Analysis and PDE seminar

Monday 13th Nov, 2023, 4 pm - 5 pm

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Venue: Ramanujan Hall

Host: Chandan Biswas

Speaker: Senthil Raani

Affiliation: IISER Berhampur

Title: Distance Set Problems

Abstract: The distance set ∆(E) of a set E in Euclidean space consists of all non-negative numbers that represent distances between pairs of points in E. How does the structure of E impact that of ∆(E)? Questions of this nature play a fundamental role in geometric measure theory. We will begin with a brief history of results and conjectures on ∆(E). Apart from measure theoretic techniques, the asymptotic of the Fourier transform of measures supported on E plays a vital role in this study. Our main goal in this talk is to discuss a few properties of ∆(E) when E is sparse but has a large Hausdorff dimension. This is based on recent joint work with Prof. Malabika Pramanik.