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In many data-driven applications, the data follows some
geometric structure, and the goal is to recover this structure. In many
cases, the observed data is noisy and the recovery task is even more
challenging. A common assumption is that the data lies on a low-dimensional manifold.

Estimating a manifold from noisy samples has proven
to be a challenging task. Indeed, even after decades of research, there
was no (computationally tractable) algorithm that accurately estimates a
manifold from noisy samples with a constant level of noise.
In this talk, we will present a method that estimates a manifold and its
tangent. Moreover, we establish convergence rates, which are essentially
as good as existing convergence rates for function estimation.