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UID:node-3068199@mathematics.huji.ac.il
DTSTAMP:20211209T080000Z
DTSTART:20211209T080000Z
DTEND:20211209T090000Z
SUMMARY:Groups & DynamicsT seminar: Ilya Khayutin (Northwestern) - The Mixing Conjecture under GRH
DESCRIPTION:*Abstract:* Let X be a complex modular curve or a Shimura curve. The Galois \norbit of a Heegner point x in X is related by the theory of complex \nmultiplication to an orbit of a Picard group of a quadratic order. A special \npoint on the Cartesian product X x X is a tuple of Heegner points (x,y). If x \nand y are associated to the same quadratic order, then the Galois orbit of \n(x,y) in X x X is also an orbit of the Picard group, acting diagonally. \nMichel and Venkatesh have conjectured that a sequence of Galois orbits of \nsuch pairs becomes equidistributed in X x X with respect to the product of \nthe hyperbolic measures, unless an obvious obstruction occurs. I have \npreviously established this conjecture for sequences of Galois orbits with \ndiscriminants satisfying a congruence condition modulo two distinct primes, \nunder the assumption of no Siegel zeros. There is also an analogous \nconjecture arising from definite inner forms of PGL2 about the \nequidistribution of diagonal orbits of Picard groups on latti...
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