Global symmetries have been generalized to non-invertible ones. For finite symmetries in $(1+1)$d, these are known as unitary fusion category symmetries. One natural question is: which fusion categories can arise as symmetries on a lattice? 
Progress has been made including the anyon chains, which realizes any fusion category symmetries. However, their Hilbert spaces do not admit the usual tensor product structure (tensor product of local Hilbert spaces over each site).
In [arxiv:2507.05185], Evans and Jones introduced an operator-algebraic framework and showed that a fusion category symmetry can be realized on a tensor product quasi-local algebra if and only if it is "integral". After reviewing this result, I will discuss a recent extension by Bunner and Jones [arxiv:2605.21327], who showed that this constraint disappears after stabilization with infinite-dimensional ancilla spaces on anyon chains. As a consequence, every unitary fusion category can be realized on tensor product Hilbert spaces.

Quantum magic quantifies the computational resources needed for quantum operations that cannot be easily performed classically. This requires unitaries, known as "Non-Clifford gates", that map Pauli operators to outside the Pauli group. I will first provide a pedagogical introduction to these concepts following [arXiv:quant-ph/9807006] and then summarise the recent results of [arXiv:2604.14271] constructing non-Clifford gates from path integrals in Chern-Simons theories, whose magic-generating properties are determined by the algebraic data of the topological field theory.

It is in general nontrivial to construct a 2d worldsheet model whose correlators evaluate to the amplitudes of a target theory. In this talk I will go through a neat, self contained (and to my knowledge, isolated) example in which the matter content and vertex operators of the dual 2d theory can be straightforwardly read off from the action of a 4d theory. Specifically, we will see that a genus 0 worldsheet model whose correlators compute all the tree amplitudes for pure 4d N=4 super Yang-Mills can be essentially derived from the twistor action in elementary steps. We will then discuss the limitations of this approach. There are no twistorial prerequisites assumed.

The period matrix of a smooth complex projective variety encodes the isomorphism between its singular homology and its algebraic De Rham cohomology. Numerical approximations with high precision of the entries of the period matrix allow to recover some algebraic invariants of the variety, such as the Néron-Severi group in the case of surfaces. In this talk, we will see a method relying on the computation of an effective description of the homology for obtaining such numerical approximations of periods of algebraic varieties, and showcase implementations and applications, in particular to computation of the Picard rank of certain K3 surfaces related to Feynman diagrams.

In an AdS compactification the no-scale-separation conjecture states that the AdS scale cannot be parametrically separated from the KK scale of the internal manifold. This calls into question the validity of the effective lower-dimensional theory whilst also making holographic duals more complicated: obtaining a dense spectrum of low-dimension operators which are strongly mixed. This also poses problems for constructing de-Sitter vacua. 
I will discuss the papers Holography vs Scale Separation, Holographic Constraints on the String Landscape and A Holographic Constraint on Scale Separation which use holography to find constraints on scale separation, with the latter two papers focussing DGKT.