Week 24.04.2023 – 30.04.2023

These three lectures will aim to provide a pedagogical introduction to the dynamics of N=2 supersymmetric gauge theory and the work of Seiberg and Witten. We will assume only basic knowledge of supersymmetry.

Please visit https://lonti.weebly.com/spring-2023-series.html for more information.

The space of measured laminations on a hyperbolic surface is a generalisation of the set of weighted multi curves. The action of the mapping class group on this space is an important tool in the study of the geometry of the surface. For orientable surfaces, orbit closures are now well-understood and were classified by Lindenstrauss and Mirzakhani. In particular, it is one of the pillars of Mirzakhani’s curve counting theorems. For non-orientable surfaces, the behaviour of this action is very different and the classification fails. In this talk I will review some of these differences. I will talk about some of these results and classify mapping class group orbit closures of (projective) measured laminations for non-orientable surfaces. This is joint work with Erlandsson, Gendulphe and Souto.

We consider a model of the evolution of one and two qubits embedded in an environment. In contrast to the well-known spin-boson model, used to model a translation invariant and macroscopic environment, we model the environment by random matrices of large size that are widely used to describe multi-connected disordered environments of mesoscopic and even nanoscopic size. An important property of the model is that it incorporates non-Markovian evolution allowing for the backflow of energy and information from the environment to the qubits.
We obtain an asymptotically exact in size of the environment expression for the reduced density matrix of qubits valid for all typical realizations of the disordered environment. By using detailed analytical and numerical analysis of expressions, we find several interesting patterns of the qubit evolution, including the disappearance of entanglement in the finite moments and, especially, its subsequent reappearance. These patterns are known in quantum information science as the sudden death and the sudden birth of entanglement. They were found earlier in special versions of the spin-boson model. Our results obtained for a non microscopic and disordered environment demonstrate the robustness and universality of the patterns. When combined with certain tools of quantum information science (e.g., entanglement distillation), the results can lead to a much slower decay entanglement down to its asymptotic persistence.

Let k be a perfect field of characteristic p>0, and let X be a proper scheme over W(k) with semistable reduction. I shall formulate an analogue of the Fontaine-Messing variational p-adic Hodge conjecture in this setting. To get there, I shall define a logarithmic version of motivic cohomology for the special fibre X_k. This theory is related to relative log-Milnor K-theory, logarithmic Hyodo-Kato Hodge-Witt cohomology, and log K-theory. With this in hand, I shall prove the deformational part of the conjecture, simultaneously generalising the semistable p-adic Lefschetz (1,1) theorem of Yamashita (the case r=1) and the deformational p-adic Hodge conjecture of Bloch-Esnault-Kerz (the good reduction case). This is joint work with Andreas Langer.

These three lectures will aim to provide a pedagogical introduction to the dynamics of N=2 supersymmetric gauge theory and the work of Seiberg and Witten. We will assume only basic knowledge of supersymmetry.

Please visit https://lonti.weebly.com/spring-2023-series.html for more information.

We focus on models for network data which contain quantitative information about relationships between nodes. In particular, we consider model that capture similarity between nodes through unobserved latent variables. We investigate how to deal with model specification uncertainty through formal Bayesian model averaging. In the context of a Poisson model with a log-Normal rate parameter, we give conditions under which a common improper prior leads to posterior existence. We derive an MCMC strategy for inference using Bayesian model averaging over the model space (constructed by including or excluding each of the covariates, including the latent ones). The model is applied to bilateral migration flows between 38 OECD countries during the period 2015-2020 and it is shown to outperform three popular gravity models.

This is joint work with Gregor Zens.