Krzysztof Frączek: Applications of smooth curves in the moduli space of translation surfaces

Abstract: I plan to review problems and recent results regarding smooth curves in the moduli space of translation surfaces and Teichmüller positive semi-orbits starting from such curves. The main part of the talk is applications that motivate abstract results. Two main applications relate to billiards on nibbled ellipses and Hamiltonian systems with reflections.