# CSASC 2013

9-13 June 2013
Koper, Slovenia
UTC timezone
Home > Contribution List
Displaying 115 contributions out of 115
Type: Oral presentation Track: Several Complex Variables
We study the neighborhood of an embedded $J$-holomorphic disc attached along its boundary to a maximal totally real submanifold in an almost complex manifold. In particular, we provide sufficient conditions for the set of all nearby attached $J$-holomorphic discs to be a manifold. Further, we present an application concerning deformations of stationary $J$-holomorphic discs.
Presented by Mr. Uroš KUZMAN
Type: Oral presentation Track: Several Complex Variables
I will report on a joint project with Elizabeth Wulcan and Ha*kan Samuelsson-Kalm. Recently, Berndtsson generalized the Ohsawa-Takegoshi-Manivel $L^2$-extension theorem for holomorphic functions to the case of $\overline{\partial}$-closed forms of higher degree. He proved an $L^2$-extension theorem for $\overline{\partial}$-closed forms from a smooth divisor in a compact manifold with g ... More
Presented by Dr. Jean RUPPENTHAL
Type: Oral presentation Track: Graph Theory
A graph G is Hamilton-connected if G has a hamiltonian (u,v)-path for any pair of vertices u, v, and, for an integer k, a graph G is k-Hamilton-connected if the graph G-X is Hamilton-connected for every set X of vertices with |X|=k. Specifically, G is 1-Hamilton-connected if G-x is Hamilton-connected for every vertex x of G. Obviously, a Hamilton-connected graph is 3-connected, and a k-Hamilton-co ... More
Presented by Prof. Zdenek RYJACEK
Type: Poster Track: Poster Session
In this case a CSASC history is a Catalan Slovenian Austrian Slovak and Czech history starting with the famous Catalan scholar Ramon Llull in the 13th century and followed by a short discussion of combinatorics and graph theory in the last 50 years since the conference of Smolenice in Slovakia in 1963, including the conference of Prachatice in Bohemia in 1990, and the many conferences in Bled in S ... More
Presented by Harald GROPP
Type: Oral presentation Track: Mathematical Methods in Image Processing
In this work, we present a nonlocal variational model for fusing the information given by a panchromatic image at high resolution and the spectral multichannel at lower resolution in order to get the high resolution of the multispectral images. Our approach is based on the Caselles et al work \cite{bciv-2006}. In this paper, the authors give a functional model based on the main assumption tha ... More
Presented by Ms. Catalina SBERT
Type: Oral presentation Track: Mathematical Methods in Image Processing
In this talk we present our advancements in designing a robust but simple algorithm for detection of cells in biological image data. Simplicity of this algorithm is to be understood as reduction of its user-defined parameters, which results in reduced calibration time. A starting point for us was the FBLSCD (Flux-Based Level-Set Center Detection) algorithm, and we studied the impact of its par ... More
Presented by Mr. Michal SMíšEK
Type: Oral presentation Track: Diferential Geometry and Mathematical Physics
The aim is to find a “dynamical picture“, i.e. geometric structure of the complete solution of equations of motion of a singular Lagrangian, and study symmetries of the corresponding implicit Euler-Lagrange equations. In case of regular Lagrangians the dynamics are completely described by a one-dimensional foliation of the phase space. For singular Lagrangians the structure of solutions is mu ... More
Presented by Ms. Monika HAVELKOVá
Type: Oral presentation Track: Numerical Methods for Partial Differential Equations
This work is devoted to the numerical simulation of an atherosclerosis model, proposed by El Khatib et al. (2007). The numerical simulation is carried out by means of a finite volume scheme based on high-order ADER methodology. Concerning the asymptotic behaviour of the solutions, the numerical examples show that a small perturbation of a healthy steady state makes the system evolve to a diseas ... More
Presented by Prof. Arturo HIDALGO
Type: Oral presentation Track: Numerical Methods for Partial Differential Equations
We propose a numerical instrument to solve, in 1D and 2D, transport problems written in conservation form. The integrand function evolves following the laws described by an advection field, whose expression depends on the nature of the system studied. Common issues in the simulation of such problems are the appearance or movement of large gradients, the filamentation of the phase space or the pr ... More
Presented by Mr. Francesco VECIL
Type: Oral presentation Track: Combinatorics
We consider a triangular gap of side 2 in a 60 degree angle on the triangular lattice whose sides are zigzag lines. We study the interaction of the gap with the corner as the rest of the angle is completely filled with lozenges (a lozenge is a unit rhombus consisting of two lattice triangles that share an edge). We show that the resulting correlation is governed by the product of the distances bet ... More
Presented by Mihai CIUCU
Type: Oral presentation Track: Algebra
Gil Kaplan invented a twisting function t(x,y)=(y^{-1}xy,x^{-1}yx) where x and y are from a finite group G. When t is bijective he proved that G is solvable. Together we refined some of these results. E.g., when t has prime order p for an odd prime p then G is already nilpotent. (This is joint work with Gil Kaplan, Yaffo College, Tel Aviv)
Presented by Wolfgang HERFORT
Type: Oral presentation Track: Diferential Geometry and Mathematical Physics
Abstract. In this lecture we study natural Einstein Riemann extensions from torsion-free affine manifolds to their cotangent bundles. Such a Riemann extension is always a semi-Riemannian manifold of signature (n, n). It is well-known that, if the base manifold is a torsion-less affine two-manifold with skew-symmetric Ricci tensor, or, a flat affine space, we obtain a (globally) Osserman struct ... More
Presented by Prof. Oldrich KOWALSKI
Type: Oral presentation Track: Numerical Methods for Partial Differential Equations
High Resolution Shock Capturing (HRSC) schemes are nowadays one of the most used schemes for the computation of accurate numerical approximations to the solution of hyperbolic systems of conservation laws. Most of these schemes emerge form a clever combination of an upwinding framework, in which the iscretization of the equations on a mesh is performed according to the direction of propagation of ... More
Presented by Ms. MªCarmen MARTí RAGA
Type: Oral presentation Track: Symmetries in Graphs, Maps and Other Discrete Structures
We briefly outline a theory of abstract polygonal complexes and their representations. The theory enables a uniform approach to maps on surfaces and their polyhedral representations. In particular, the relationship between automorphism groups of abstract polygonal complexes and the symmetry groups of their geometric representation is explored. The talk will be illustrated by computer implementati ... More
