Margherita Maria Ferrari’s research applies combinatorial and topological methods to analyze complex biomolecular processes, focusing on DNA self-assembly and DNA:RNA interactions. She develops mathematical models and graph-theoretical approaches—using graph invariants, edge-colorings, and decompositions—to optimize the design of DNA nanostructures from branched junctions. Her work also utilizes formal stochastic grammars and directed graphs to predict R-loop formations and investigate RNA-mediated DNA repair mechanisms. Furthermore, she employs graph algorithms for analyzing RNA secondary structures, building upon her expertise in discrete mathematics and graph theory.