Prof. Dr. em. Peter Gritzmann
Department of Mathematics
School of Computation, Information and Technology
Technische Universität München
Germany
Title: Diagrams, clustering, and coresets – and the representation of polycrystals
Abstract: We report on recent results for anisotropic diagrams and their relation to constrained clustering with a view towards representing and analyzing polycrystalline materials and their dynamics. In particular, weight-constrained anisotropic clustering allows to compute diagram representations of polycrystals from data on the volume, center and moments of the grains which are available through tomographic measurements. Also we develop new coreset techniques, interesting for their own, which are utilized to significantly accelerate the computations. This effect is demonstrated on 3D real-world data sets.
(The talk is based on recent joint work with A. Alpers, M. Fiedler, F. Klemm.)
Peter Gritzmann received his Ph.D. in 1980, his habilitation in 1984, and held positions as professor at various universities before joining the Dept. of Mathematics of the Technical University of Munich in 1997. Since 2008 he is also courtesy member of the Dept. of Informatics. P.G. was long-term visiting professor at various universities including the University of Washington, Seattle, the Institute for Mathematics and its Applications, University of Minnesota, Minneapolis and Université Paris 7.
P.G’s research focusses on discrete mathematics, applied geometry and optimization. In addition to his academic research he has also been working with industry on problems of predictive analytics, logistics, optimization of airport schedules, consolidation of farmland, etc.
P.G.’s work lead to more than 160 publications and his research was recognized, among others, by a Feodor-Lynen Research Stipend of the Alexander von Humboldt-Foundation, a Max-Planck Research Award, and the Euro Excellence in Practice Award.
P.G. served as President of the German Math. Soc. (2002-2003), Founding President of the Carl von Linde-Academy (2004-2008), Vice President of TU München (2008-2011), Member of the Board of Regents of the University Graz, Austria (2013-2023), Member of the Academic and Scientific Advisory Councils of the African Institute for Mathematical Sciences (since 2015), as Chair of the selection committees for the German Research Chairs in Senegal, Ghana, Cameroon, South Africa, Tanzania, and Rwanda, and as chairman of the advisory board of the Elite Network Bavaria (since 2023).
Prof. Dr. Lajos Hajdu
Institute of Mathematics
University of Debrecen
Hungary
Title: Applications of algebra and number theory in digital image processing
Abstract: In the talk we present applications of algebra and number theory to two problems in digital image processing.
The first application is related to discrete tomography, where the basic problem is to recover a function defined on a finite subset A of \mathbb Z^2 from its line sums measured along a finite set of directions. We sketch an algebraic framework for the problem, which enables us to describe the structure of the ghosts, i.e. functions defined on A having zero line sums in the given directions. We show how this knowledge makes it possible to describe the solutions with integer values, and how it contributes to the description of binary solutions (i.e. of functions having only values 0 and 1).
The second application is motivated by a problem from medical image processing, and is related to detect periodicity on images. We model this problem in the following way: find the grid which fits “best” a given finite set of points in \mathbb R^n. We show how lattice theory (geometry of numbers) come into play, and use tools from Diophantine approximations to handle the problem. We also show how to use the LLL algorithm to construct “well” approximating grids efficiently in concrete cases.
Lajos Hajdu received his Ph.D. in 1998, his habilitation in 2003, the D.Sc. of the Hungarian Academy of Sciences in 2011. He was a postdoc at Leiden University, and a visiting professor at the Alfréd Rényi Mathematical Research Institute. He works at the University of Debrecen from 1996, since 2012 as a full professor, and he recieved the ’Professor of the Count István Tisza Foundation for the University of Debrecen’ title in 2023.
L.H.’s main research areas are number theory and discrete tomography, but he has several papers related to various problems in discrete mathematics, as well. He also worked on problems related to digital image processing and industrial mathematics.
L.H. has more than 150 scientific publications. His achievements were recognized, among others, by the János Bolyai Research Stipend, the Turán Prize and the Academic Prize of the Hungarian Academy of Sciences, and by the Szele Prize of the János Bolyai Mathematical Society.
L.H. is the leader of a HUN-REN research group, and served as Secretary of the Doctoral Committee of the Section of Mathematics of the Hungarian Academy of Sciences (2010-2012), the Head of the Institute of Mathematics, University of Debrecen (2013-2021), Head of the OTKA (NKFIH) Mathematics – Computer Science Jury (2021-2023), Vice President of the Mathematical Committee of the Section of Mathematics of the Hungarian Academy of Sciences (2024-), Member of the Doctoral Committee of the Hungarian Academy of Sciences (2024-), Vice President of the János Bolyai Mathematical Society (2024-).