Topological Phases of Interacting Quantum Systems (19w5034)

The Casa Matemática Oaxaca (CMO) will host the "Topological Phases of Interacting Quantum Systems" workshop in Oaxaca, from June 2, 2019 to June 7, 2019.

There is presently a tremendous activity in the field of topological insulators. There has been a swift progress on understanding the effect of disorder and aperiodicity at the one-particle level, mostly from mathematical physics community, as well as on understanding the effect of interaction in periodic systems, this time mostly from the theoretical physics community. The progress on the effect of both interaction and aperiodicity has been, however, extremely slow. The methods used by these two communities are quite different yet they all make appeal to advance concepts from pure mathematics. The first objective will therefore be to disseminate the important results in the field and to survey its state of the art. The second objective will be a comprehensive survey of the open problems and an honest discussion of the limitations of the present approaches. The third objective will be to connect and integrate the frameworks already used by the researchers and hopefully to put forward proposals with potential for a breakthrough in the problem of topological interacting aperiodic systems. For example, to the present day, $K$-theory, index theory and non-commutative geometry have not yet been applied to interacting systems in a conceptual way and one of the aims of the workshop is to exchange ideas on such matters. The overarching goal of the meeting will be to further intensify the contact between mathematical physicists and theoretical physicists working in the field of topological insulators. This is reflected by the mix of the participants, coming both from physics and mathematics. The organizers have absolutely no doubt that this 5-day conference it will be successful and will have a strong impact on the field, both on an international level, as well as on the local mathematical physics community in Mexico.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT