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This survey course introduces some advanced topics in quantum field theory and string theory. Topics may include anomalies, conformal field theory, and bosonic string theory and are subject to change depending on the topics covered in the TBD elective course.

This Cosmology course will provide a theoretical overview of the standard cosmological model.
Topics will include: FRW universe, Thermal History, Inflation, Cosmological Perturbation Theory, Structure Formation and Quantum Initial Conditions.

Quantum phases have become a staple of modern physics, thanks to their appearance in fields as diverse as condensed matter physics, quantum field theory, quantum information processing, and topology. The description of quantum phases of matter requires novel mathematical tools that lie beyond the old symmetry breaking perspective on phases. Techniques from topological field theory, homotopy theory, and (higher) category theory show great potential for advancing our understanding of the characterization and classification of quantum phases. The goal of this workshop is to bring together experts from across mathematics and physics to discuss recent breakthroughs in these mathematical tools and their application to physical problems. 

Scientific Organizers

Lukas Mueller
Alex Turzillo
Davide Gaiotto
 

Sponsored in part by the Simons Collaboration on Global Categorical Symmetries 

New observational programs and techniques are opening a window to the first galaxies in the universe and bringing surprises along the way. In this workshop, we'll explore how dark matter phenomenology may have impacted the first stars and galaxies, focusing on how improved modeling and simulations can allow us to use new and upcoming high-redshift data to gain insight into dark matter's fundamental nature.

Sponsored in part by:

This course will introduce you to some of the geometrical structures underlying theoretical physics. Previous knowledge of differential geometry is not required. Topics covered in the course include: Introduction to manifolds, differential forms, symplectic manifolds, symplectic version of Noether’s theorem, integration on manifolds, fiber bundles, principal bundles and applications to gauge theory.

The Gravitational Physics course takes your knowledge and practice of gravity to the next level. We start by recapping the essential elements of differential geometry, adding some new techniques to the toolbox, then apply some of these methods to learning about submanifolds, extra dimensions, and black hole thermodynamics. Towards the end of the course, we delve into the frontiers, with a sample of recent research topics.

A quantum field theory is deemed topological if it exhibits the remarkable property of being independent of any background metric. In contrast to most other types of quantum field theories, topological quantum field theories possess a well-defined mathematical framework, tracing its roots back to the pioneering work of Atiyah in 1988. The mathematical tools employed to define and study topological quantum field theories encompass concepts from category theory, homotopy theory, topology, and algebra.
In this course, we will delve into the mathematical foundations of this field, explore examples and classification results, especially in lower dimensions. Subsequently, we will explore more advanced aspects, such as invertible theories, defects, the cobordism hypothesis, or state sum models in dimensions 3 and 4 (including Turaev-Viro and Douglas-Reutter models), depending on the interests of the audience.
Today, the mathematics of topological quantum field theories has found numerous applications in physics. Recent applications include the study of anomalies, non-invertible symmetries, the classification of topological phases of matter, and lattice models. The course aims to provide the necessary background for understanding these applications.