This workshop will focus on recent advances in moduli theory and algebraic cycles, with a particular emphasis on Hodge-theoretic aspects and new connections between these two subjects.
One such point of contact is the representation theory of the Mumford-Tate group, which gives a powerful toolbox for classifying variations and degenerations of Hodge structure, and its interplay with recent activity on compactications of moduli stemming from geometric invariant theory, the minimal model program, and mirror symmetry. The normal functions arising from cycles and the interesting loci in moduli supporting them, as well as the Hodge Conjecture, provide further sources of interactions between the two subjects.
The talks on moduli will additionally explore Torelli-type results, hyperkähler manifolds, and conformal block bundles over moduli spaces of curves; while on the cycles side we expect to feature normal functions, enriched Hodge structures, and applications of the Beilinson regulator to Mahler measure and Feynman integrals.
Please note that the workshop will be held at the Pavillon J.-Armand-Bombardier at the Université de Montréal.
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