From 2 November 2020, the autumn semester 2020 will take place online. Exceptions: Courses that can only be carried out with on-site presence.
Please note the information provided by the lecturers via e-mail.

Will Merry: Catalogue data in Autumn Semester 2019

Name Prof. Dr. Will Merry
FieldMathematics
Address
Professur für Mathematik
ETH Zürich, HG J 56
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telephone+41 44 632 30 16
E-mailmerry@math.ethz.ch
URLhttps://www.merry.io
DepartmentMathematics
RelationshipAssistant Professor

NumberTitleECTSHoursLecturers
401-0000-00LCommunication in Mathematics2 credits1VW. Merry
AbstractDon'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.
ObjectiveKnowing how to present written mathematics in a structured and clear manner.
ContentTopics 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 notesFull lecture notes will be made available on my website:

https://www.merry.io/teaching/
Prerequisites / NoticeThere are no formal mathematical prerequisites.
401-0000-99LCommunication 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 credit1VW. Merry
AbstractDon'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.
ObjectiveKnowing how to present written mathematics in a structured and clear manner.
ContentTopics 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 notesFull lecture notes will be made available on my website:

https://www.merry.io/teaching/
Prerequisites / NoticeThere are no formal mathematical prerequisites.
401-3371-00LDynamical Systems I10 credits4V + 1UW. Merry
AbstractThis course is a broad introduction to dynamical systems. Topic covered include topological dynamics, ergodic theory and low-dimensional dynamics.
ObjectiveMastery of the basic methods and principal themes of some aspects of dynamical systems.
ContentTopics 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])
LiteratureThe 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 / NoticeThe 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.
401-4530-69LGauge Theory Restricted registration - show details 4 credits2SW. Merry
Abstract
ObjectiveThe 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.
ContentWhat 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 notesLecture notes will be written by the participants!
LiteratureAn 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