The phase retrieval problem arises naturally in different applications, such as crystallography and signal processing. Regardless of its various implementations, this topic has become a very active area of research, receiving significant attention from diverse areas in mathematics – although almost exclusively in the case where the underlying space is Rᵈ. In this talk we will show that STFT phase retrieval is possible for a large class of locally compact abelian groups. This is a joint work with N. Accommazzo, D. Carando, R. Nores and V. Paternostro.

We will review some general concepts of deformation theory. Then we will apply these ideas in order to explore the geometry of the moduli space Inv of foliations on a given variety $X$ around the points corresponding to foliations induced by Lie group actions. More precisely, let $X$ be a smooth projective variety over the complex numbers and $S(d)$ the scheme parametrizing $d$-dimensional Lie subalgebras of $H^0(X,\mathcal{T} X)$. For every $\mathfrak{g} \in S(d)$ one can consider the corresponding element $\mathcal{F}(\mathfrak{g})\in Inv$, whose generic leaf coincides with an orbit of the action of $\exp(\mathfrak{g})$ on $X$. We will show that under mild hypotheses, after taking a stratification $\coprod_i S(d)_i\to S(d)$ this assignment yields an isomorphism $\coprod_i S(d)_i\to Inv$ locally around $\mathfrak{g}$ and $\mathcal{F}(\mathfrak{g})$.

Abstract: In this talk, I will outline how I went from solving Killing spinor equations with pen and paper to a career in coding-intensive Data Science. I'll talk about my experience of working as a Data Scientist for Tesco and how leaving academia didn't mean the end of doing research for me.

Bio: Sebastian completed his PhD in Theoretical Physics at King's in 2019. He then transitioned from the less big data-driven classification of SUGRA backgrounds to a career in computationally heavy machine learning. Since 2020, he's been working as a (by now) Senior Data Scientist at Tesco where he mainly works within the Price Optimisation space and looks after collaborations with academia.

Speaker: Alex Best, 14:00-14:20

Title: p-adic integration and points on curves

Abstract: The problem of algorithmically determining the set of rational and integral points on curves has seen impressive progress in the last 20 years, especially in the area surrounding Chabauty's method.
I'll give an overview of recent work involving $p$-adic integration applied to such problems and their strengths and limitations.

Speaker: Sebastian Monnet, 14:30-14:50

Title: S4-quartics with prescribed norms.

Abstract: Let $K$ be a number field with $\mathbb{Q}$-basis $\{e_1, ..., e_n\}$, and let $\alpha$ be a rational number. It is natural to ask whether the "norm equation" $N_{K/Q}(x_1e_1 + ... + x_ne_n) = \alpha$ has rational solutions. Since the answer depends only on $K$, we may ask how often this norm equation has rational points as we vary $K$. The case of abelian number fields was solved by Frei-Loughran-Newton, and in this talk we present one of the simplest non-abelian cases: $S_4$-quartics.