# Scope

**Description of the workshop**

Triggered by recent studies on topological insulators, the concept of topology has become one of the major building blocks of modern condensed matter physics. Looking back to history, the importance of this concept was realized through efforts to understand unexpected experimental results in phenomena such as the quantum Hall effect, vortices in superconductivity and so on. On the other hand, it is interesting to note that, in the realm of mathematics, the corresponding framework such as cohomology, characteristic class, K-theory were already developed during the early 20th century, way before the development in physics, but now plays an essential role in explaining experiments. However, the situation is still not satisfactory. This is because, with only few exceptions, it is difficult to directly “measure the topology” in topological states. The exception lies at the boundary. The real surprise is that one can observe the topology through edge states as low energy boundary modes living near the system edges as well as local states near impurities. These edge states/boundary states are physical observables. Enormous success of the ARPES (angular resolved photoemission spectroscopy) experiments are the key achievements in the recent big bang in the topological business. The surface sensibility of the ARPES enables us to directly see the topology as a number of edge channels. Indeed, topology and edge states are directly related. This is the bulk-edge correspondence. Topology is not a mere concept but a real observable! With this breakthrough, we can recast new understanding to many of localized modes in quite different areas such as cold atoms, photonics, solid states and even classical mechanics. Some of them are traditional local states/modes and might be well known. But they could be well understood by this new way of thinking. THINK DIFFERENT topologically through the bulk-edge correspondence. The workshop is for people in different fields to get together and discuss topological phases in solids, atoms, light and more. Let's look at physics from boundaries and impurities, which are geometrical perturbation for the bulk. Everyone interested in topological phases/materials/lights are welcome. Target systems can be topological materials (topological insulators, (anomalous) quantum (spin/valley) Hall states, graphene, silicene, anisotropic superconductors, Majorana/Andreev bound states), photonics crystals, light, topological mechanics and more. Needless to say, people working in topological condensed matter (theories and experiments) without any edge states are welcome, of course.

We are planning to have a mathematician as a speaker in order to make an even larger hop, between physics and pure mathematics.

* This workshop is a continuation of a series of the workshops*

*BEC2015 in Tokyo, Sep. 27-29 (2015)**BEC2016 in Kyoto, Sep. 27-30 (2016) as a YITP workshop of the Yukawa Institute for theoretical physics (Kyoto University) t**BEC2018-Jan in Tsukuba, Sep. 27-29 (2018)**BEC2018X in Tokyo, Dec. 9-13 (2018)**BEC2019-NTTI2019 in Hiroshima, July 14-19 (2019) together with New Trends in Topological Insulators*

*that we enjoyed a lot. Then we further try to get together again and discuss new developments. Also hope to get interdisciplinary interaction among various areas from physics to math by the keyword "BEC" (Bulk-Edge-Correspondence) and BE/BC(Bulk-Edge/Boundary-Correspondence).*