Presented by Prof. Tomaž PISANSKI
Type: Oral presentation Track: Mathematical Methods in Image Processing
We present new finite volume method for solving diffusion PDEs used in image processing on adaptive grids, i.e. grids adapted to the data with the aim to decrease the number of unknowns in computations [1], [4]. The diffusion equations are solved on the consistent adaptive grid built by modifying the quadtree structure in such way, that the connection of representative points of two ... More
Presented by Mrs. Zuzana KRIVá
Type: Oral presentation Track: Diferential Geometry and Mathematical Physics
The work of Kentaro Yano on the Lie derivative nearly sixty years ago was important in establishing the properties of infinitesimal symmetries of various types of geometric object, in particular of spaces with an affine connection. In this talk I shall discuss an approach to this problem using Lie groupoids of affine maps, and I shall show how the associated Lie algebroids may usefully be represen ... More
Presented by Prof. David SAUNDERS
Type: Oral presentation Track: Symmetries in Graphs, Maps and Other Discrete Structures
A map is a $2$-cell decomposition of a closed surface. A map on an orientable surface is called orientably regular if its group of orientation-preserving automorphisms acts transitively on the set of darts (edges endowed with an orientation). We investigate orientably regular maps with an unfaithful action of the automorphism group simultaneously at vertices and faces. In particular, we say that a ... More
Presented by Prof. Roman NEDELA
Type: Oral presentation Track: Discrete and Computational Geometry
We address the problem of counting geometric graphs on point sets. Using analytic combinatorics we show that the so-called double chain point configuration of $N$ points has $\Omega^*(12.31^N)$ non-crossing spanning trees and $\Omega^*(13.40^N)$ non-crossing forests. This improves the previous lower bounds on the maximum number of non-crossing spanning trees and of non-crossing forests among all s ... More
Presented by Clemens HUEMER
Type: Oral presentation Track: Symmetries in Graphs, Maps and Other Discrete Structures
In this talk I will introduce all the arc-transitive cyclic regular covers of the dodecahedron graph using a new approach of constructing regular covers given by Conder and Ma. Two families of infinite 3-arc-transitive abelian regular covers of the dodecahedron graph will be introduced which gives more concrete examples that for a s-arc-transitive graph there exists (s + 1)-arc-transitive covering ... More
Presented by Dr. Jicheng MA
Type: Oral presentation Track: Discrete and Computational Geometry
We consider an Erd\H{o}s type question on $k$-holes (empty $k$-gons) in bichromatic point sets. For a bichromatic point set $S=R\union B$, %in general position and integer $k\geq2$, a balanced $2k$-hole in $S$ is %a simple polygon spanned by $k$ points of $R$ and $k$ points of $B$. %which does not contain any points of $S$ in its interior. We show that if $|R|=|B|=n$, then the number o ... More
Presented by Ms. Birgit VOGTENHUBER
Type: Oral presentation Track: Several Complex Variables
The Mane-Sad-Sullivan theorem is a basic result concerning the stability of holomorphic families of rational maps on the Riemann sphere. We parially extend it to families of endomorphisms of P^k using pluripotential techniques. This is a joint work with Christophe Dupont.
Presented by Prof. Francois BERTELOOT
Type: Oral presentation Track: Several Complex Variables
We talk about recent joint work with Martin Kolar about the biholomorphic classification of infinite type hypersurfaces in $\mathbb{C}^2$. We will put an emphasis on examples of hypersurfaces which support symmetries, discuss general bounds on the dimension of automorphism groups, and give a number of applications.
Presented by Dr. Bernhard LAMEL
Type: Oral presentation Track: Plenary Talk
The Bogomolov multiplier is a group theoretical invariant isomorphic to the unramiﬁed Brauer group of a given quotient space, and represents an obstruction to the problem of stable rationality of ﬁxed ﬁelds. In this talk we survey some recent results regarding Bogomolov multipliers. We derive a homological version of the Bogomolov multiplier, prove a Hopf-type formula, ﬁnd a ﬁve ter ... More
Presented by Primoz MORAVEC
Type: Oral presentation Track: Plenary Talk
We discuss one instance of so-called "borrowing strength" in statistics, in the context of compound decision strategy also referred to as the empirical Bayes approach. We show how certain plausible qualitative restrictions (in the vein of monotonicity, convexity, logarithmic concavity and similar) are capable of regularizing (without introducing ambiguous tuning parameters) the otherwise ill ... More
Presented by Ivan MIZERA
Type: Oral presentation Track: Several Complex Variables
We show that a compact, connected, oriented, CR manifold of hypersurface type in C^n is extended to a "strip" complex variety Y in C^n. The extension is obtained as a union of discs attached to M at points of local minimality (Trepreau-Tumanov); this extension "propagates" to points where minimality fails by a generalized Hanges-Treves theorem on account of the fact that these points are connecte ... More
Presented by Luca BARACCO
Type: Oral presentation Track: Graph Theory
Median graphs are one of the central classes of graphs in metric graph theory. They arise in different guises and applications, and relate to many other mathematical structures. Several natural non-bipartite generalizations that capture various properties of median graphs have also been studied, in particular quasi-median graphs, weakly median graphs and fiber-complemented graphs. In this talk we ... More
Presented by Prof. Boštjan BREšAR
Type: Oral presentation Track: Symmetries in Graphs, Maps and Other Discrete Structures
Let $G$ be a group and let $S$ be an inverse-closed subset of $G$. The \emph{Cayley graph} $\mathrm{Cay}(G,S)$ is the graph with vertex-set $G$ and with $g$ being adjacent to $h$ if and only if $gh^{-1}\in S$. It is easy to see that $G$ acts regularly as a group of automorphisms of $\mathrm{Cay}(G,S)$ by right multiplication. Moreover, if $G$ is abelian and $\iota$ is the automorphism of $G$ ... More
Presented by Mr. Gabriel VERRET
Type: Oral presentation Track: Algebra
A group $G$ is called capable if there exists a group $H$ such that $H/Z(H)$ is isomorphic to $G$. It was recognised by P. Hall that capability has application in classifying $p$-groups. This application was developed and applied by M. Hall and Senior to classify the groups of order $64$. There are several methods for determining whether a $p$-group is capable. In this talk we will review ... More
