Joint PU/IAS Number Theory

We prove an effective equidistribution theorem for semisimple
closed orbits on compact adelic quotients. The obtained error depends
polynomially on the minimal complexity of intermediate orbits and the
complexity of the ambient space. As an application, we establish a
local-global principle for representations of quadratic forms, improving
the codimension assumptions and providing effective bounds in a theorem
of Ellenberg and Venkatesh. This is joint work with Manfred Einsiedler,
Elon Lindenstrauss, and Amir Mohammadi.