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Summer Term 2024, Doctoral School Events
2024-03-22 Doctoral School Seminar (13:30–16:00, Univ. Graz, Heinrichstr. 36, HS 11.02)
Florian Russold (TU Graz, advisor M. Kerber): Convergence of Leray Cosheaves for Decorated Mapper Graphs [show abstract]
New Students (TU/KFU): V. Havlovec, J. Jendrysiak, T. Kldiashvili, E. Morina, E. Stefanescu, N. Weber
Alexander Pfleger (Univ. Graz, advisor G. Haase): Track Reconstruction of High Energy Particles with a Global χ² Fitter [show abstract]
Rodolfo Assereto (Univ. Graz, advisor K. Bredies): An Optimal Transport-based approach to Total-Variation regularization for the Diffusion MRI problem [show abstract]
2024-04-26 Doctoral School Seminar (10:30–13:00, TU Graz, Kopernikusg. 24)
Sabina Kiss (TU Graz, advisor E. Dragoti-Cela): Adjustable Robust Optimisation for Transport Planning with Uncertain Demands [show abstract]
Sergio Fernandez de Soto Guerrero (TU Graz, advisor C. Ceballos): Triangulations of Flow Polytopes and their Duals via Tropical Geometry [show abstract]
New Students (TU/KFU): M. Hasenbichler, M. Kariman
Jakob Führer (TU Graz, advisor C. Elsholtz): Line-free sets in Fpn [show abstract]
2024-05-17 Doctoral School Seminar (13:30–16:00, Univ. Graz, Heinrichstr. 36, HS 11.02)
Mara Pompili (Univ. Graz, advisor D. Smertnig): When upper cluster algebras are UFD? [show abstract]
Nesibe Ayhan (Univ. Graz, advisor Q. B. Tang): symptotic Smoothing and Pullback Attractor for the Korteweg-de Vries-Burgers Equation [show abstract]
Bruno Viti (Univ. Graz, advisor E. Karabelas): Gaussian Processes for Few-Shot Segmentation in Cardiac MRI [show abstract]
Lukas Richter (TU Graz, advisor E. Stadlober): Statistical modelling in public health: SARS-CoV-2 - Analysis of Epidemiological Parameters [show abstract]
2024-06-21 Doctoral School Seminar (10:30–13:00, TU Graz, Kopernikusg. 24)
Juan Yang (Univ. Graz, advisor Q. B. Tang): Analysis of mass-controlled reaction-diffusion systems with nonlinearities having critical growth rates

Abstract: We analyze semilinear reaction–diffusion systems that are mass controlled, and have nonlinearities that satisfy critical growth rates. The systems under consideration are only assumed to satisfy natural assumptions, namely the preservation of non-negativity and a control of the total mass. It is proved in dimension one that if nonlinearities have (slightly super-) cubic growth rates then the system has a unique global classical solutions. Moreover, in the case of mass dissipation, the solution is bounded uniformly in time in sup-norm.

Francesco Mantegazza (Univ. Graz, advisor G. Haase): Taming the Computational Burden: PBDW for Efficient State Estimation

Abstract: State estimation is crucial for data assimilation but can be computationally demanding. Conventional approaches employ variational formulations, at high computational cost. To address this issue, reduced-order models have been introduced, replacing the full-order model. The state estimation can be also cast as an optimal recovery approach. In this context, the Parametrized Background Data-Weak method offers a promising strategy. It enables state estimation without parameter estimation, circumventing the complexity of nonlinear inverse problems. We explore applications to the reconstruction time-dependent problems, incorporating artificial sensor measurements and sensor selection algorithms to enhance performance.

Matthias Söls (TU Graz, advisor M. Kerber): A zoo of simplicial bifiltrations: From 1-critical to ∞-critical (and back)

Abstract: Given a data set X, the standard pipeline of topological data analysis involves the construction of a commutative diagram of simplicial complexes F(X) as an intermediate step. A simplicial bifiltration is a diagram F(X) indexed by a product of two totally ordered sets. A further classification is then made depending on the number of generators of each simplex, classifying F(X) to be either k-critical for or ∞-critical. We will construct examples of bifiltrations and sketch a way to reduce k-critical bifiltrations to the 1-critical case.

Ángel Alonso (TU Graz, advisor M. Kerber): Delaunay Bifiltrations of Functions on Point Clouds

Abstract: The Delaunay filtration D(X) of a point cloud X is a central tool of computational topology. Its use is justified by the topological equivalence of D(X) and the offset (i.e., union-of-balls) filtration of X. Given a function γ:X→R, we introduce a Delaunay bifiltration DC(γ) that satisfies an analogous topological equivalence and is of small size, ensuring that DC(γ) topologically encodes the offset filtrations of all sublevel sets of γ, as well as the topological relations between them