A Split Version of the Mixing Conjecture and Applications

Explore a mathematical lecture examining the split version of the mixing conjecture and its applications in number theory. Delve into the conjecture originally proposed by Venkatesh and Michel two decades ago, which postulates that pairs of CM-points that are multiplicatively connected equidistribute on products of locally homogeneous spaces associated to forms of PGL₂. Learn about Khayutin's establishment of the conjecture for sequences of fundamental discriminants splitting two given primes, achieved through measure classification results of Einsiedler-Lindenstrauss under the assumption of no Landau-Siegel zero. Discover the ongoing efforts by Blomer, Brumley, and Radziwill to remove splitting conditions and weaken the Landau-Siegel zero assumption using purely analytic number theory methods. Focus on the split version concerning the distribution of multiplicatively paired Hecke points of large modulus, which has been unconditionally established by Blomer and Michel for the prime modulus case and by Assing in general. Examine the proof techniques for the split version of the mixing conjecture and explore recent applications of these methods to the generation of Hecke fields by algebraic L-values, based on joint work with Blomer, Burungale, and Min. Gain insights into advanced topics in algebraic number theory, automorphic forms, and equidistribution theory from this 59-minute presentation by Philippe Michel from EPFL at the Institut des Hautes Etudes Scientifiques.