##### Department of Mathematics,

University of California San Diego

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### Math 278C: Optimization and Data Science

## Prof. Mihai Putinar

#### UCSB

## Analysis of principal semi-algebraic sets

##### Abstract:

Among all nD Euclidean shapes carrying a degree of shade function, only those black and white ones, defined by a single polynomial inequality are determined by finitely many moments. In the single variable situation, a landmark moment transform discovered by A. Markov untangles the above uniqueness feature. The 2D case is not less interesting, touching some spectral inverse problem for pairs of non-commuting self-adjoint transforms. A super-resolution phenomenon will be described in some detail with optimization and asymptotic expansion techniques.

Host: Jiawang Nie

### March 1, 2023

### 3:00 PM

The Zoom Meeting link is

https://urldefense.com/v3/__ht

Meeting ID: 940 3029 8286

Password: 278CWN23

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