A quantum circuit defines a discrete-time evolution for a set of quantum spins/qubits, via a sequence of unitary 'gates’ coupling nearby spins. I will describe how random quantum circuits, where each gate is a random unitary matrix, serve as minimal models for various universal features of many-body dynamics. These include the dynamical generation of entanglement between distant spatial regions, and the quantum "butterfly effect". I will give a very schematic overview of mappings that relate averages in random circuits to the classical statistical mechanics of random paths. Time permitting, I will describe a new phase transition in the dynamics of a many-body wavefunction, due to repeated measurements by an external observer.

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Speaker: Elena Gal (4pm)

Title: Associativity and Geometry

Abstract: An operation # that satisfies a#(b#c)=(a#b)#c is called "associative". Associativity is "common" - if we are asked to give an example of operation we are more likely to come up with one that has this property. However if we dig a bit deeper we encounter in geometry, topology and modern physics many operations that are not associative "on the nose" but rather up to an equivalence. We will talk about how to describe and work with this higher associativity notion.

Speaker: Alexandre Bovet (4:30pm)

Title: Investigating disinformation in social media with network science

Abstract:
While disinformation and propaganda have existed since ancient times, their importance and influence in the age of
social media is still not clear.  We investigate the spread of disinformation and traditional misinformation in Twitter in the context of the 2016 and 2020 US presidential elections. We analyse the information diffusion networks by reconstructing the retweet networks corresponding to each type of news and the top news spreaders of each network are identified. Our investigation provides new insights into the dynamics of news diffusion in Twitter, namely our results suggests that disinformation is governed by a different diffusion mechanism than traditional centre and left-leaning news. Centre and left leaning traditional news diffusion is driven by a small number of influential users, mainly journalists, and follow a diffusion cascade in a network with heterogeneous degree distribution which is typical of diffusion in social networks, while the diffusion of disinformation seems to not be controlled by a small set of users but rather to take place in tightly connected clusters of users that do not influence the rest of Twitter activity. We also investigate how the situation evolved between 2016 and 2020 and how the top news spreaders from the different news categories have driven the polarization of the Twitter ideological landscape during this time.

Speaker: Katherine Staden
Introduced by: Frances Kirwan
Title: Inducibility in graphs
Abstract: What is the maximum number of induced copies of a fixed graph H inside any graph on n vertices? Here, induced means that both edges and non-edges have to be correct. This basic question turns out to be surprisingly difficult, and it is not even known for all 4-vertex graphs H. I will survey the area and discuss some key results, ideas and techniques -- combinatorial, analytical and computer-assisted.

Speaker: Pierre Haas
Introduced by: Alain Goriely
Title: Shape-Shifting Droplets
Abstract: Experiments show that small oil droplets in aqueous surfactant solution flatten, upon slow cooling, into a host of polygonal shapes with straight edges and sharp corners. I will begin by showing how plane (and rather plain) geometry explains the sequence of these polygonal shapes. I will go on to show that geometric considerations of that ilk cannot however explain the three-dimensional polyhedral shapes that the initially spherical droplets evolve through while flattening. I will conclude by showing that the experimental data agree with the predictions of a model based on a partial phase transition of the oil near the droplet edges.

Networks are an imperfect representation of a dataset, yet often there is little consideration for how these imperfections may affect network evolution and structure.

In this talk, I want to discuss a simple set of generative network models in which the mechanism of network growth is decomposed into two layers. The first layer represents the “observed” network, corresponding to our conventional understanding of a network. Here I want to consider the scenario in which the network you observe is not self-contained, but is driven by a second hidden network, comprised of the same nodes but different edge structure. I will show how a range of different network growth models can be constructed such that the observed and hidden networks can be causally decoupled, coupled only in one direction, or coupled in both directions.

One consequence of such models is the emergence of abrupt transitions in observed network topology – one example results in scale-free degree distributions which are robust up to an arbitrarily long threshold time, but which naturally break down as the network grows larger. I will argue that such examples illustrate why we should be wary of an overreliance on static networks (measured at only one point in time), and will discuss other possible implications for prediction on networks.

Since the seminal work of Keating and Snaith, the characteristic polynomial of a random (Haar-distributed) unitary matrix has seen several of its functional studied in relation with the probabilistic study of the Riemann Zeta function. We will recall the history of the topic starting with the Montgommery-Dyson correspondance and will revisit the last twenty years of computations of integer moments of some functionals, with a particular focus on the mid-secular coefficients recently studied by Najnudel-PaquetteSimm. The new method here introduced will be compared with one of the classical ways to deal with such functionals, the Conrey-Farmer-Keating-Rubinstein-Snaith (CFKRS) formula.

Will a large economy be stable? In this talk, I will present a model for a network economy where firms' productions are interdependent, and study the conditions under which such input-output networks admit a competitive economic equilibrium, where markets clear and profits are zero. Insights from random matrix theory allow to understand some of the emergent properties of this equilibrium and to provide a classification for the different types of crises it can be subject to. After this, I will endow the model with dynamics, and present results with strong links to generalised Lotka-Volterra models in theoretical ecology, where inter-species interactions are modelled with random matrices and where the system naturally self-organises into a critical state. In both cases, the stationary points must consist of positive species populations/prices/outputs. Building on these ideas, I will show the key concepts behind an economic agent-based model that can exhibit convergence to equilibrium, limit cycles and chaotic dynamics, as well as a phase of spontaneous crises whose origin can be understood using "semi-linear" dynamics.