June 14-20, 2026 in TBD
Mentored by Corey Jones of North Carolina State University and David Penneys of the Ohio State University
Preliminary syllabus will be posted when available
Notes will be posted when available
Description: Topological quantum field theories (TQFTs) provide a fundamental link between higher categorical algebra, topology, and quantum physics. In quantum many-body physics, TQFTs have become an essential tool for describing long-range, macroscopic patterns of entanglement called topological order. However, TQFTs are an intrinsically global phenomenon, and accessing these mathematical objects with only local information is a fundamental problem for physicists in the context of quantum many-body systems. Recently a new conceptual framework called topological holography has emerged from the physics literature that helps bridge this gap. It proposes that certain associative algebras associated with "physical boundaries" of a topologically ordered many-body system should remember the emergent TQFT of the bulk with only local, microscopic structure in one spatial dimension lower than the system. This is a very active area of research at the interface of mathematics and theoretical physics with many applications, including deep connections to the emerging paradigm of (higher) fusion-categorical symmetry in quantum field theory.
Outline: This workshop will begin by introducing the algebraic approach to quantum many-body systems. We will then explain recent work formalizing topological holography for systems defined on lattices in Rn exhibiting local topological order, with an emphasis on examples (particularly Levin-Wen and Walker-Wang models) and the machinery of DHR bimodules. We will also explain recent work applying the ideas of topological holography to understand fusion category symmetries in a single spatial dimension. We will see how this story is the first step in a larger program to extract higher categorical algebra from physical systems.
Background: The workshop will be aimed towards graduate students with a basic understanding of (higher) category theory and TQFTs. While some interest in physics might be helpful, it is not required or expected: we will get you excited about it!
The workshop discussions will have an expository character and a majority of the talks will be given by participants. Breaks will be built into the schedule for informal discussions and collaborations. Here is some advice on how to give a good Talbot talk. The workshop will take place in a communal setting, with participants sharing living space and cooking and cleaning responsibilities.
The workshop will be held entirely in-person. We cover all local expenses, including lodging and food. We also have limited funding available for participant travel costs, but we encourage participants to seek other sources of travel funding if possible.
Talbot is meant to encourage collaboration among young researchers, with an emphasis on graduate students. We also aim to gather participants with a diverse array of knowledge and interests, so applicants need not be an expert in the field; in particular, students at all levels of graduate education are encouraged to apply. In accordance with the Statement of Inclusiveness, this workshop will be open to everybody, regardless of race, sex, religion, national origin, sexual orientation, gender identity, disability, age, pregnancy, immigration status, or any other aspect of identity. We are committed to ensuring that the Talbot Workshop is a supportive, inclusive, and safe environment for all participants, and that all participants are treated with dignity and respect.
Please email the organizers at talbotworkshop (at) gmail (dot) com if you have any questions.