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