of a matrix interpreted as Pluecker coordinates. Particular emphasis is put on the restriction to Lie circle geometry which is intimately related to the master dCKP equation of discrete integrable systems theory. We discuss the geometric interpretation, construction and integrability of fundamental line complexes in Moebius, Laguerre and hyperbolic geometry. In the process, we encounter avatars of classical and novel incidence theorems and associated cross and multiratio identities for particular hypercomplex numbers. In the context of Moebius geometry, this leads to novel doubly hexagonal circle patterns.
Discretizations of ordinary differential equations are often studied through their modified equation. This is a differential equation with solutions that interpolate the solutions of the discrete system. The modified equation is usually obtained as a power series in the step size of the discretization. It is wellknown that if a symplectic integrator is applied to a Hamiltonian system, then its modified equation is again Hamiltonian. We discuss this property from the variational (Lagrangian) side. We present a technique to construct a Lagrangian for the modified equation directly from the discrete Lagrangian, without passing through the Hamiltonian side.
Ulrich Bauer  (TU München) 
Pavle Blagojevic  (Gastprofessor, FU Berlin) 
Alexander Bobenko  (TU Berlin) 
Raphael Boll  (TU Berlin) 
Folkmar Bornemann  (TU München) 
Magnus Botnan  (NTNU Trondheim) 
Ulrike Bücking  (TU Berlin) 
Wolfgang Carl  (TU Graz) 
Marco Cicalese  (TU München) 
Diane ClaytonWinter  (TU München) 
Lucia De Luca  (TU München) 
Nikolay Dimitrov  (TU Berlin) 
Ekaterina Eremenko  (TU Berlin) 
Moritz Firsching  (FU Berlin) 
Massimo Fornasier  (TU München) 
Gero Friesecke  (TU München) 
Felix Günther  (IPDE  IHÉS, BuressurYvette) 
André Heydt  (TU Berlin) 
Tim Hoffmann  (TU München) 
Oliver Junge  (TU München) 
Johannes Keller  (TU München) 
Dirk Knoblauch  (TU Berlin) 
Felix Knöppel  (TU Berlin) 
Benno König  (TU München) 
Hana Kourimska  (TU Berlin) 
Felix Krahmer  (TU München) 
Stefan Kranich  (TU München) 
Sara KrauseSolberg  (Uni Hamburg) 
JeanPhilippe Labbé  (HU Jerusalem) 
WaiYeung Lam  (TU Berlin) 
Carsten Lange  (TU München) 
Caroline Lasser  (TU München) 
Lauri Loiskekoski  (FU Berlin) 
Jackie Ma  (TU Berlin) 
Daniel Matthes  (TU München) 
Anton Nikitenko  (IST Austria) 
Florian Pausinger  (TU München) 
Philipp Petersen  (TU Berlin) 
Matteo Petrera  (TU Berlin) 
Ulrich Pinkall  (TU Berlin) 
Simon Plazotta  (TU München) 
Konrad Polthier  (FU Berlin) 
Helmut Pottmann  (TU Wien) 
Jürgen RichterGebert  (TU München) 
Thilo Rörig  (TU Berlin) 
Günter Rote  (FU Berlin) 
Raman Sanyal  (FU Berlin) 
Katharina Schaar  (TU München) 
Jürgen Scheurle  (TU München) 
Wolfgang Schief  (UNSW, Australia) 
Lara Skuppin  (TU Berlin) 
Boris Springborn  (TU Berlin) 
Michael Strobel  (TU München) 
John Sullivan  (TU Berlin) 
Yuri Suris  (TU Berlin) 
Jan Techter  (TU Berlin) 
Stephanie Troppmann  (TU München) 
Mats Vermeeren  (TU Berlin) 
Bernhard Wagner  (TU München) 
Johannes Wallner  (TU Graz) 
Georg Wechslberger  (TU München) 
Zi Ye  (TU München) 
Günter Ziegler  (FU Berlin) 
Jonathan Zinsl  (TU München) 
The "Haus der bayerischen Landwirtschaft" (HdbL) lies on the shore of the Ammersee in Herrsching, at the end of the SBahn tube line S8.
This tube line is directly accessed at the main train station in Munich (50 minutes travelling time) and at Munich Airport (1,5 hrs. travelling time)
We will arrange shuttle bus transfers between the tube station at Herrsching and the HdBL.
By aeroplane: Flights which arrive in Munich before 10:30 will allow sufficient time to travel to Herrsching in time for lunch on Monday (see below).
Tube connections  S8 to Herrsching:
Dep. Flughafen MUC 09:24 / Arr. Herrsching: 10:55
Dep. Flughafen MUC 09:44 / Arr. Herrsching: 11:15
Dep. Flughafen MUC 10:24 / Arr. Herrsching: 11:55
Dep. Flughafen MUC 10:44 / Arr. Herrsching: 12:15
Dep. Flughafen MUC 11:24 / Arr. Herrsching: 12:55
Dep. Flughafen MUC 11:44 / Arr. Herrsching: 13:15
Dep. Flughafen MUC 12:04 / Arr. Herrsching: 13:35