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An operator-algebraic formulation of self-testing
We give a new definition of self-testing for correlations in terms of states on C*-algebras. We show that this definition is equivalent to the standard definition for any class of...
Nov 16, 2022
The Complexity and (Un)Computability of Quantum Phase Transitions
The phase diagram of a material is of central importance in describing the properties and behaviour of a condensed matter system. Indeed, the study of quantum phase transitions has formed...
Oct 26, 2022
Holographic scattering from quantum error-correction
We revisit the problem of how interactions emerge in quantum gravity. Namely, we show that bulk scattering of multiple particles in the AdS space requires multipartite entanglement on the boundary...
Oct 26, 2022
Integrable line defects and 4d Chern-Simons theory
I discuss an application of a recent construction of 2d integrable field theories from 4d Chern-Simons theory by Costello and Yamazaki. After a review of the construction, I consider integrable...
Oct 17, 2019
Equivariant localization and Atiyah-Segal completion for Hochschild and cyclic homology
There is a close relationship between derived loop spaces, a geometric object, and Hochschild homology, a categorical invariant, made possible by derived algebraic geometry, thus allowing for both intuitive insights...
Oct 24, 2019
3D Mirror Symmetry and HOMFLY-PT Homology
A recent construction of HOMFLY-PT knot homology by Oblomkov-Rozansky has its physical origin in “B-twisted” 3D N=4 gauge theory, with adjoint and fundamental matter. Mathematically, the construction uses certain categories...
Oct 31, 2019
Fusion rules from entanglement
Connections between 2D gapped quantum phases and the anyon fusion theory have been proven in various ways under different settings. In this work, we introduce a new framework connecting them...
Nov 06, 2019
Bridgeland stability conditions relative to a boundary
In this talk I will present a construction of relative Bridgeland stability conditions that appeared in my work on stability of topological Fukaya categories of surfaces. This construction gives a...
Nov 07, 2019
Solving physics many-body problems with deep learning
Solving classical and quantum physics many-body systems are amongst the hardest problems in the natural sciences, but also of fundamental importance for applications such as material and drug design. In...
Nov 12, 2019
The Diamond Lemma for (multiplicative) preprojective algebras
Bergman's Diamond Lemma for ring theory gives an algorithm to produce a (non-canonical) basis for a ring presented by generators and relations. After demonstrating this algorithm in concrete, geometrically-minded examples...
Nov 14, 2019