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Explore the fundamental concepts of normal functions and their infinitesimal invariants as essential Hodge theoretic invariants in this 55-minute conference lecture. Delve into the mathematical framework surrounding pairs (X,Z) where X represents a smooth projective variety and Z denotes an algebraic subvariety or algebraic cycle within X. Examine both the structural aspects and practical applications of normal functions through detailed exposition, with particular emphasis on understanding the singularity structure and identifying current open problems in the field. Gain insights into advanced topics in algebraic geometry and Hodge theory as presented at the New Developments in Singularity Theory conference, where leading mathematicians discuss cutting-edge research and theoretical developments in this specialized area of mathematics.
