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. 

Existential decidability of a ring is the question as to whether an algorithm exists which determines whether a given system of polynomial equations and inequations has a solution. It is a classical result (``Hilbert's 10th problem'') that the ring of integers is not existentially decidable. Over the years there has been many results related to Hilbert 10th problem over different fields. For instance, the existential decidability of a Henselian valued field of mixed characteristic and finite ramification can be reduced to the positive existential decidability of its residue field, plus some additional structure.

An example of a mixed characteristic Henselian field is the fraction field of Witt Vectors. It is a construction analogous to the construction of the p-adic numbers from $\mathbb{F}_p$, and it takes a perfect field $F$ of characteristic $p$ and constructs a field with value group $\mathbb{Z}$ and residue field $F$. We will look at the existential decidability of the Henselian valued fields arising from finite extensions of the Witt vectors over a positive characteristic Henselian valued field. I will report on our progress so far, the problems that we have encountered, and the goals we are working toward.