Archimedean Height Pairings for Higher Cycles

Explore the intricacies of archimedean height pairings for higher cycles in this 1-hour 3-minute lecture by Greg Pearlstein from the University of Texas A&M. Delve into the interpretation of archimedean height pairing on ordinary algebraic cycles as an invariant of associated mixed Hodge structures, based on Richard Hain's work. Examine a similar construction for higher cycles in the Bloch complex and learn how families of higher cycles produce admissible variations of mixed Hodge structure. Investigate the asymptotic behavior of the height pairing in cases where the associated variation of mixed Hodge structure is Hodge-Tate. Gain insights into this collaborative research with J. Burgos Gil and S. Goswami, presented at the University of Miami on November 18, 2020.