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• Speaker: Alex Vañó-Viñuales (IST Lisbon)
• Friday 21 February 2025, 13:00-14:00
• Venue: Potter room.
• Series: DAMTP Friday GR Seminar; organiser: Daniela Cors.

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The Kerr-de Sitter metric, originally proposed by Carter in four dimensions and later extended by Gibbons, Lü, Page and Pope to all dimensions, is likely to play a relevant role among Lambda positive vacuum spacetimes. To better understand what makes it special, we calculate the asymptotic data characterizing the metric near conformal infinity. This requires a review of tools in conformal geometry, such as the Fefferman-Graham expansion, and its relation with the asymptotic initial value problem in arbitrary dimensions. The asymptotic data obtained for Kerr-de Sitter admits a straightforward generalization to a broader class of spacetimes that depends on a set of parameters, which we refer to as Kerr-de Sitter-like class. This class of metrics is obtained explicitly as limits or analytic extensions of Kerr-de Sitter and the space of parameters inherits a natural topological structure from the asymptotic data. Furthermore, we discuss additional characterizations within the Kerr-Schild type metrics and the algebraically special metrics that highlight the geometrical significance of the class.

• Speaker: Carlos Peón Nieto (UPM, Madrid)
• Friday 24 January 2025, 13:00-14:00
• Venue: Potter Room / Zoom link https://cam-ac-uk.zoom.us/j/87235967698.
• Series: DAMTP Friday GR Seminar; organiser: Daniela Cors.

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The Kerr-de Sitter metric, originally proposed by Carter in four dimensions and later extended by Gibbons, Lü, Page and Pope to all dimensions, is likely to play a relevant role among Lambda positive vacuum spacetimes. To better understand what makes it special, we calculate the asymptotic data characterizing the metric near conformal infinity. This requires a review of tools in conformal geometry, such as the Fefferman-Graham expansion, and its relation with the asymptotic initial value problem in arbitrary dimensions. The asymptotic data obtained for Kerr-de Sitter admits a straightforward generalization to a broader class of spacetimes that depends on a set of parameters, which we refer to as Kerr-de Sitter-like class. This class of metrics is obtained explicitly as limits or analytic extensions of Kerr-de Sitter and the space of parameters inherits a natural topological structure from the asymptotic data. Furthermore, we discuss additional characterizations within the Kerr-Schild type metrics and the algebraically special metrics that highlight the geometrical significance of the class.

• Speaker: Carlos Peón Nieto
• Friday 24 January 2025, 13:00-14:00
• Venue: Potter Room / Zoom link https://cam-ac-uk.zoom.us/j/87235967698.
• Series: DAMTP Friday GR Seminar; organiser: Daniela Cors.

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Abstract not available

• Speaker: Post-doc talks, DAMTP
• Friday 21 February 2025, 15:00-17:00
• Venue: MR2.
• Series: Fluid Mechanics (DAMTP); organiser: Professor Grae Worster.

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The colourful bands of Jupiter are sustained by intense east-west winds called zonal jets, which extend well below Jupiter’s weather layer into its mantle of liquid hydrogen. These jets constitute a fascinating natural example of how a rapidly-rotating turbulent flow self-organises at large scale. Despite decades of observations and modelling, understanding the long-term, nonlinear equilibration of zonal jets and the feedback with the underlying turbulence and waves is still a challenge. In this seminar, I will discuss the dynamics of zonal jets from a wave-mean flow interaction perspective, using a combination of rapidly-rotating laboratory experiments, numerical models and theoretical analyses. I will highlight the essential role of Rossby waves in the emergence and nonlinear saturation of turbulent jets, as demonstrated experimentally and theoretically with a simple quasi-linear model. Following a similar approach as in the Holton-Lindzen-Plumb model for mean flow reversals in stratified fluids, I will extend this quasi-linear analytical model to study jets’ coarsening, and discuss the final scale and amplitude of zonal winds when they are locally versus globally-driven.

• Speaker: Dr Daphné Lemasquerier, University of St Andrews
• Friday 14 March 2025, 16:00-17:00
• Venue: MR2.
• Series: Fluid Mechanics (DAMTP); organiser: Professor Grae Worster.

