Sobre o Evento
Since the works of Shannon and Nyquist, one of the main problems in the theory of Signal Processing has been that of recovering a signal from the minimal possible amount of information. Throughout the 20th century, many different approaches have been used in order to best solve this problem, among which we highlight the creation of Wavelet theory, which has been further refined and improved in recent years by its combination with Compressed Sensing and other stochastic methods. In particular, a fundamental question which arises based on the Wavelet analysis approach is: how well does Wavelet localization to a given set actually capture information of a fixed signal? That is, how much can a signal be concentrated on a given time-frequency domain? In this talk, we shall explore the rich history of the mathematical framework behind Signal Processing in general, arriving at the theory of time-frequency localization operators as a means to solve the question mentioned above. We will discuss classical and modern results and their relationship to other areas of pure and applied mathematics, with a view towards open questions and future directions.
Texto informado pelo autor.
* Os participantes dos seminários não poderão acessar às dependências da FGV usando bermuda, chinelos, blusa modelo top ou cropped, minissaia ou camiseta regata. O uso da máscara é facultativo, porém é obrigatória a apresentação do comprovante de vacinação (físico ou digital).
Apoiadores / Parceiros / Patrocinadores
Palestrantes
João Pedro Ramos
I am currently a postdoctoral researcher at EPFL under supervision of Prof. Maryna Viazovska. Previously, I was a postdoctoral researcher under supervision of Prof. Alessio Figalli for 3 years at ETH Zürich. I received my Ph.D. from the University of Bonn on January 30th, 2020, under supervision of Prof. Christoph Thiele. The title of my thesis was Pointwise convergence, maximal functions and regularity issues in harmonic analysis. Before that, I had earned my Master's degree from IMPA on February 29th, 2016, under the supervision of Prof. Claudio Landim, and my bachelor degree from the Federal University of Rio de Janeiro (UFRJ), on March 31st, 2016. My final project in these last two was Time-frequency analysis and Carleson's theorem: a student's point of view, an elaboration on the celebrated Proof of boundedness of the Carleson Operator, by M. Lacey and C. Thiele. Currently, my research interests lie on Analysis, Partial Differential Equations and affine fields. More specifically, I am interested in several topics within these areas, such as: - Fourier uncertainty principles and interpolation formulae; - Existence, uniqueness and unique continuation of PDE;- Stability estimates for geometric inequalities; - Time-frequency analysis and signal processing.
Local
Endereço
a) Opção presencial *
Praia de Botafogo, 190
5o andar, Auditório 537
b) Opção remota (via Zoom)
Link: ID: 95348442773
Informações adicionais:
Tel: 55 21 3799-5917