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This summer school series aims at training their participants in key strategic problems in mathematics and their applications, with the core idea that theory and applications strengthen each other. The school is focused in training of young researchers whilst opening new fields for senior ones.

The Hypatia Graduate Summer School will consist in two keynote courses on subjects of exceptional promise and scientific importance delivered by highly distinguished speakers in the area plus a high-level colloquium on a complementary subject.

The Hypatia Graduate Summer School will be developed in an informal atmosphere based on discussions, exchange of ideas and critical analysis of results. Moreover, to honour its namesake, it is committed to work under a friendly gender perspective that highlights the role of women in mathematics and encourages and helps the participation and promotion of young female researchers at a professional level.

Registration deadline 21 / 05 / 2023

COURSE 1: Contact geometry and the many facets of complexity of hydrodynamics

Lecturer: Eva Miranda (UPC-CRM) / Daniel Peralta (ICMAT)

Abstract: In this course we will unveil various connections between three seemingly unconnected topics: contact geometry, fluid mechanics, and Turing machines.

The point of departure will be Euler’s equations with a focus on the study of stationary solutions. Our constructions combine techniques from various areas of mathematics that we will thoroughly analyze in this course. An important ingredient will be the close inspection of various notions of complexity of our constructions: dynamic, computational and logical. Several applications to Celestial mechanics will also be discussed.

COURSE 2: Symbolic Dynamics in Celestial Mechanics

Lecturer: Susanna Terracini (Dipartimento di Matematica “Giuseppe Peano”)

Abstract: it is part of the mathematical folklore that Dynamical Systems featuring many nonlinear interactions should display chaotic behavior and possess complex dynamics, whatever this means.

On the other hand, for natural systems, this lacks a rigorous statement and even more, a rigorous proof, specially when we are leaving the perturbative setting.

The purpose of the minicourse is to illustrate how to contstruct complex trajectories by the use of global variational methods in some relevant models from Celestial Mechanics.