Recent developments in orbit counting methods
Robert Hough (Stony Brook)
Abstract: Bhargava pioneered methods from the geometry of numbers to count integral orbits in representation spaces ordered by invariants. I will discuss recent analytic techniques in development to strengthen the methods, including spectral expansion of the underlying homogeneous spaces, classification of local orbits and their finite Fourier transforms, and subconvex estimates for the enumerating zeta functions. In particular, we have obtained a strong answer to a question of Bhargava and Gross at a conference at the American Institute of Math explaining a barrier to equidistribution in the shape of cubic fields by obtaining poles and residues in the zeta function enumerating the Weyl sums in the Eisenstein spectrum. Joint work with Eun Hye Lee.
number theory
Audience: researchers in the topic
| Organizers: | Chi-Yun Hsu*, Brian Lawrence* |
| *contact for this listing |