Charles Doran's research focuses on variations of Hodge structure and their applications to families of algebraic varieties, including elliptic curves, K3 surfaces, and Calabi–Yau threefolds. He computes Hodge numbers using Picard–Fuchs equations, exploring the connections between these equations and the underlying geometry of the varieties. A significant part of his work involves studying the monodromy of these families and its implications for the Hodge structures.
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This work connects to string theory, particularly through the study of Calabi–Yau manifolds, central to compactification schemes in string theory. His research includes the exploration of normal functions, related to the algebraic cycles on Calabi–Yau threefolds. These normal functions have interpretations in terms of D-branes, objects in string theory that generalize the notion of a point particle to higher-dimensional surfaces.

His studies on mirror symmetry, a duality between pairs of Calabi–Yau manifolds, further enhance the understanding of string theory. Mirror symmetry not only relates the Hodge numbers of dual Calabi–Yau manifolds but also connects complex geometry with symplectic geometry, revealing deep mathematical structures in theoretical physics.

Partially generated by ChuckGPT, a custom GPT trained on my papers.  
​Charles Doran
Professor of Mathematics, University of Alberta 
Distinguished Visiting Professor of Mathematics and Physics, Bard College 
Associate Member, Center of Mathematical Sciences and Applications, Harvard University