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# Gennady Uraltsev

H.C. Wang Assistant Professor

### Keywords

### Departments/Programs

- Mathematics

## Research

My main research interest lies in the area of Real Harmonic Analysis and particularly in what is often referred to as time-frequency analysis. I study boundedness properties of operators with large classes of symmetries such as translations, scaling, and modulations, where classical techniques like Calderón-Zygmund theory, wavelet analysis, Gabor frames alone fail to encode the relevant properties.

Time-frequency analysis arises in the study of operators like the Carleson Operator and the Bilinear Hilbert Transform. The developed techniques and the boundedness properties of these operators have surprisingly close relations to Ergodic Theory, Additive Combinatorics, but also to the study of dispersive PDEs and SDEs.

## Courses

## Publications

- Variational Carleson embeddings into the upper 3-space. arXiv preprint arXiv:1610.07657 (2016).
- Positive sparse domination of variational Carleson operators (with Francesco Di Plinio and Yen Q. Do), to appear in Annali della Scuola Normale Superiore di Pisa - Classe di Scienze.
- On the distributional Hessian of the distance function (with Carlo Mantegazza and Giovanni Mascellani), Pacific Journal of Mathematics 270.1 (2014): 151-166.