Abstract

One of the most interesting questions in fluid theory is to describe the emergence of non- smooth waves and the mechanism responsible for the breakdown of regularity. In the last decades several models were proposed of non-smooth waves with integrable structure, the best known of which are Camassa-Holm and Degasperis-Processi equations. These equations possess stable non-smooth solutions, called peakons which, to a large extent, determine the essential properties of solutions, in particular the breakdown of regularity and the onset of shocks (DP).

Dr. Sergio Medina Peralta will begin with a partial differential equation, due to the interest of this topic in the department and will make the connection with approximation theory, which is principal field of his research activity. Hence, we will begin a trip from these peakons solutions of the Degasperis-Processi equations to the Hermite-Pad ģe approximants. We will focus our attention in this last object, but we will visit other places such as inverse string problems, multiple orthogonal polynomials, Cauchy biorthogonal polynomials, random matrices models and Riemann-Hilbert problems.

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https://fiu.zoom.us/j/93170907458?pwd=V2JscUJQU0gyQ3lMU2pEZmhMTStLQT09

Meeting ID: 931 7090 7458

Passcode: FIU2021