Conference: C*-Algebraic Quantum Mechanics and Topological Phases of Matter

University Of Colorado At Boulder, Boulder CO

Investigators

Abstract

This award supports the summer school “C*-Algebraic Quantum Mechanics and Topological Phases of Matter”, which will take place July 29-August 2, 2024, at the University of Colorado at Boulder. This workshop will be an opportunity for graduate students and postdocs from a wide variety of institutions and backgrounds to learn about the interplay between algebraic quantum mechanics, topology, and condensed matter theory. There will be problem sessions to help participants better learn the topics presented. Materials from the conference will be disseminated broadly: The talks will be filmed and posted on the Rocky Mountain Mathematical Physics Seminar YouTube Channel. Problem sets and course notes will be made available on the summer school webpage. This will create a permanent resource for all those seeking to learn the topics of the summer school. Another goal is to give some early-career researchers an opportunity to disseminate their work. This will be done through contributed talks by junior participants. The event will also create opportunities for junior participants to interact with the speakers and more established researchers. Funding from the NSF will make it possible to support participants who would not be able to attend without support and will be primarily offered to graduate students and postdocs. More information about the summer school can be found at https://sites.google.com/colorado.edu/caqm. The scientific goal of the summer school is to explore how C*-algebras are used to study topological phases of matter in the thermodynamic limit, and how methods from topology can be applied in this setting to study phases of quantum systems. Topics will cover background on C*-algebras and the topology of state spaces, lattice spin systems, Lieb-Robinson bounds, automorphic equivalence and symmetry protected phases. In the study of quantum many-body systems with infinitely many degrees of freedom, the thermodynamic limit is often of practical and conceptual importance. A precise mathematical description of such systems requires the use of a C*-algebraic formulation of quantum mechanics, a formalism that comes with deep insights and technical challenges in equal measure. C*-algebraic quantum mechanics has a long history, with notable discoveries in the seventies, including Lieb- Robinson bounds and the Doplicher-Haag-Roberts description of superselection sectors which continue to spur modern research in mathematical physics and condensed matter physics. In just the past five years, C*-algebraic quantum mechanics has provided the basis for cutting edge research on the rigorous classification of topological phases of matter. This summer school will bring some of the foremost experts in the field to teach the next generation of mathematical physics, providing students with both a strong foundation in the C*-algebraic formalism and a broad view of active frontiers of research. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.