Recent advances in Hodge theory: period domains, algebraic cycles, and arithmetic

CONFERENCE OVERVIEW AND LAYOUT

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 arises in part from the non-algebraicity of these integrals. According to the beautiful conjectures of Hodge, Bloch and Beilinson, what algebraic structure they have should be explained by (generalized) algebraic cycles. There has been much recent progress on these conjectures and on classifying spaces for periods, as well as their asymptotic and arithmetic; this conference will bring together leading scholars and students of these topics.

Given that our desire is to create a number of new collaborations, we would aim at a small number of high-quality talks per day with ample breaks between each. In addition to bringing together leading scholars on the different aspects of the asymptotic, symmetries, and arithmetic of periods together for a research conference, the organizers will also arrange for a prior workshop for graduate students and recent Ph.D.'s on major themes of the conference. We expect this expository part to run approximately 4 days, with lectures by the organizers and some of the invited speakers.