Richard Hain

Richard Hain is Professor Emeritus of Mathematics at Duke University, Department of Mathematics. His research focuses on the topology of complex algebraic varieties, Hodge theory, and moduli of curves. He is a topologist interested in the interaction between the topology, geometry, and arithmetic of varieties defined over subfields of the complex numbers, particularly those over number fields. His work includes the study of fundamental groups of algebraic varieties, moduli spaces, and enriched structures such as Hodge structures and Galois actions. Hain's research also involves polylogarithms, mixed zeta values, and their elliptic generalizations. He has organized several conferences and contributed to various research initiatives at Duke and internationally.

Richard Hain is a mathematician specializing in algebraic geometry, topology, arithmetic geometry, and Hodge theory. His research explores the interplay between these fields, particularly through the study of moduli spaces, mapping class groups, and variations of Hodge structures. He has contributed significantly to the understanding of Torelli groups, normal functions, and the geometry of moduli spaces of curves and abelian varieties. His work also includes the development of de Rham homotopy theory and the study of universal mixed elliptic motives. Hain's publications often focus on the cohomology of algebraic varieties, regulators, and characteristic classes of flat bundles, reflecting his deep engagement with both algebraic and topological methods in modern geometry.