Manfred Einsiedler: Effective Equidistribution of semisimple adelic periods (NTWS 226)

Abstract: We will discuss an effective equidistribution theorem for semisimple closed orbits on compact adelic quotients, obtained in ongoing joint work with E. Lindenstrauss, A. Mohammadi, and A. Wieser. The obtained error depends polynomially on the minimal complexity of intermediate orbits and the complexity of the ambient space. The proof uses dynamical arguments, Clozel's property (tau), Prasad's volume formula, an effective closing lemma, and a novel effective generation result for subgroups. The latter in turn relies on an effective version of Greenberg's theorem.
We apply the above to the problem of establishing a local-global principle for representations of quadratic forms, improving the codimension assumptions and providing effective bounds in a theorem of Ellenberg and Venkatesh.
Link to slides: drive.google.c...
Number Theory Web Seminar: www.ntwebsemin...
Original air date:
Thursday, October 31, 2024 (9am PDT, 12pm EDT, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, November 1, 2024 (12am CST, 3am AEDT, 5am NZDT)