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SUMMARY:Robert Hough (Stony Brook)
DTSTART:20211004T220000Z
DTEND:20211004T225000Z
DTSTAMP:20260423T041409Z
UID:UCLA_NTS/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCLA_NTS/32/
 ">Recent developments in orbit counting methods</a>\nby Robert Hough (Ston
 y Brook) as part of UCLA Number Theory Seminar\n\n\nAbstract\nBhargava pio
 neered methods from the geometry of numbers to count integral orbits in re
 presentation 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 o
 rbits and their finite Fourier transforms\, and subconvex estimates for th
 e enumerating zeta functions.  In particular\, we have obtained a strong a
 nswer 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 enumera
 ting the Weyl sums in the Eisenstein spectrum.  Joint work with Eun Hye Le
 e.\n
LOCATION:https://researchseminars.org/talk/UCLA_NTS/32/
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