Presented by Dr. Robert MORSE
Type: Oral presentation Track: Combinatorics
We use the cluster method to enumerate permutations avoiding consecutive patterns. We reprove and generalize in a unified way several known results and obtain new ones, including some patterns of length 4 and 5, as well as some infinite families of patterns of a given shape. By enumerating linear extensions of certain posets, we find a differential equation satisfied by the inverse of the exponen ... More
Presented by Prof. Marc NOY
Type: Poster Track: Poster Session
Configurations are linear regular uniform hypergraphs, mainly discussed in a geometrical language, closely related to bipartite graphs, combinatorial designs and similar structures. The current knowledge will be discussed together with the discussion how future research should go on. Probably also more general structures such as lambda-configurations will be considered. For further information see ... More
Presented by Harald GROPP
Type: Oral presentation Track: Mathematical Methods in Image Processing
In the talk we present mathematical models and numerical methods which lead to early embryogenesis reconstruction and extraction of the cell lineage tree from the large-scale 4D image sequences. Robust and efficient finite volume schemes for solving nonlinear PDEs related to filtering, object detection and segmentation of 3D images were designed to that goal and studied mathematically. They ... More
Presented by Prof. Karol MIKULA
Type: Oral presentation Track: Proving in Mathematics Education at University and at School
Different ways of the use of computer in proving in secondary school mathematics will be discussed. By means of particular examples, the author, former secondary school teacher, now teacher educator, will illustrate advantages and disadvantages of the computer assisted proving in secondary school mathematics. The aim of the presentation is to contribute to the discussion about the use of TP softwa ... More
Presented by Roman HASEK
Type: Poster Track: Poster Session
In this talk I shall give a short survey on configurations as combinatorial and geometrical discrete structures from a historical point of view with a special focus on the question of notation. Configurations were formally defined in 1876 by Reye and investigated mainly in the last quarter of the nineteenth century and in the last 30 years with a long break in between. Due to the special aspect o ... More
Presented by Harald GROPP
Type: Oral presentation Track: Plenary Talk
I will survey algorithms for testing whether two given finite geometric objects are congruent. Under reasonable assumptions, the objects can be reduced to (labeled) point sets. I will introduce the two important techniques for congruence testing, namely dimension reduction and set pruning, and I will indicate how these techniques might lead for the first time to an algorithm for four dimensions wi ... More
Presented by Prof. Günter ROTE
Type: Oral presentation Track: Diferential Geometry and Mathematical Physics
The set of constrained Noetherian symmetries of nonholonomic mechanical systems of the first order is studied and the corresponding conservation laws are presented.
Presented by Dr. Martin SWACZYNA
Type: Oral presentation Track: Plenary Talk
In complex analysis in higher dimension it is often easier to do analysis on convex domains. Sometimes one can obtain convexity after changes of coordinates. I will discuss this topic, including joint recent work with Erlend F. Wold and Klas Diederich.
Presented by Prof. John Erik FORNAESS
Type: Oral presentation Track: Algebra
This work was inspired by a question of Gabriel Navarro about orbit lengths of groups acting on fi nite vector spaces. If a fi nite group H acts irreducibly on a finite vector space V, then for every pair of non-zero vectors, their orbit lengths a, b have a non-trivial common factor. This could be interpreted in the context of permutation groups. The group V H is an affine primitive group on ... More
Presented by Dr. Pablo SPIGA
Type: Oral presentation Track: Symmetries in Graphs, Maps and Other Discrete Structures
Finite connected cubic symmetric graphs of girth $6$ have been classified by K. Kutnar and D. Maru\v{s}i\v{c} ({\it J. Combin. Theory Ser. B} {\bf 99} (2009), 162--184), in particular, each of these graphs has an abelian automorphism group with two orbits on the vertex set. In this paper all cubic symmetric graphs with the latter property are determined. In particular, with the exception of the ... More
Presented by Istvan KOVACS
Type: Oral presentation Track: General Session
We use a remarkable connection between real hypersurfaces in complex space and second-order differential equations in complex domains for the study of nonminimal real hypersurfaces in complex affine 2-space. We find necessary and sufficient conditions for a local CR-mapping at a Levi nondegenerate point into a sphere (if the latter exists) to extend holomorphically to the complex locus. As an appl ... More
Presented by Dr. Ilya KOSSOVSKIY
Type: Oral presentation Track: Discrete and Computational Geometry
Two players alternately claim vertices of a graph for $t$ rounds. In the end, the remaining vertices are divided such that each player receives the vertices that are closer to his or her claimed vertices. We prove that there are graphs for which the second player gets almost all vertices in this game, but this is not possible for bounded-degree graphs. For trees, the first player can get at least ... More
Presented by Dr. Viola MéSZáROS
Type: Oral presentation Track: Numerical Methods for Partial Differential Equations
Discrete duality finite volume (DDFV) scheme established in recent years for elliptic problems is used for solving regularized level set equation. Semi-implicit DDFV numerical scheme for the solution of the regularized curvature driven level set equation is derived in 2D and 3D. Stability and convergence of the numerical solution to the weak solution is proved in 2D. Numerical experiments in ... More
Presented by Mrs. Angela HANDLOVICOVA
Type: Oral presentation Track: Several Complex Variables
I will present a joint work with Nir Lev. We study the equidistribution of Fekete points in a compact complex manifold. These are extremal point configurations defined through sections of powers of a positive line bundle. Their equidistribution is a known result. The novelty of our approach is that we relate them to the problem of sampling and interpolation on line bundles, which allows us to est ... More
Presented by Joaquim ORTEGA CERDà
Type: Oral presentation Track: Numerical Methods for Partial Differential Equations