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Dense granular packings, both dry and suspended in liquid, are among the most abundant materials on earth. They are relevant to manifold geophysical phenomena, e.g., landslides and debris flows, and to industrial processes such as paste extrusion. Understanding their deformation and flow properties is thus of major practical importance. It is also of fundamental interest in statistical physics, fluid mechanics and rheology. Here we use particle simulations to map comprehensively the shear rheology of dry and wet granular matter comprising particles of finite stiffness, in both fixed pressure and fixed volume protocols. At fixed pressure we find nonmonotonic constitutive curves that are shear thinning, whereas at fixed volume we find nonmonotonic constitutive curves that are shear thickening. We show that the presence of one nonmonotonicity does not imply the other. Instead, there exists a signature in the volume fraction measured under fixed pressure that, when present, ensures nonmonotonic constitutive curves at fixed volume. In the context of dry granular flow we show that gradient and vorticity bands arise under fixed pressure and volume respectively, as implied by the constitutive curves. For wet systems our results are consistent with a recent experimental observation of shear thinning at fixed pressure. Reconciling these rich banding dynamics with a detailed mechanistic description accounting also for non-locality and boundary effects remains an open challenge.

• Speaker: Dr Christopher Ness, University of Edinburgh
• Friday 21 March 2025, 16:00-17:00
• Venue: MR2.
• Series: Fluid Mechanics (DAMTP); organiser: Professor Grae Worster.

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A family of k-regular finite graphs is expanding if the graphs are uniformly highly connected. More precisely, for every partition V(X) = A \cup B of the set of vertices of a graph X in the family, the number of edges connecting A and B must be at least c min{|A|, |B|}, where c>0 is independent of X, A and B.

Such families were first constructed by random methods, but explicit constructions were desirable for applications, e.g. for derandomization of algorithms.

Many families of expander graphs have been constructed as Cayley graphs of non-abelian groups G, i.e. taking G itself as the set of vertices, and connecting vertices g and h with an edge if hg^{-1} belongs to a fixed symmetric generating set S of G.

Much care has been taken in choosing the generating sets S, and in some cases this was shown to be necessary. However, our new result shows that for many standard families of groups, every generating set works.

The talk will begin with a gentle introduction to expander graphs.

Based on joint work with Emmanuel Breuillard.

• Speaker: Oren Becker (Cambridge)
• Thursday 30 January 2025, 14:30-15:30
• Venue: MR12.
• Series: Combinatorics Seminar; organiser: ibl10.

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A family of k-regular finite graphs is expanding if the graphs are uniformly highly connected. More precisely, for every partition V(X) = A \cup B of the set of vertices of a graph X in the family, the number of edges connecting A and B must be at least c min{|A|, |B|}, where c>0 is independent of X, A and B.

Such families were first constructed by random methods, but explicit constructions were desirable for applications, e.g. for derandomization of algorithms.

Many families of expander graphs have been constructed as Cayley graphs of non-abelian groups G, i.e. taking G itself as the set of vertices, and connecting vertices g and h with an edge if hg^{-1} belongs to a fixed symmetric generating set S of G.

Much care has been taken in choosing the generating sets S, and in some cases this was shown to be necessary. However, our new result shows that for many standard families of groups, every generating set works.

The talk will begin with a gentle introduction to expander graphs.

Based on joint work with Emmanuel Breuillard.

• Speaker: Oren Becker (Cambridge)
• Thursday 30 January 2025, 14:30-15:30
• Venue: MR12.
• Series: Combinatorics Seminar; organiser: ibl10.

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Arrow’s Theorem tells us that there is no rule for determining the outcome of an election satisfying a series of strong conditions. Eric Maskin proposed relaxing the critical IIA (independence of irrelevant alternatives) condition to allow for more elections, and in particular the Borda rule, where a candidate gets points for every other candidate she beats in every ballot. We exhibit a number of cases where other rules also exist satisfying Maskin’s conditions. In other cases, we prove that only the Borda rule works. We use a satisfying argument from the spectral theory of the Boolean slice.

• Speaker: Gabriel Gendler (Hebrew University, Jerusalem)
• Thursday 27 February 2025, 14:30-15:30
• Venue: MR12.
• Series: Combinatorics Seminar; organiser: ibl10.

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Arrow’s Theorem tells us that there is no rule for determining the outcome of an election satisfying a series of strong conditions. Eric Maskin proposed relaxing the critical IIA (independence of irrelevant alternatives) condition to allow for more elections, and in particular the Borda rule, where a candidate gets points for every other candidate she beats in every ballot. We exhibit a number of cases where other rules also exist satisfying Maskin’s conditions. In other cases, we prove that only the Borda rule works. We use a satisfying argument from the spectral theory of the Boolean slice.

• Speaker: Gabriel Gendler (Hebrew University, Jerusalem)
• Thursday 27 February 2025, 14:30-15:30
• Venue: MR12.
• Series: Combinatorics Seminar; organiser: ibl10.

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