## PIMS Summer School on the Topology and Geometry of Quantum Matter (Postponed)

- Start Date: 08/10/2020
- End Date: 08/14/2020

University of Alberta

Recent advances in condensed matter physics have ushered in a new era of cross-fertilization between mathematics and physics. The study of topological materials, a radically new class of quantum materials discovered in the mid-2000s and the subject of the 2016 Nobel Prize in Physics, has enriched the band theory of solids with concepts from algebraic and differential topology such as homotopy theory, characteristic classes, K-theory, and index theory. Advances in the difficult problem of the classification of symmetry-protected topological phases, a generalization of free-fermion topological materials to interacting systems of fermions or bosons, have involved aspects of group cohomology, topological quantum field theory, and cobordism theory. The description of topological phases with anyon excitations using modular tensor categories and rational conformal field theory, originally limited to 2+1 spacetime dimensions, has been extended to 3+1 dimensions in some cases. Beyond purely topological aspects, geometrical aspects of topological phases have also recently come to the fore. Proposed classifications of free-fermion or interacting topological phases protected by crystalline symmetries have involved sophisticated mathematical tools such as equivariant cohomology and the Atiyah-Hirzebruch spectral sequence. Studies of geometrical aspects of the fractional quantum Hall effect, such as its thermal or elastic responses and the physics of its neutral collective excitations, have led to a renewed interest in complex geometry and the theory of Riemann surfaces.

While this exciting interplay between condensed matter physics and pure mathematics has produced and undoubtedly will continue to produce transformative advances, it is often difficult for beginning researchers with a training focused on one or the other discipline to contribute to this rapidly evolving field, due to discipline-specific language barriers. Through a combination of pedagogical lectures and discussions of recent research topics, this interdisciplinary summer school will break these language barriers by introducing graduate students and postdoctoral fellows to the modern mathematical physics of quantum matter, with a focus on topological and geometrical aspects.

This event is part of the PIMS CRG on Quantum Topology and its Applications.

Organizers: Lindsay LeBlanc, Joseph Maciejko, and Steven Rayan- USaskatchewan

To be eligible to participate in the school:

- You must be a graduate student registered in an MSc or PhD program in mathematics or physics, or a postdoctoral fellow in mathematics or physics;
- Your research interests must be related to the topology and geometry of quantum matter.

As we can only accommodate a limited number of participants, prospective eligible participants will be required to submit a short application online, to be made available shortly. Successful applicants will be notified by e-mail following a review of applications, and will be invited to formally register for the school.

For more details on the summer school, and to register, please visit the main site here: https://tgqm2020.ca/