We present an original method for improving numerical solution of equations modeling evolution of surfaces and other manifolds. The technique uses tangential movement of points along the surface during the evolution process. We show how an appropriately chosen tangential velocity helps to obtain a correct solution of the discretized problem. We present several test examples and practical applicati ... More
Presented by Ms. Mariana REMESIKOVA
Type: Oral presentation Track: Graph Theory
The partial representation extension problem is a recently introduced generalization of the recognition problem. In this problem, aside a graph a part of a representation is given. The question is whether this partial representations can be extended to a representation of the entire graph. For example in the case of interval graphs, a part of intervals is pre-drawn and the question is whether the ... More
Presented by Mr. Pavel KLAVIK
Type: Oral presentation Track: Symmetries in Graphs, Maps and Other Discrete Structures
In matrix theory a preserver problem' demands a characterization of all maps $\Phi$ on a certain set $\mathcal{M}$ of matrices, which leave some function, subset, or relation invariant. In the case a symmetric binary relation $R$ is preserved, such maps $\Phi$ are precisely the endomorphisms of the graph $\Gamma$ with the vertex set $V(\Gamma)=\mathcal{M}$ and the edge set $E(\Gamma)=\{\{m_1,m_2\ ... More Presented by Marko OREL Type: Oral presentation Track: Numerical Methods for Partial Differential Equations Level set methods are popular algorithms in applied mathematics to treat dynamic interfaces. There are many variants of such numerical methods, and the flux-based level set method [3] has some distinct features among them. The method is based on finite volume discretization rather than more usual finite difference approximation. In such a way the method is defined with no additional difficultie ... More Presented by Dr. Peter FROLKOVIC Type: Oral presentation Track: Combinatorics Fully Packed Loop configurations (FPLs) are subgraphs of a square grid such that each internal node is of degree two. While these objects arise naturally in a statistical physics context as a model for ice, they also lead to intriguing enumerative problems. Fully Packed Loop configurations in a triangle (TFPLs) first appeared in the study of ordinary Fully Packed Loop configurations where they wer ... More Presented by Mrs. Ilse FISCHER Type: Oral presentation Track: Symmetries in Graphs, Maps and Other Discrete Structures Roughly speaking an end of a graph G(V,E) is an equicalence class of one-way infinite paths such that any two different equivalence classes can be sparated from each other by removing a finite subset S of V(G). In this talk we consider infinite subsets of V(G) with certain growth rates which can be separated from each other by a connected subgraph of G with smaller growth rate. Following the i ... More Presented by Prof. Norbert SEIFTER Type: Oral presentation Track: Symmetries in Graphs, Maps and Other Discrete Structures I will present certain computational aspects of lifting automorphisms along regular covering projections of graphs. Joint work with Rok Po\v zar. Presented by Prof. Aleksander MALNIC Type: Oral presentation Track: Combinatorics Tamari lattice is the lattice of all parenthesizations of a string, where two parenthesizations are in a relation if we can get one from the other by using the associative rule (xy)z -> x(yz). It is a classical result that the Tamari lattice can be realized as the 1-skeleton (edges) of the associahedron. Recently, the r-Tamari lattice was defined, and F. Bergeron has conjectured that it can be ... More Presented by Matjaz KONVALINKA Type: Oral presentation Track: Diferential Geometry and Mathematical Physics A better understanding of the Hamilton-Jacobi equation can be obtained by a careful analysis of the relevant geometric structures that are involved in it. This analysis is performed by working on an appropriate generalisation of the Hamilton-Jacobi equation following the lines of the article by Cariñena et al (2006). Presented by Xavier GRàCIA Type: Oral presentation Track: Algebra This talk will begin with a brief review of group cohomology and discrete vector fields. It will then explain how discrete vector fields can be used to compute the integral cohomology of a range of groups including certain finite simple groups, certain crytallographic groups and certain arithmetic groups. Presented by Graham ELLIS Type: Oral presentation Track: Combinatorics A useful way to classify sequences which appear in combinatorial enumeration is by the type of recurrences which they do (or do not) satisfy. Holonomic sequences are those satisfying homogeneous li\-near recurrences with polynomial coefficients, whose well-known special cases include sequences satisfying linear recurrences with constant coefficients, and hypergeometric sequences whose consecutive- ... More Presented by Marko PETKOVšEK Type: Oral presentation Track: Proving in Mathematics Education at University and at School Verification of a claim is just one of the aims of proving in school geometry and, in general, in school mathematics. Often other aspects of proofs and proving are more important, e.g. explanation, systematisation, communication. These aims mutually interact with the used technology and also with the proving related content. Introducing new technologies into school geometry thus requires a re-eval ... More Presented by Dr. Zlatan MAGAJNA Type: Oral presentation Track: Numerical Methods for Partial Differential Equations Explicit schemes for the solution of nonlinear convection-diffusion equations have severe time step restrictions for accurate simulations with dominant diffusion. Therefore Implicit-explicit (IMEX) methods are suitable for the solution of those equations, since the stability restrictions, coming from the explicitly treated convective part, are much less severe than those that would be deduced ... More Presented by Prof. Pep MULET-MESTRE Type: Oral presentation Track: Numerical Methods for Partial Differential Equations IMEX methods are a suitable choice for the solution of nonlinear convection-difussion equations, since the stability restrictions coming from the explicitly treated convective part, are much less severe than those that would be deduced from an explicit treatment of the diffusive term. We combine an explicit Runge-Kutta scheme for the convective part and an implicit one for the diffusive part. The ... More Presented by Dr. Francisco GUERRERO Type: Oral presentation Track: Several Complex Variables We construct random point processes in the complex plane that are asymptotically close to a given doubling measure. The processes we construct are the zero sets of random entire functions that are constructed through generalised Fock spaces. We show that the average distribution of the zero set is close to the given doubling measure, and that the variance is much less than the variance of the corr ... More Presented by Jerry BUCKLEY Type: Oral presentation Track: Several Complex Variables We will discuss a result on L^2 interpolation to the ambient space, of data given on a singular hypersurface in C^n, with respect to so-called generalized Bargmann-Fock L^2 norms. It is known that the ability to interpolate all data places restrictions on the singularities, but the precise restrictions are not yet known. We will consider so-called transversal singularities, which include for ... More Presented by Dr. Dror VAROLIN Type: Oral presentation Track: Diferential Geometry and Mathematical Physics Lagrangian and Hamiltonian formalism certainly belong to the most useful and extensively used mathematical frameworks in physics. The relationship between these two theories is provided by the Legendre transformation, and is one-to-one when the Lagrangian is regular: in such a case the Legendre transformation is a local diffeomorphism. In the standard treatment of many important physical systems, ... More Presented by Prof. Olga ROSSI Type: Oral presentation Track: Numerical Methods for Partial Differential Equations The method of fundamental solutions (MFS) is used to derive the geopotential and its first derivatives from the second derivatives observed by the GOCE satellite mission. The MFS is based on the fundamental solution of a partial differential equation that represents its basis functions. In contrast to the boundary element method, the MFS is an inherent mesh-free method and avoids the numerical int ... More Presented by Dr. Robert CUNDERLIK Type: Oral presentation Track: Symmetries in Graphs, Maps and Other Discrete Structures For cyclic codes, there are multiple notions of isomorphism. For example, we can consider isomorphisms that only permute the coordinates of codewords, or isomorphisms that not only permute the coordinates of codewords but also multiply each coordinate by a scalar (not necessarily the same scalar for each coordinate) as it permutes the codewords. Isomorphisms of cyclic codes of the first kind ha ... More Presented by Prof. Ted DOBSON Type: Oral presentation Track: Numerical Methods for Partial Differential Equations The presentation is devoted to the numerical solution of the two-dimensional stochastic volatility Heston model aimed to find a fair price of a financial derivative contract. The governing backward parabolic partial differential differential equation will be derived and main points concerning boundary conditions will be highlighted. In order to find the solution we propose a diamond-cell-based num ... More Presented by Mr. Pavol KUTIK Type: Oral presentation Track: Several Complex Variables This is a report on a joint work with Shulim Kaliman. We start by reminding definitions and importance of the notions of density property and volume density property introduced by Varolin. To prove that a manifold has one of these properties can be a cumbersome calculation with Lie brackets of vector fields. We present a criterion, proved using the theory of coherent sheafs, which can reduce ... More Presented by Prof. Frank KUTZSCHEBAUCH Type: Oral presentation Track: Algebra It has been a longstanding goal of group theory to somehow describe if not characterize finite p-groups. In the 1940's, P. Hall proposed to tackle the problem by considering groups only up to their commutator structure, a suggestion that has turned out to be quite efficient. Many authors have since studied the relations between commutators, in particular some universal ones via the exterior p ... More Presented by Urban JEZERNIK Type: Oral presentation Track: Graph Theory A well-covered graph is a graph in which all maximal stable sets are of the same size, or in other words, they are all maximum. A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. A circulant is a Cayley graph over a cyclic group. It is not difficult to show that a circulant G is a CIS graph if and only if G and its complement G are both well-covered an ... More Presented by Dr. Martin MILANIC Type: Oral presentation Track: Discrete and Computational Geometry A set$P$of points in$R^2$is$n$-universal, if every planar graph on$n$vertices admits a plane straight-line embedding on$P$. Answering a question by Kobourov, we show that there is no$n$-universal point set of size$n$, for any$n\ge 15$. Conversely, we use a computer program to show that there exist universal point sets for all$n\le 10$and to enumerate all corresponding order types. Fi ... More Presented by Michael HOFFMANN Type: Oral presentation Track: Symmetries in Graphs, Maps and Other Discrete Structures Generalized Cayley graphs were defined by D.Marušič, R. Scapellato and N. Zagaglia Salvi in 1992. They studied properties of such graphs, mostly related to double coverings of graph. They also posed a question whether there exists a generalized Cayley graph which is vertex-transitive but not Cayley graph. In this talk, as an affirmative answer to this question, I will present an infinite family ... More Presented by Mr. Ademir HUJDUROVIć Type: Oral presentation Track: Several Complex Variables We consider a smoothly bounded domain in complex projective space, which admits a plurisubharmonic defining function. We discuss the existence of 1-convex boundary points for such a domain. Presented by Prof. Judith BRINKSCHULTE Type: Oral presentation Track: Several Complex Variables If$w$is a weight in${\bf S}^n$, the weighted Hardy-Sobolev space$H_s^p(w)$,$0\leq s$,$0 \lt p \lt +\infty$, consists of functions$f$holomorphic in$\B^n$such that if${\displaystyle f(z)=\sum_k f_k(z)}$is its homogeneous polynomial expansion, and${\displaystyle (I+R)^s f(z):=\sum_k (1+k)^s f_k(z)},$we have that$${\displaystyle ||f||_{H_s^p(w)}^p:= \sup_{r\lt 1}\int_{{\b ... More Presented by Prof. Carme CASCANTE Type: Oral presentation Track: Discrete and Computational Geometry The Erd"os-Szekeres theorem states that, for every k, there is a number n_k such that every set of n_k points in general position in the plane contains a subset of k points in convex position. If we ask the same question for subsets whose convex hull does not contain any other point from the set, this is not true: as shown by Horton, there are sets of arbitrary size that do not contain an empty 7- ... More Presented by Dr. Panos GIANNOPOULOS Type: Oral presentation Track: Graph Theory Consider the uniform random graph G(n,M) with n vertices and M edges. Erdös and Rényi (1960) conjectured that the limit lim P[G(n,n/2) is planar] exists and is a constant strictly between 0 and 1. Luczak, Pittel and Wierman (1994) proved this conjecture and Janson, Luczak, Knuth and Pittel (1993) gave lower and upper bounds for this probability. In this work we determine the exact pr ... More Presented by Dr. Juanjo RUé Type: Oral presentation Track: Mathematical Methods in Image Processing We extend the concept of optical flow to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. In this talk we introduce variational motion estimation for images that are defined on an evolving surface. Volumetric microscopy images depicting a live zebrafish embryo serve as biological motivation. Presented by Mr. Clemens KIRISITS Type: Oral presentation Track: Mathematical Methods in Image Processing We extend the concept of optical flow to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. We introduce variational motion estimation for images that are defined on an evolving surface. Volumetric microscopy images depicting a live zebrafish embryo serve as biological motivation. In this talk we discuss numerical aspects, a possible surface par ... More Presented by Mr. Lukas LANG Type: Oral presentation Track: Graph Theory A class of graphs F satisfies the Erdös-Pósa property if there exists a function f such that, for every integer k and every graph G, either G contains k vertex-disjoint subgraphs each isomorphic to a graph in F, or there is a set S ⊆ V (G) of at most f(k) vertices such that G \ S has no subgraph in F. Erdös and Pósa [1965] proved that the set of all cycles satisfies this property with f(k)=O ... More Presented by Dr. Ignasi SAU Type: Oral presentation Track: Discrete and Computational Geometry Polycubes are polyforms made of cubes of the same size joined face to face. Various algebraical, geometrical, topological, combinatorial and symmetrical properties of polycubes may be studied. The boundary of a non-singular polycube is a surface (every boundary point has a neighborhood homeomorphic to a disc). We focus on the morphology of such polycubes: 1) We present an algebraic desc ... More Presented by Mr. Jurij KOVIč Type: Oral presentation Track: Discrete and Computational Geometry Discrete Morse theory introduced by Robin Forman in 1998 is a combinatorial version of smooth Morse theory. It has proven to be a useful tool for computing homology of cell complexes and persistent homology of filtered cell complexes, and is also widely used in topological data analysis. We will present a parametric version of discrete Morse theory and an algorithm based on it for tracking critica ... More Presented by Neza MRAMOR KOSTA Type: Oral presentation Track: Several Complex Variables We shall consider degenerate CR embeddings$f$of a strictly pseudoconvex hypersurface$M\subset \mathbb C^{n+1}$into a sphere$\mathbb S$in a higher dimensional complex space$\bathbb C^{N+1}$. The degeneracy of the mapping$f$will be characterized in terms of the ranks of the CR second fundamental form and its covariant derivatives. In 2004, the speaker, together with X. Huang and D. Zaitse ... More Presented by Prof. Peter EBENFELT Type: Oral presentation Track: Plenary Talk We discuss direct and inverse spectral theory for the isospectral problem of the dispersionless Camassa-Holm equation, where the weight is allowed to be a finite signed measure. In particular, we prove that this weight is uniquely determined by the spectral data and solve the inverse spectral problem for the class of measures which are sign definite. The results are applied to deduce several facts ... More Presented by Prof. Gerald TESCHL Type: Oral presentation Track: Symmetries in Graphs, Maps and Other Discrete Structures A {\em bicirculant} is a graph admitting an automorphism with two cycles of equal length in its cycle decomposotion. A graph is said to be {\em arc-transitive} if its automorphism group acts transitively on the set of its arcs. In this talk I will present a recent complete classification of connected pentavalent arc-transitive bicirculants. This is joint work with Iva Anton\v ci\v c and Ademir Huj ... More Presented by Klavdija KUTNAR Type: Oral presentation Track: Graph Theory We prove that a cubic nonprojective graph cannot have a finite planar emulator, unless one of two very special cases happen (in which the answer is open). This shows that Fellows’ planar emulator conjecture, disproved for general graphs by Rieck and Yamashita in 2008, is nearly true on cubic graphs, and might very well be true there definitely. Presented by Dr. Petr HLINěNý Type: Oral presentation Track: Mathematical Methods in Image Processing Root system architecture is essential for plant nutrient and water uptake and is therefore crucial for plant development. Root system responses to heterogeneous soil conditions are of highest interest in plant nutrition, plant hydrology as well as plant breeding. Root architectural development includes architectural, morphological, anatomical as well as physiological traits. For the systematic inv ... More Presented by Dr. Daniel LEITNER Type: Oral presentation Track: Several Complex Variables I will talk about some new developments in the study of plurisubharmonic polynomials. Jointly with G. Bharali I have been working on bumping of pseudoconvex domains with real analytic boundary. In our study we met an obstacle that prevented us from getting an optimal result for all such domains. Recently we have been able to prove a theorem that removes this obstacle. Presented by Prof. Berit STENSONES Type: Oral presentation Track: Graph Theory We call a graph$G$inscribable of order$m$(in brief,$m$-inscribable) if its vertices can be located on the sphere$S^2$in such a way that for each vertex$v$, the vertices at distance$m$from$v$lie in a common plane ($m=1,2,...$). If, in particular,$G$is planar and 3-connected, then, on account of Steinitz' characterization theorem, we can define the same property for a 3-polytope$P$wh ... More Presented by Dr. Gábor GéVAY Type: Oral presentation Track: Algebra I shall review some results in abstract groups that are obtained using profinite graphs and groups. I will concentrate on properties like conjugacy separability in abstract groups. Presented by Prof. Luis RIBES Type: Oral presentation Track: Proving in Mathematics Education at University and at School Computer Theorem Provers (TP) are becoming ready for industrial use -- and raise demands to educate engineers in "Formal Methods", based on mechanised mathematics, modeling and proving. This demand calls for rethinking mathematics education in general -- and for adapting TPs to educational requirements. Particular educational requirements are: (1) check user input automatically, flexibly an ... More Presented by Dr. Walther NEUPER Type: Oral presentation Track: Proving in Mathematics Education at University and at School There are two different approaches to proofs presentation in secondary school mathematics: 1) proofs, as a special separate topic, 2) proofs, as a part of mathematics building. Although proving has an irreplaceable position in the mathematics curricula, its