Applied and Computational Topology
Members
Group lead
Team assistant
Research group
53 Publikationen
Cycling signatures
Efficient Computation of Image Persistence
Multi-parameter Persistence Modules are Generically Indecomposable
Tight quasi-universality of Reeb graph distances
Parameterized inapproximability of Morse matching
Topological analysis of 3D digital ovules identifies cellular patterns associated with ovule shape diversity
Universal distances for extended persistence
Persistent homology for functionals
Topologically Faithful Multi-class Segmentation in Medical Images
Wrapping Cycles in Delaunay Complexes
On Computing Homological Hitting Sets
Lifespan functors and natural dualities in persistent homology
Efficient Computation of Image Persistence
Efficient Two-Parameter Persistence Computation via Cohomology
Topologically Faithful Image Segmentation via Induced Matching of Persistence Barcodes
Homology of configuration spaces of hard squares in a rectangle
A unified view on the functorial nerve theorem and its variations
Quasi-Universality of Reeb Graph Distances
Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Vietoris-Rips Filtrations
Ripser
The Reeb Graph Edit Distance is Universal
CLDICE – A novel topology-preserving loss function for tubular structure segmentation
Cotorsion torsion triples and the representation theory of filtered hierarchical clustering
Persistence Diagrams as Diagrams
Research
Our research group works in the field of applied and computational topology and geometry. The focus lies on questions regarding the connectivity of data on multiple scales. This is global information, concerning the data as a whole, and inaccessible by standard means of data analysis. Popular methods in this context are persistent homology, Vietoris–Rips complexes, and Delaunay complexes (Alpha shapes).
We consider theoretical questions, such as the stability of persistence barcodes or connections to representation theory, but also computational problems, such as finding the Vietoris–Rips persistence barcode of a set of points. We study the hardness of certain computational problems arising in applied topology, and develop fast code that is widely used in applications.
Our research is supported by DFG (Collaborative Research Center Discretization in Geometry and Dynamics), MCML (Munich Center for Machine Learning), and MDSI (Munich Data Science Institute).
People
Nadja Vadlau
- Room: MA 02.08.052
- Phone: +49 89 289 17984
- Email: vadlau@ma.tum.de
Diane Clayton-Winter (SFB/TR109 Discretization in Geometry & Dynamics)
- Benedikt Fluhr
- David Hien (co-supervised with Oliver Junge)
- Fabian Lenzen
- Fabian Roll
- Nico Stucki
- Maximilian Schmahl (co-supervised with Peter Albers)
- Magnus Botnan
- Abhishek Rathod
- Florian Pausinger
- Erika Roldán
- Persistence and Stability of Geometric Complexes
- Ripser: Efficient Computation of Vietoris-Rips Persistence Barcodes: Ripser is a lean C++ code for the computation of Vietoris–Rips persistence barcodes. It can do just this one thing, but does it extremely well. To see a live demo of Ripser's capabilities, go to live.ripser.org. The computation happens inside the browser (using Emscripten to compile Ripser to WebAssembly, supported on recent browsers).
- Approximation Algorithms and Parametrized Complexity in Computational Topology
- Coarse Cohomological Models for Dynamical Systems: The aim of this project is to develop methods for constructing coarse models of the global behavior of a system with complicated dynamics. These models will abstract from individual trajectories and rather provide dynamical information on a discretization of the underlying invariant set in form of a directed graph or a finite state Markov chain. In contrast to existing approaches, our models will incorporate information about cycling motion, generalizing the classic notion of periodic or quasiperiodic dynamics.
- Topological and Geometric Data Analysis of Random Growth Models
- Derived Persistence Theory for Functions