Fri, 23 Feb 2024
14:30
C6

Flat from anti de Sitter - a Carrollian perspective

Prof Marios Petropoulos
(Ecole Polytechnique, Paris)
Abstract

In recent years, the theme of asymptotically flat spacetimes has come back to the fore, fueled by the discovery of gravitational waves and the growing interest in what flat holography could be. In this quest, the standard tools pertaining to asymptotically anti-de Sitter spacetimes have been insufficiently exploited. I will show how Ricci-flat spacetimes are generally reached as a limit of Einstein geometries and how they are in fact constructed by means of data defined on the conformal Carrollian boundary that is null infinity. These data, infinite in number, are obtained as the coefficients of the Laurent expansion of the energy-momentum tensor in powers of the cosmological constant. This approach puts this tensor back at the heart of the analysis, and at the same time reveals the versatile role of the boundary Cotton tensor. Both appear in the infinite hierarchy of flux-balance equations governing the gravitational dynamics.  

Thu, 30 Nov 2023

11:00 - 12:00
C6

Homotopy type of categories of models

Jinhe Ye
(University of Oxford)
Abstract

For a complete theory T, Lascar associated with it a Galois group which we call the Lacsar group. We will talk about some of my work on recovering the Lascar group as the fundamental group of Mod(T) and some recent progress in understanding the higher homotopy groups.

Thu, 16 Nov 2023

11:00 - 12:00
C6

On a proposed axiomatisation of the maximal abelian extension of the p-adic numbers

Leo Gitin
(University of Oxford)
Abstract

The local Kronecker-Weber theorem states that the maximal abelian extension of p-adic numbers Qp is obtained from this field by adjoining all roots of unity. In 2018, Koenigsmann conjectured that the maximal abelian extension of Qp is decidable. In my talk, we will discuss Koenigsmann's proposed axiomatisation. In contrast, the maximal unramified extension of Qp is known to be decidable, admitting a complete axiomatisation by an informed but simple set of axioms (this is due to Kochen). We explain how the question of completeness can be reduced to an Ax-Kochen-Ershov result in residue characteristic 0 by the method of coarsening.

Thu, 02 Nov 2023

11:00 - 12:00
C6

Unlikely Double Intersections in a power of a modular curve (Part 1)

Francesco Ballini
(University of Oxford)
Abstract

The Zilber-Pink Conjecture, which should rule the behaviour of intersections between an algebraic variety and a countable family of "special varieties", does not take into account double intersections; some results related to tangencies with special subvarieties have been obtained by Marché-Maurin in 2014 in the case of powers of the multiplicative group and by Corvaja-Demeio-Masser-Zannier in 2019 in the case of elliptic schemes. We prove that any algebraic curve contained in Y(1)^2 is tangent to finitely many modular curves, which are the one-codimensional special subvarieties. The proof uses the Pila-Zannier strategy: the Pila-Wilkie counting theorem is combined with a degree bound coming from a Weakly Bounded Height estimate. The seminar will be divided into two talks: in the first one, we will explain the general Zilber-Pink Conjecture philosophy, we will describe the main tools used in this context and we will see what the differences in the double intersection case are; in the second one, we will focus on the proofs and we will see how o-minimality plays a main role here. In the case of a curve in Y(1)^2, o-minimality is also used for height estimates (which are then ineffective, which is usually not the case).

Thu, 19 Oct 2023

11:00 - 12:00
C6

New ideas in Arakelov intersection theory

Michał Szachniewicz
(Mathematical Insitute, Oxford)
Abstract

I will give an overview of new ideas showing up in arithmetic intersection theory based on some exciting talks that appeared at the very recent conference "Global invariants of arithmetic varieties". I will also outline connections to globally valued fields and some classical problems.

Wed, 13 Sep 2023

14:00 - 15:00
C6

Nonlinear SPDE approximation of the Dean-Kawasaki equation

Professor Ana Djurdjevac
(Free University Berlin)
Abstract

Interacting particle systems provide flexible and powerful models that are useful in many application areas such as sociology (agents), molecular dynamics (proteins) etc. However, particle systems with large numbers of particles are very complex and difficult to handle, both analytically and computationally. Therefore, a common strategy is to derive effective equations that describe the time evolution of the empirical particle density, the so-called Dean-Kawasaki equation.

 

Our aim is to derive and study continuum models for the mesoscopic behavior of particle systems. In particular, we are interested in finite size effects. We will introduce nonlinear and non-Gaussian models that approximate the Dean-Kawasaki equation, in the special case of non-interacting particles. We want to study the well-posedness of these nonlinear SPDE models and to control the weak error of the SPDE approximation.  This is the joint work with H. Kremp (TU Wien) and N. Perkowski (FU Berlin).

Tue, 06 Jun 2023
14:00
C6

Dr. Guillaume St-Onge

Dr. Guillaume St-Onge
(Northeastern University Network Science Institute)
Abstract

TBA

Tue, 23 May 2023
14:00
C6

What we do in the shadows: mining temporal motifs from transactions on the Dark Web

Dr. Naomi Arnold
(Northeastern University London)
Abstract
Dark web marketplaces are forums where users can buy or sell illicit goods/services and transactions are typically made using cryptocurrencies. While there have been numerous coordinated shutdowns of individual markets by authorities, the ecosystem has been found to be immensely resilient. In addition, while transactions are open and visible by anyone on the blockchain, the sheer scale of the data makes monitoring beyond basic characteristics a huge effort.

In this talk, I propose the use of temporal motif counting, as a way of monitoring both the system as a whole and the users within it. Focusing on the Alphabay and Hydra dark markets, I study all the motifs formed by three sequential transactions among two to three users, finding that they can tell us something more complex than can be captured by simply degree or transaction volume. Studying motifs local to the node, I show how users form salient clusters, which is a promising route for classification or anomaly detection tasks.
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