At the heart of our work is the development of innovative models and algorithms.
These are born from rigorous study, thorough research, and ongoing testing, ensuring we stay aligned with real-world needs. Every achievement paves the way for new insights, bringing us closer to our goal: driving our clients’ business success with original, sustainable solutions
PhD Researchers
Published Papers
Years of Combined Experience
Subject: Topological Data Analysis & Network Analysis
Description: Extends persistent homology theory to analyze simple graphs, digraphs, and quivers with full computational robustness. Introduces categorical persistence functions to study connectedness properties (clique communities, k-vertex and k-edge connectedness) directly on network structures, thereby going beyond the limitations of traditional simplicial complexes.
Subject: Computational Topology & Graph Analysis
Description: Introduces standardized methods (steady and ranging sets) for producing persistence diagrams directly from graph-theoretical features without relying on simplicial complexes. Proposes indexing-aware persistence functions, provides sufficient conditions for stability, and applies these constructions to toy examples and real-world applications in graph analysis.
Subject: Category Theory & Topological Data Analysis
Description: Unifies topological and combinatorial persistence in a common categorical framework by defining generalized rank functions on objects in target categories. Ports interleaving and bottleneck distances to this novel framework, defines colorable ranks and persistence diagrams, and proves fundamental equalities and inequalities between multicolored bottleneck and interleaving distances in semisimple Abelian categories.
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