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In Summer 2025, Dr. Yang Hu mentored a five-week undergraduate research program titled "zeta functions of graphs", with undergraduate students Mark Benecke, Mason Gardner, and Shokhina Jalilova as participants. The Riemann zeta function is a classical mathematical object which has been generalized in a variety of mathematical contexts, including algebraic geometry, algebraic number theory, and dynamical systems. The main focus of this project is to explore how zeta functions interact with the topological structure of graph coverings. During the five weeks, people studied the history of the classical Riemann zeta function, the definition of the graph-theoretic zeta function, together with the needed background knowledge from algebra (group theory, fields and Galois theory) and topology (point set topology, fundamental groups, and covering spaces). In the final paper, they presented a proof of the determinant formula for the zeta function of graphs, and a divisibility result for (the inverse of) zeta functions of covering graphs.
Dr. Yang Hu
Participants
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| Mark Benecke |
Shokhina Jalilova |
Mason Gardner |
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