priority in mathematics education is steadily marginalized by students as well as by teachers. The presentation will describe the current ... More Presented by Mrs. Irena ŠTRAUSOVá Type: Oral presentation Track: Numerical Methods for Partial Differential Equations Photoacoustic imaging is a hybrid tomographic technique based on the photoacoustic effect. Tissue irradiated by a short laser pulse generates an ultrasound signal (due to thermal expansion) which can be measured by ultrasound transducers. From these measurements, the ultrasound initial pressure can be reconstructed uniquely by photoacoustic inversion. The goal of quantitative photoacoustic imaging ... More Presented by Mr. Wolf NAETAR Type: Oral presentation Track: Discrete and Computational Geometry The straight skeleton is a skeleton structure similar to the (generalized) Voronoi diagram. Since their introduction to computational geometry by Aichholzer et al. two decades ago, straight skeletons turned out to be a useful tool for a large number of applications in different areas of science and industry. The straight skeleton S(H) of a planar straight-line graph (PSLG) H consists of straight- ... More Presented by Stefan HUBER Type: Oral presentation Track: Discrete and Computational Geometry We introduce the notion of recursive regularity. A polyhedral subdivision of a point set is said to be recursively regular if it can be coarsened by a regular subdivision that divides the original one into regular parts. The class of such subdivisions is a subset of the visibility-acyclic subdivisions and a superset of the regular subdivisions of a point set. However, the associated graph of flips ... More Presented by Mr. Rafel JAUME Type: Oral presentation Track: Mathematical Methods in Image Processing Many applications in computer vision require the 3D reconstruction of a shape from its different views. When the available information in the images is just a binary mask segmenting the object, the problem is called shape from silhouette (SfS). As first proposed by Baumgart, the shape is usually computed as the maximum volume consistent with the given set of silhouettes. This is called visua ... More Presented by Dr. Gloria HARO Type: Oral presentation Track: Plenary Talk The notion of rectifiability plays an essential role in the L^2 boundedness of some important operators arising in complex and harmonic analysis, such as the Cauchy and Riesz transforms. Indeed, by a well known result of David, it turns out that the Cauchy transform originates an operator bounded in L^2 with respect to the arc length measure on (AD regular) rectifiable curves of the plane. In the ... More Presented by Prof. Xavier TOLSA Type: Oral presentation Track: Symmetries in Graphs, Maps and Other Discrete Structures Covering techniques have received considerable attention over the years, with its main incentive in constructing regular coverings of graphs with specific symmetry properties. Accordingly, one would like to find algorithms that would deliver answers to certain natural questions regarding symmetry issues of graphs and their coverings; this adds further motivation to the topic. In the talk we will ... More Presented by Rok POZAR Type: Poster Track: Poster Session \begin{abstract} For a graph$G=(V,E)$, \emph{a Roman dominating function} (RDF) is a function$f \colon V \to \{0,1,2\}$satisfying the condition that every vertex$u$for which$f(u)=0$is adjacent to at least one vertex$v$for which$f(v)=2$. The weight of an RDF equals$w(f)=\sum_{v\in V}f(v)=|V_1|+2|V_2|$. An RDF for which$w(f)$achieves its minimum is called \emph{a}$\gamma_R$\emph{-func ... More Presented by Prof. Antoaneta KLOBUCAR Type: Oral presentation Track: Several Complex Variables The spectrum of the$\overline \partial$-Neumann Laplacian on the Fock space$L^2(\mathbb C^n, e^{-|z|^2})$is explicitly computed. It turns out that it consists of positive integer eigenvalues each of which is of infinite multiplicity. Spectral analysis of the$\overline \partial$-Neumann Laplacian on the Fock space is closely related to Schr\"odinger operators with magnetic field and to the com ... More Presented by Prof. Friedrich HASLINGER Type: Oral presentation Track: Graph Theory The rooted product of a graph$H$by a sequence of rooted graphs$G_i$,$i\in V(H)$, is obtained by identifying the vertex$i$of$H$with the root of$G_i$. The rooted product of graphs was defined by Godsil and McKay in 1978, and they also determined its characteristic polynomial. Here we consider the special case when all rooted graphs are isomorphic either to a given rooted graph$G$or to a s ... More Presented by Prof. Dragan STEVANOVIC Type: Oral presentation Track: Combinatorics We say that a permutation p is merged' from permutations q and r, if we can color the elements of p red and blue so that the red elements are order-isomorphic to q and the blue ones to r. With Claesson and Steingr{\'\i}msson, we have shown, as a special case of more general results, that every permutation that avoids the subpermutation 1324 can be merged from a permutation that avoids 132 and a p ... More Presented by Vít JELíNEK Type: Oral presentation Track: Several Complex Variables Squeezing functions are certain holomorphic invariant of bounded domains. Roughly speaking, the value$s_D(z)$of the squeezing function of a bounded domain$D$at a point$z\in D$reflects how does$D$look like the unit ball, observed at the point$z$. In this talk, I'll give an introduction to squeezing functions, with emphasis on their boundary estimates, and the relations to geometric and ... More Presented by Prof. Fusheng DENG Type: Oral presentation Track: Numerical Methods for Partial Differential Equations Hybrid imaging techniques couple different imaging modalities in order to maximize contrast and resolution. In general, a ground modality provides interior data, from which the material parameters are then reconstructed in a second step, given a PDE model. We treat the elastography problem, where the displacement vector field is given and the Lam\'e parameters are sought. The estimation of the ela ... More Presented by Mr. Thomas WIDLAK Type: Oral presentation Track: Graph Theory This talk is concerned with automorphism breaking of finite and infinite graphs. Albertson and Collins~\cite{alco-96} introduced the {\it distinguishing number}$\D(G)$of a graph$G$as the least cardinal$d$such that$G$has a labeling with$d$labels that is only preserved by the trivial automorphism. This concept has spawned numerous papers on finite and infinite graphs. Here we foc ... More Presented by Prof. Wilfried IMRICH Type: Oral presentation Track: Diferential Geometry and Mathematical Physics In Riemannian geometry, scalar curvature is introduced starting from the Riemann curvature tensor associated to a connection, by taking two successive contractions