Schedule & Abstracts

All talks will be held in Stevenson Center 1432. All breaks will be held in Stevenson Center 1425.

Schedule

Saturday, March 28

9:00am-9:50am Feng Xu, UC Riverside

Coffee Break

10:30am-11:20am Nima Lashkari, Purdue University

11:30am-12:30pm Corey Jones, NC State University

Lunch Break

2:10pm-3:00pm Theo Johnson-Freyd, Dalhousie University and Perimeter Institute

3:20pm-4:10pm Sahand Seifnashri, IAS Princeton

Coffee Break

5:00pm-5:50pm Terry Gannon, University of Alberta

Open Problems/Discussion

6:30pm Conference Dinner in SC 1425

Sunday, March 29

9:10am-10:00am Colleen Delaney, Purdue University

Coffee Break

10:40am-11:30am Oem Trivedi, Vanderbilt University 

12:00pm-12:50pm Yasuyuki Kawahigashi, The University of Tokyo

Lunch/End of Conference

Titles & Abstracts

Saturday, March 28

Feng Xu, UC Riverside

Title: On singular limits of relative entropies

Abstract: In this talk we will discuss a result relating singular limits of certain relative entropies with index in the setting of conformal nets, which has played an important role  in the mathematical theory of relative entropies in the context of Conformal Field Theory.

Nima Lashkari, Purdue University

Title: Non-invertible symmetries as non-unitarily correctible error correction

Abstract: By focusing on operator algebra of invariant operators, we argue that many examples of non-invertible symmetries in physics such as RepG and 2d CFTs can be viewed as non-unitarily correctible quantum error correction codes. Going beyond groups, many 0-form non-invertible symmetries can be viewed as an inclusion of von Neumann algebras with finite index. In the analogy with error correction, the smaller algebra is the subalgebra of exactly correctible operators (logical operators) sitting inside the set of all physical operators.  The index of the inclusion is a notion of rate for the code.

Corey Jones, NC State University

Title: Fusion category symmetries on the lattice

Abstract: Fusion categories arise as symmetries of 1+1D quantum field theories. A natural question is: which fusion category symmetries can be realized on spin chains? We will explain recent work with David Evans which shows a fusion category is realizable on a spin chain if and only if it is integral. We will then show that any fusion category can be realized as symmetries on a tensor product of infinite dimensional Hilbert spaces.

Theo Johnson-Freyd, Dalhousie University and Perimeter Institute

Title: McNamara-Wang reconstruction and rigid monoidality in categories of trace-class operators

Abstract: During their investigation of entropy in quantum gravity, McNamara and Wang have discovered an amazing reconstruction result: Every unitary functorial field theory (unextended, not necessarily topological) is determined up to isomorphism by its partition function; a partition function extends to a unitary field theory if and only if it is reflection positive. Their proof is written in physical style: it is given as a recipe, not a theorem, and it does not precisely handle the abstract category theoretic issues. I will explain some of those abstract categorical issues. Namely, the construction relies on a version of category theory which does not have unit morphisms, but which has a replacement called "firmness". In the absence of units, the notion of "rigid monoidality" becomes richer: (infinite-dimensional Hilbert spaces, trace class operators) is an example of of a rigid symmetric monoidal firm dagger category; it is symmetric-monoidally firm-Morita equivalent to (finite-dimensional Hilbert spaces, operators). The McNamara–Wang reconstruction theorem applies to any rigid symmetric monoidal firm dagger category with unitary dual functor. This talk is based on conversations with McNamara and Reutter.

Sahand Seifnashri, IAS Princeton

Title: Operator-Algebraic Definition of Non-Invertible Symmetries in Quantum Lattice Systems

Abstract: We propose a general definition of non-invertible symmetries on the lattice based on their action on the local operator algebra. We formulate them as locality-preserving, unital completely positive (UCP) maps that satisfy additional conditions. We conjecture that these conditions ensure the existence of a sequential circuit presentation (topological defect) defined in terms of localizable Hilbert C*-bimodules. Our framework naturally leads to a notion of non-invertible Quantum Cellular Automata (QCAs), and we discuss an index theory that classifies their blend-equivalence classes in 1+1 dimensions.

Terry Gannon, University of Alberta

Title: An autistic approach to vertex algebras

Abstract: Vertex operator algebras are still fairly poorly understood. In this talk I'll probe their structure and representations in somewhat atypical directions. I'll argue these directions are natural and underappreciated. Though to be fair, after this work VOAs will remain poorly understood....

Sunday, March 29

Colleen Delaney, Purdue University

Title: From topological entanglement entropy to modular data and beyond 

Abstract: I will riff on the theme of the workshop and discuss various mathematical aspects of the characterization of (2+1)D topological phases of matter through the lens of information and computation, both classical and quantum.

Oem Trivedi, Vanderbilt University 

Title: Hermiticty as a Symmetry, Quasilocal Probability and Gravity

Abstract: Hermiticity is usually treated in an axiomatic way in quantum mechanics, ensuring key properties of observables in a Hilbert space. In this talk I will discuss how Hermiticity may be something deeper; a symmetry law associated with the conservation of the inner product current in space-time. We will see that this symmetry breaks in the presence of gravitational fields, causal horizons, or space-time curvature for a restricted observer. I will motivate the background for such a symmetry showing what cosmology and near-horizon black hole thermodynamics tell us about it, namely that to preserve global flatness of the universe one needs effective Hermiticity to hold true, but local Hermiticity needs to break near black hole horizons to ensure the second law of thermodynamics. I then discuss how all of this leads to the notion that Probability itself, like energy in general relativity, becomes Quasilocal in curved spacetimes. We then conclude by discussing the implications of all this on quantum field theory in curved spacetimes and quantum gravity in general.

Yasuyuki Kawahigashi, The University of Tokyo

Title: Subfactors, tensor categories and tensor networks

Abstract: Researchers in condensed matter physics use 4-tensors to study two-dimensional topological order. We further clarify relations between their 4-tensors and bi-unitary connections in subfactor theory using tensor networks. Particularly, we present a general framework to deal with tensors satisfying the zipper condition and intertwiners between bimodules arising from flat fields of strings.