Name | Prof. Dr. Vincent Tassion |

Field | Mathematics |

Address | Professur für Mathematik ETH Zürich, HG G 36.2 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 87 93 |

vincent.tassion@math.ethz.ch | |

URL | http://www.math.ethz.ch/~vtassion |

Department | Mathematics |

Relationship | Associate Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-4597-67L | Probability on Transitive Graphs | 4 credits | 2V | V. Tassion | |

Abstract | In this course, we will present modern topics at the interface between probability and geometric group theory. We will define two random processes on Cayley graphs: the simple random walk and percolation, and discuss their respective behaviors depending on the geometric properties of the underlying group. | ||||

Learning objective | Present in an original framework important tools in the study of - random walks: spectral gap, harmonic functions, entropy,... - percolation: uniqueness of the infinite cluster, mass-transport principle,... | ||||

Content | In this course, we will present modern topics at the interface between probability and geometric group theory. To every group with a finite generating set, one can associate a graph, called Cayley graph. (For example, the d-dimensional grid is a Cayley graph associated to the group Z^d.) Then, we will define two random processes on Cayley graphs: the simple random walk and percolation, and discuss their respective behaviors depending on the geometric properties of the underlying group. The focus will be on the random processes and their properties, and we will use very few notions of geometric group theory. | ||||

Literature | Probability on trees and network (R. Lyons, Y. Peres) | ||||

Prerequisites / Notice | - Probability Theory - No prerequisite on group theory, all the background will be introduced in class. | ||||

401-4600-67L | Student Seminar in Probability Limited number of participants. Registration to the seminar will only be effective once confirmed by email from the organizers. | 4 credits | 2S | A.‑S. Sznitman, J. Bertoin, V. Tassion, W. Werner | |

Abstract | |||||

Learning objective | |||||

Content | The seminar is centered around a topic in probability theory which changes each semester. | ||||

Prerequisites / Notice | The student seminar in probability is held at times at the undergraduate level (typically during the spring term) and at times at the graduate level (typically during the autumn term). The themes vary each semester. The number of participants to the seminar is limited. Registration to the seminar will only be effective once confirmed by email from the organizers. | ||||

401-5600-00L | Seminar on Stochastic Processes | 0 credits | 1K | J. Bertoin, A. Nikeghbali, B. D. Schlein, A.‑S. Sznitman, V. Tassion, W. Werner | |

Abstract | Research colloquium | ||||

Learning objective |