with respect to a metric compatible with the given connection. This contraction process could be (in principle) done with any 2-covariant non-degenerate tensor, compatible with the connection, and such that it has a geometrical interest ... More Presented by Dr. Jose Antonio VALLEJO Type: Oral presentation Track: Discrete and Computational Geometry We study the problem of visibility in polyhedral terrains, in the presence of multiple viewpoints. We consider a triangulated terrain with$m>1$viewpoints (or guards) located on the terrain surface. A point on the terrain is considered \emph{visible} if it has an unobstructed line of sight to at least one viewpoint. We study several natural and fundamental visibility structures: (1) the visibili ... More Presented by Dr. Maria SAUMELL Type: Oral presentation Track: Algebra The intrinsic relation between lattice theory and topology has been reestablished with the works of M. H. Stone. Persistent homology is a recent addition to topology, where it has been applied to a variety of problems including to data analysis. It has been in the center of the interest of computational topology for the past twenty years. In this talk we will introduce a generalized version of pe ... More Presented by Prof. Joao PITA COSTA Type: Oral presentation Track: Several Complex Variables In this talk, new results for using the$1$-dimensional extension property to determine analyticity are discussed. The case under consideration is what has been referred to as the strip problem. Let$C$be a strictly convex closed curve in the complex plane whose horizontal translates$C_t$fill out a strip$S.$Given a function$f(z)$defined on the strip, such that the restriction of$f$to e ... More Presented by Mark LAWRENCE Type: Oral presentation Track: Diferential Geometry and Mathematical Physics The inverse problem of the calculus of variations in a nonholonomic setting is studied. The concept of constraint variationality of a mechanical system is introduced, based on a nonholonomic variational principle. Variational properties of mechanical systems of the first order with general constraints are presented. It is proved that constraint variationality is equivalent with the existence of a ... More Presented by Prof. Jana MUSILOVá Type: Oral presentation Track: Proving in Mathematics Education at University and at School The use of dynamic geometry systems (DGS) and computer algebra systems (CAS) changed methods of teaching mathematics at all school levels considerably. Dynamic features of DGS enable to do several activities which were not possible in the past, for instance dynamic experimentation with geometric figures, stating conjectures, searching for loci of points or visual proving. On the other hand with C ... More Presented by Prof. Pavel PECH Type: Oral presentation Track: Proving in Mathematics Education at University and at School The Theorema system is a mathematical assistant system that is designed to support a mathematician during all phases of mathematical activity. The focus lies, however, on proving mathematical theorems. Theorema employs algorithms that aim at generating proofs in a "natural style" that can then also be presented in a style similar to how proofs are given in textbooks. In the context of teach ... More Presented by Wolfgang WINDSTEIGER Type: Oral presentation Track: Graph Theory Given a partition of edges of a graph$G$into \emph{near} and \emph{far} edges, a \emph{threshold coloring} is a labeling of$V(G)$so that every pair of vertices adjacent with a \emph{near} edge receive integer labels that are closer than a certain threshold, and every pair of vertices adjacent with a \emph{far} edge receive labels at greater distance. Not every planar graph is threshold colo ... More Presented by Gašper FIJAVž Type: Oral presentation Track: Combinatorics I present some results obtained jointly with Andrea Jimenez and Mihyun Kang. Presented by Prof. Martin LOEBL Type: Oral presentation Track: Mathematical Methods in Image Processing We present a method for tracking the cell movement and divisions in early zebrafish embryo development. First, we create an approximate segmentation of 4D tubular structures representing time-space cell nuclei shapes. Then we compute a combined 4D distance function d1 using all cell nuclei identifiers in all time steps and a 4D distance function d2 from the boundaries of the segmented tubular stru ... More Presented by Mr. Róbert ŠPIR Type: Oral presentation Track: Discrete and Computational Geometry We consider two systems of curves$(\alpha_1,\ldots,\alpha_m)$and$(\beta_1,\ldots,\beta_n)$drawn on$M$, which is a compact two-dimensional orientable surface of genus$g\ge 0$and with$h\ge 1$holes. Each$\alpha_i$and each$\beta_j$is either an arc meeting the boundary of$M$at its two endpoints, or a closed curve. The$\alpha_i$are pairwise disjoint except for possibly sharing end ... More Presented by Martin TANCER Type: Oral presentation Track: Symmetries in Graphs, Maps and Other Discrete Structures A$(k;D)$-graph is a (finite, simple)$k$-regular graph of diameter$D$. The Degree/Diameter Problem is the problem of determining the order$n(k;D)$of the largest$(k;D)$-graphs. The well-known Moore bound serves as an upper bound on the order of$(k;D)$-graphs. In terms of$k$and$D$, it can be stated as follows:$M(k; g) = 1 + k + k(k - 1) + \dots + k(k -1)^{D-1}.\$ In our talk we s ... More
Presented by Martin MAčAJ
Type: Oral presentation Track: Discrete and Computational Geometry
FO (first-order logic) properties include, for instance, the dominating set and subgraph isomorphism problems. We investigate the question, on which subclasses of interval graphs these problems have efficient (parameterized) algorithms--while this is the case of unit interval graphs, no such general algorithmic metatheorem is possible on all interval graphs. We prove that fixed-parameter tractabil ... More
Presented by Dr. Petr HLINěNý
Type: Oral presentation Track: Plenary Talk
Let G be a class of labelled graphs endowed with a probability distribution on the set G(n) of graphs in G with n vertices. We say that a zero-one law holds in G if every first order graph property holds or does not hold in G(n) with probability 1 as n goes to infinity. Many zero-one laws have been established for the classical binomial model G(n,p) of random graphs, as well as for other classe ... More
Presented by Prof. Marc NOY
Type: Oral presentation Track: Diferential Geometry and Mathematical Physics
The aim of this paper is to show that the Lagrange--d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them, here we consider the generalization of the Hamiltonian principle for nonholonomic systems with nonzero transpositional relations. By applying this variational principle which ta ... More
Presented by Dr. Rafael RAMíREZ, Dr. Natalia SADOVSKAIA