Starts 15 Jul 2019
Ends 30 Jul 2019
Central European Time
Week 1: Introductory courses Course 1: Introductory Topology Lecturer: Venuste Nyagahakwa (University of Rwanda) Description: This course will introduce the basic ideas of topology, starting with an abstract definition of topological space, and treating many examples. Course 2: The Fundamental Group Lecturer: Jean-Baptiste Gatsinzi (Botswana Institute of Science and Technology) Description: The fundamental group is a basic but key algebraic invariant of a topological space. This course will define this group and give some interesting examples of how to compute it. Course 3: Introduction to knot theory Lecturer: Balazs Szendroi (University of Oxford) Description: A knot is a tangled piece of rope in the three dimensional space, with the two loose ends glued together. Knot theory asks questions such as: can this knot be untangled by continuously deforming the rope? Are there ways to tell two knots apart? This course will discuss these motivating questions and present some ideas how to solve them. Week 2: Advanced courses Course 3: Manifolds Lecturer: Claudia Scheimbauer (NTNU, Trondheim) Description: Manifolds provide a very interesting class of examples of topological spaces, of great interest in applications to geometry, physics and elsewhere. This course will introduce this notion with many examples, mainly from dimensions 1, 2 and 3. Course 4: Topological Data Analysis Lecturer: Ulrike Tillmann (University of Oxford) Description: Topological data analysis is a recent and fast-growing field providing a set of new topological and geometric tools to infer global features from complex data. This course will give an introduction to this circle of ideas.