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Modular forms and higher Chow cycles
[2018 KAIST Math. Colloquium]
Date: 2018-11-08
Speaker : Ramesh Sreekantan (Indian Statistical Institute, Bangalore)
Abstract : Gross and Zagier made a conjecture on the algebraicity of values of certain `higher' Greens functions at special points. Mellit proved a few cases by linking it to the existence of certain higher Chow cycles. Viazovska proved a few cases by linking it to Borcherds lifts of modular forms. We formulate a conjecture linking modular forms and higher Chow cycles which relates the two approaches and also describe a construction of higher Chow cycles which allows us to prove special cases of the Gross-Zagier conjecture as well as provide evidence for our conjecture.
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