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Learn about combinatorial theory related to evolutionary phylogenetic trees and networks in this 55-minute academic lecture from the 17th MACS Colloquium at Kyoto University. Dr. Momoko Hayamizu, Assistant Professor at Waseda University's Faculty of Science and Engineering, presents a comprehensive exploration of phylogenetic analysis, beginning with fundamental background knowledge of phylogenetic trees and networks. Progress through mathematical terminology and notation specific to phylogenetic studies, examine important considerations when estimating phylogenetic trees from networks, and discover structural theorems of rooted binary phylogenetic networks and their applications. The lecture, delivered online via Zoom on November 19, 2021, provides both theoretical foundations and practical insights into this specialized field of mathematical biology.