NSF Award
2406319
This award supports the summer school<br/>“C*-Algebraic Quantum Mechanics and Topological Phases of Matter”,<br/>which will take place July 29-August 2, 2024, at the University of<br/>Colorado at Boulder. This workshop will be an opportunity for graduate<br/>students and postdocs from a wide variety of institutions and<br/>backgrounds to learn about the interplay between algebraic<br/>quantum mechanics, topology, and condensed matter theory. There will be<br/>problem sessions to help participants better learn the topics<br/>presented. Materials from the conference will be disseminated broadly:<br/>The talks will be filmed and posted on the Rocky Mountain Mathematical<br/>Physics Seminar YouTube Channel. Problem sets and course notes will be<br/>made available on the summer school webpage. This will create a<br/>permanent resource for all those seeking to learn the topics of the summer<br/>school. Another goal is to give some early-career researchers an opportunity to disseminate their<br/>work. This will be done through contributed talks by junior<br/>participants. The event will also create opportunities for junior<br/>participants to interact with the speakers and more established<br/>researchers. Funding from the NSF will make it possible to support<br/>participants who would not be able to attend without support and will<br/>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.<br/><br/>The scientific goal of the summer school is to explore how C*-algebras<br/>are used to study topological phases of matter in the thermodynamic<br/>limit, and how methods from topology can be applied in this setting to<br/>study phases of quantum systems. Topics will cover background on<br/>C*-algebras and the topology of state spaces, lattice spin systems,<br/>Lieb-Robinson bounds, automorphic equivalence and symmetry protected<br/>phases. In the study of quantum many-body systems with infinitely many<br/>degrees of freedom, the thermodynamic limit is often of practical and<br/>conceptual importance. A precise mathematical description of such<br/>systems requires the use of a C*-algebraic formulation of quantum<br/>mechanics, a formalism that comes with deep insights and technical<br/>challenges in equal measure. C*-algebraic quantum mechanics has a long<br/>history, with notable discoveries in the seventies, including Lieb-<br/>Robinson bounds and the Doplicher-Haag-Roberts description of<br/>superselection sectors which continue to spur modern research in<br/>mathematical physics and condensed matter physics. In just the past<br/>five years, C*-algebraic quantum mechanics has provided the basis for<br/>cutting edge research on the rigorous classification of topological<br/>phases of matter. This summer school will bring some of the foremost<br/>experts in the field to teach the next generation of mathematical<br/>physics, providing students with both a strong foundation in the<br/>C*-algebraic formalism and a broad view of active frontiers of<br/>research.<br/><br/>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.
