SwissMAP PhD Meeting 2018

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Program

Monday 4th june

3:30-4:15 pm: Welcome coffee
4:15-6:15 pm: Minicourse: Classical mechanics and integrable systems
6:30-7:30 pm: Minicourse: Classical mechanics and integrable systems

Tuesday 5th june

9-12 am: Minicourse: Classical mechanics and integrable systems
2-4 pm: Invited speaker, Maxime Gagnebin
5-6 pm: Invited speaker: Anthony Conway, Über Verschlingungsinvarianten

Wednesday 6th june

9-12 am: Minicourse: An Introduction to Stochastic Differential Equations and their numerical analysis.
Afternoon: Hike*

Thursday 7th june

9-12 am: Minicourse: An Introduction to Stochastic Differential Equations and their numerical analysis.
2-3:30 pm: Talk, Jeremy Dubout: Spectral theory, applications

*The hike time might change depending on the weather.

Abstracts

An Introduction to Stochastic Differential Equations and their numerical analysis

The goal of this talk is to give an understandable introduction to Stochastic Differential Equations (SDEs). To this aim, we will focus on examples and present the main ideas of some important proofs. We shall first recall basic notions on ODEs and probability, then apply them to define the Brownian motion and the stochastic integral. Finally we will define the SDEs and will study the basics of numerical analysis on SDEs using some examples.

Classical mechanics and integrable systems

In this minicourse, we will introduce integrable systems, with an eye on the famous problem of planetary motion. We will start by reformulating Newton's laws in the Hamiltonian formalism. In this setting, one can define integrable systems and prove an important Arnold-Liouville theorem. A main example will be the Kepler problem, of a planet orbiting a star. Finally, we will look into more advanced topics, such as stability of orbits and appearance of Hopf fibration in two pendulums.

Über Verschlingungsinvarianten

Linking forms occur in the study of odd dimensional manifolds and appear frequently in knot theory. In this talk, we chose to take a more algebraic approach to these objects: after reviewing some definitions and examples, we discuss the classification of linking forms over $\Z$ (following Wall). If time permits, we will also describe some classification results over Laurent polynomial rings.