Topology is a branch of mathematics concerned with properties of objects, which are preserved under continuous deformations, including stretching and bending. In past few years a new field of topological insulators and superconductors has emerged in condensed matter physics, based on the realization that certain properties of these systems can be expressed as topological invariants, which are insensitive to all local perturbations. The purpose of this course is to review the theoretical foundations for topological insulators and superconductors and to describe the recent experiments in which signatures of topological insulators and superconductors have been observed. The lectures start with a description of topological band theory, which will be illustrated with the help of examples. Then the Majorana bound states and Majorana edge states will be considered in the BdG theory of topological superconductors. Finally a classification of topological insulators and superconductors will be presented, and the foundations of this classification will be discussed from different perspectives. The defining signature of topological materials are the topologically protected boundary states. Different ways to understand this topological protection and the influence of these boundary states on the transport properties of these materials are therefore the central topics of this course.

Course leader
Lecturer: Dr. Andreas Schnyder (Max-Planck-Institut fr Festkrperforschung, Germany)Coordinators: Prof. Tero Heikkil (University of Jyvskyl, Finland), and Dr. Timo Hyart (University of Jyvskyl, Finland)

Target group
The Summer School annually offers courses for advanced master's students, graduate students, and post-docs in the various fields of science and information technology.

Course aim
The most important aims of the Summer School are to develop post-graduates scientific readiness and to offer students the possibility to study in a modern, scientific environment and to create connections to the international science community.

Credits info
2 ECTS Passing: Obligatory attendance at lectures.Grading: Pass/fail

Fee info
EUR 0: Participating the Summer School is free of charge, but student have to cover the costs of own travel, accommodation and meals at Jyvskyl.

Scholarships
The 25th Jyvskyl Summer School is not able to grant any Summer School students financial support. In order to ensure your participation, we recommend that you take steps to secure your own funding, for example, by turning first to your home institution

University of Jyv%C3%A4skyl%C3%A4
Address: Faculty of Mathematics and Science and Faculty of Information Technology, Jyv%C3%A4skyl%C3%A4 Summer School, Faculty of Mathematics and Science P.O.Box 35 (YK312), FIN-40014 University of Jyv%C3%A4skyl%C3%A4, Finland
Postal code: FIN-40014
City: Jyv%C3%A4skyl%C3%A4
Country: Finland
Website: http://www.jyu.fi/summerschool
E-mail: jss@jyu.fi
Phone: +358505818351