# Will Merry: Catalogue data in Autumn Semester 2019

Name | Prof. Dr. Will Merry |

Field | Mathematics |

Address | Professur für Mathematik ETH Zürich, HG J 56 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 30 16 |

merry@math.ethz.ch | |

URL | https://www.merry.io |

Department | Mathematics |

Relationship | Assistant Professor |

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

401-0000-00L | Communication in Mathematics | 2 credits | 1V | W. Merry | |

Abstract | Don't hide your Next Great Theorem behind bad writing. This course teaches fundamental communication skills in mathematics: how to write clearly and how to structure mathematical content for different audiences, from theses, to preprints, to personal statements in applications. In addition, the course will help you establish a working knowledge of LaTeX. | ||||

Objective | Knowing how to present written mathematics in a structured and clear manner. | ||||

Content | Topics covered include: - Language conventions and common errors. - How to write a thesis (more generally, a mathematics paper). - How to use LaTeX. - How to write a personal statement for Masters and PhD applications. | ||||

Lecture notes | Full lecture notes will be made available on my website: https://www.merry.io/teaching/ | ||||

Prerequisites / Notice | There are no formal mathematical prerequisites. | ||||

401-0000-99L | Communication in Mathematics (Upgrade 2018 → 2019)This course unit is only for students who got 1 ECTS credit from last year's course unit 401-0000-00L CiM. (Registration now closed.) | 1 credit | 1V | W. Merry | |

Abstract | Don't hide your Next Great Theorem behind bad writing. This course teaches fundamental communication skills in mathematics: how to write clearly and how to structure mathematical content for different audiences, from theses, to preprints, to personal statements in applications. In addition, the course will help you establish a working knowledge of LaTeX. | ||||

Objective | Knowing how to present written mathematics in a structured and clear manner. | ||||

Content | Topics covered include: - Language conventions and common errors. - How to write a thesis (more generally, a mathematics paper). - How to use LaTeX. - How to write a personal statement for Masters and PhD applications. | ||||

Lecture notes | Full lecture notes will be made available on my website: https://www.merry.io/teaching/ | ||||

Prerequisites / Notice | There are no formal mathematical prerequisites. | ||||

401-3371-00L | Dynamical Systems I | 10 credits | 4V + 1U | W. Merry | |

Abstract | This course is a broad introduction to dynamical systems. Topic covered include topological dynamics, ergodic theory and low-dimensional dynamics. | ||||

Objective | Mastery of the basic methods and principal themes of some aspects of dynamical systems. | ||||

Content | Topics covered include: 1. Topological dynamics (transitivity, attractors, chaos, structural stability) 2. Ergodic theory (Poincare recurrence theorem, Birkhoff ergodic theorem, existence of invariant measures) 3. Low-dimensional dynamics (Poincare rotation number, dynamical systems on [0,1]) | ||||

Literature | The most relevant textbook for this course is Introduction to Dynamical Systems, Brin and Stuck, CUP, 2002. I will also produce full lecture notes, available from my website https://www.merry.io/teaching/ | ||||

Prerequisites / Notice | The material of the basic courses of the first two years of the program at ETH is assumed. In particular, you should be familiar with metric spaces and elementary measure theory. | ||||

401-4530-69L | Gauge Theory | 4 credits | 2S | W. Merry | |

Abstract | |||||

Objective | The goal of the seminar is to understand Donaldson’s famous theorem that certain topological 4-manifolds do not admit a smooth structure. The idea is to study the topology of the moduli space of anti-self dual connections. | ||||

Content | What is gauge theory? Very roughly speaking, gauge theory (or Yang-Mills theory) is the study of the space of connections on a principal bundle. A Yang-Mills connection is an extremal of the Yang-Mills functional. These connections are important in both mathematics and physics. The most interesting case occurs when the base manifold is four-dimensional. Here one can also speak of instantons (or anti-self-dual connections). The instanton equations on four-manifolds were first studied in the late 70s. In 1981 as part of his PhD studies Simon Donaldson used these equations to make spectacular progress on (exotic) four-manifold topology. A rough outline of the topics intended to be covered is: 1. The classification of complex line bundles, and the classification of unitary connections (up to gauge equivalence) over them. 2. The Hodge Theorem. 3. Yang-Mills connections. 4. Anti-self dual connections and instantons (in dimension 4). 5. Uhlenbeck Compactness. 6. Donaldson’s Theorem. | ||||

Lecture notes | Lecture notes will be written by the participants! | ||||

Literature | An overview of the literature available will be posted on my forum. | ||||

Prerequisites / Notice | **THIS SEMINAR IS ONLY OPEN TO STUDENTS WHO HAVE PRE-REGISTERED WITH ME ON MY FORUM.** This is an advanced seminar. It is assumed you are familiar with: - Differential Geometry I - Differential Geometry II - Algebraic Topology I In addition it would be helpful if you knew: - Algebraic Topology II - Functional Analysis I |