Dynamics, geometry and Number Theory Seminar
Thursday, July 20, 4 pm
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Venue: Ramanujan Hall
Host: Ravi Raghunathan
Speaker: Shreyasi Datta
Title: Quantitative Simultaneous Approximation (Seminar talk)
Abstract: One of the most fascinating problems in number theory is to study rationals that are close to a specific curve, more generally, close to a manifold. Showing that given a nice
decaying function, the points on any 'curved' manifold approximated at this function's rate are 'pnegligible' was a long-standing problem. In recent ground-breaking work (arXiv:2105.13872), Beresnevich and Yang solved this problem.
In this talk, we will explain an effective version of their result. This is based on the work https://arxiv.org/abs/2209.14196.