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SUMMARY:Alexander Smith (Northwestern University)
DTSTART:20260129T171500Z
DTEND:20260129T183000Z
DTSTAMP:20260423T021928Z
UID:NEDNT/99
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/99/">D
 iophantine approximation for hypersurfaces</a>\nby Alexander Smith (Northw
 estern University) as part of New England Dynamics and Number Theory Semin
 ar\n\nLecture held in Online.\n\nAbstract\nAmong the nondegenerate C^4 hyp
 ersurfaces\, we characterize the rational quadrics as the hypersurfaces th
 at are the least well approximated by rational points. For all other hyper
 surfaces\, we give a heuristically sharp lower bound for the number of rat
 ional points near them\, improving the sensitivity of prior results of Ber
 esnevich and Huang. Our methods are dynamical\, involving the application 
 of Ratner’s theorems for unipotent orbits\, and we will show how our wor
 k relates to the dynamical resolution of the Oppenheim conjecture by Margu
 lis.\n
LOCATION:https://researchseminars.org/talk/NEDNT/99/
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