Recent Advances in Hodge Theory: Period Domains, Algebraic Cycles, and Arithmetic

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A summer school and conference on Hodge theory will be held at the University of British Columbia (Vancouver, Canada) from June 10-20, 2013. This award will support 30 US participants at various stages of their careers. The 24 invited speakers are leading experts in aspects of complex and arithmetic geometry, algebraic cycles, and representation theory, which are in the early stages of a synthesis around the study of period mappings and generalized period domains. The conference will accelerate this process and give graduate students and recent Ph.D.'s an opportunity to enter an emerging discipline.In its simplest form, Hodge theory is the study of periods -- integrals of algebraic differential forms which arise in the study of complex geometry, number theory and physics. Its difficulty and richness arise in part from the non-algebraicity of these integrals. What algebraic structure they do have is recorded by symmetry groups called Mumford-Tate groups, and according to the Hodge conjecture (and its variants) should be explained by the presence of objects called algebraic cycles. The conference will serve to disseminate recent progress on both of these fronts, create new interdisciplinary collaborations, and train the next generation of Hodge theorists.The web site for the conference ishttp://www.pims.math.ca/scientific-event/130610-rahtpdaca