Mathematical Foundations of Data Analysis (MGDA)
Working Group
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Head of the working group MGDA
Prof. Dr. Anastasios Stefanou
Assistant Professor (W1) in the Institute for Algebra, Geometry, Topology and Applications of Math Dept. at Uni-Bremen.
Office: MZH 7190
Email: stefanou (at) uni-bremen (dot) de
Research: Topological data analysis (TDA) provides a rigorous mathematical foundation of data analysis which uses techniques from algebra, geometry and topology to study the shape of data. In my working group (MGDA) we focus primarily on developing the foundations of multiparameter persistence module theory in TDA using techniques from computational commutative algebra and homological algebra, e.g. multigraded modules, interleaving distance, minimal presentations, Groebner bases, interleaving-stable invariants, multiparameter persistent homology and cohomology theory, etc. I am also interested in applying tools of TDA to dynamic spaces, Reeb graphs, phylogenetic networks, and other settings (e.g. MALDI imaging). See below for the publications.
Links: My Google Scholar Profile ALTA institute Dioscuri Centre in TDA Applied Topology (AATRN) Youtube channel
PhD students
Fritz Grimpen
Email: grimpen (at) uni-bremen (dot) de
Personal webpage: https://user.math.uni-bremen.de/~grimpen/
Iason Papadopoulos
Email: iason (at) uni-bremen (dot) de
Personal webpage: https://sites.google.com/view/iasonpapadopoulos/startseite
Publications
Peer-Reviewed Publications indexed by MathSciNet
[9] F. Grimpen, A. Stefanou, On minimal flat-injective presentations over local graded rings, Communications in Algebra, (2025).
[8] P. Dlotko, J. F. Senge, A. Stefanou, Combinatorial Topological Models for Phylogenetic Networks and the Mergegram Invariant, Foundations of Data Science, AIMS, (2024).
[7] F. Mémoli, A. Stefanou, L. Zhou, Persistent Cup Product Structures and Related Invariants, Journal of Applied and Computational Topology, (2023).
[6] W. Kim, F. Mémoli, A. Stefanou, Interleaving by Parts: Join Decompositions of Interleavings and Join-Assemblage of Geodesics, Order (2023).
[5] M. Contessoto, F. Mémoli, A. Stefanou, L. Zhou, Persistent Cup-Length, 38th International Symposium on Computational Geometry (SoCG 2022), 31:1--31:17, Leibniz International Proceedings in Informatics (LIPIcs) (2022).
[4] F. Belchi-Guillamon, A. Stefanou, A-infinity persistence estimates the topology from pointclouds, Discrete and Computational Geometry (2021).
[3] A. Stefanou, Tree decomposition of Reeb graphs, parametrized complexity, and applications to phylogenetics, Journal of Applied and Computational Topology, (2020).
[2] E. Munch, A. Stefanou, The L-infinity-cophenetic metric for phylogenetic trees as an interleaving metric, Research in Data Science, 109-127, AWMS, Springer, (2019).
[1] V. de Silva, E. Munch, A. Stefanou, Theory of interleavings on categories with a flow, Theory and Applications of Categories, 33(21): 583-607, (2018).
Peer-Reviewed Publications not indexed by MathSciNet
[4] G. Klaila, V. Vutov, A. Stefanou, Supervised topological data analysis for MALDI imaging applications, BMC Informatics (2023).
[3] F. Grimpen, A. Stefanou, Persistence of complements of spanning trees, Young Researchers Forum, Proceedings of the 39th International Symposium on Computational Geometry, (2023).
[2] A. Stefanou, Dynamics on Categories and Applications (Thesis), ProQuest Dissertations Publishing, State University of New York at Albany, (2018).
[1] V. de Silva, E. Munch, A. Stefanou, A Hom-tree lower bound for the Reeb graph interleaving distance, Young Researchers Forum, Proceedings of the 31st International Symposium on Computational Geometry, (2015).
Arxiv Preprints
[2] F. Grimpen, A. Stefanou, Cofiltrations of spanning trees in multiparameter persistent homology, Arxiv, (2023).
[1] G. Klaila, A. Stefanou, L. Ranke, Stability of the persistence transformation (2023).
Teaching
Summer semester 2025
B.Sc. Course: Mathematics 2: Analysis (Vorlesung)
M.Sc. Course: Commutative Algebra (Vorlesung und Übung)
Winter semester 2024-2025
M.Sc. Seminar: Advanced Topics in Algebra/Number Theory (2 Sessions)
Summer semester 2024
B.Sc. Course: Introduction to Discrete Structures (Vorlesung und Plenum)
Winter semester 2023-2024
Proseminar: 33 Miniatures of Linear Algebra
Summer semester 2023
B.Sc. Course: Mathematics 2: Analysis (Vorlesung)
Winter semester 2022-2023
M.Sc. Course: Commutative Algebra (Vorlesung und Übung)
Summer semester 2022
(Pro-)Seminar: Computational Algebra
M.Sc. Course: Applied Algebraic Topology (Vorlesung und Übung)
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