The *South Wales Analysis and Probability Seminar (SWAP)* is a regional seminar bringing together mathematicians based in South Wales, with interests in analysis, probability, PDEs, SDEs, dynamical systems, and other related fields.

The next meeting is scheduled for **13 December 2019** at **Cardiff University**.

9:30-10:00 | Coffee & Registration | |

10:00-10:45 | Frank Rösler (Cardiff) |
TBA |

10:45-11:30 | TBA TBA (Swansea) |
TBA |

11:30-11:50 | Coffee | |

11:50-12:35 | TBA TBA (Cardiff) |
TBA |

12:35-14:05 | Lunch | |

Colloquium: |
||

14:10-15:00 | Xavier Ros-Oton (Zürich) |
Generic regularity in free boundary problems |

15:00-15:30 | Coffee | |

15:30-16:15 | TBA TBA (Swansea) |
TBA |

Frank** Rösler** (Cardiff) - TBA

TBA

TBA** TBA **(Swansea) - TBA

TBA

TBA **TBA** (Cardiff) - TBA

TBA

Xavier **Ros-Oton** (Zürich) - Generic regularity in free boundary problems

Free boundary problems are those described by PDE's that exhibit a priori unknown (free) interfaces or boundaries. They appear in Geometry, Physics, Probability, Biology, or Finance, and their study uses tools from PDE, Geometric Measure Theory, and Calculus of Variations. The goal of this talk is to present different free boundary problems, explain the main known results in this context, and give an overview of the current research and open problems. In particular, we will discuss a long-standing open question in the field which concerns the generic regularity of free boundaries, and present some new results in this direction.

TBA **TBA** (Swansea) - TBA

TBA

Jonathan Ben-Artzi (Cardiff)

Dmitri Finkelshtein (Swansea)