School of Physical Sciences

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.

Add to your calendar or Include in your list

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.

Add to your calendar or Include in your list

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.

Add to your calendar or Include in your list

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.

Add to your calendar or Include in your list

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.

Add to your calendar or Include in your list

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.

Add to your calendar or Include in your list

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.

Add to your calendar or Include in your list

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.

Add to your calendar or Include in your list

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.

Add to your calendar or Include in your list

In this talk I review the hierarchy problem, and I will describe recent progress in understanding the additional constraints that UV/IR mixing places on a theory that may be giving hints as to how it can be solved. As an example that can be treated rigorously, I will consider the UV/IR mixing associated with modular invariance in closed strings, and show that this yields a novel set of supertrace constraints. These constraints are similar to the nonrenormalisation theorems of supersymmetry but they are applicable in full generality. I discuss the various phenomenological consequences that arise including the lack of any power law running, and the apparent UV fixed-point behaviour. The talk will be pedagogical.

• Speaker: Steven Abel (Durham U., IPPP)
• Friday 24 January 2025, 16:00-17:00
• Venue: MR19 (Potter Room, Pavilion B), CMS.
• Series: HEP phenomenology joint Cavendish-DAMTP seminar; organiser: Terry Generet.

Add to your calendar or Include in your list

I will discuss three recent combinatorial theorems about hyperplane arrangements: the top-heavy conjecture, log concavity of the characteristic polynomial, and non-negativity of the Kazhdan-Lusztig polynomial. Each of these results is proved by studying the cohomology of a projective algebraic variety associated with the arrangement.

• Speaker: Nicholas Proudfoot, University of Oregon
• Wednesday 19 March 2025, 14:15-15:15
• Venue: CMS MR13.
• Series: Algebraic Geometry Seminar; organiser: Dhruv Ranganathan.

Add to your calendar or Include in your list

Abstract not available

• Speaker: Nicholas Proudfoot, University of Oregon
• Wednesday 19 March 2025, 14:15-15:15
• Venue: CMS MR13.
• Series: Algebraic Geometry Seminar; organiser: Dhruv Ranganathan.

Add to your calendar or Include in your list

The geometry, topology and intersection theory of moduli spaces of stable vector bundles on curves have been topics of interest for more than 50 years. In the 90s, Jeffrey and Kirwan managed to prove a formula proposed by Witten for the intersection numbers of tautological classes on such moduli spaces. In this talk, I will explain a different way to calculate those numbers and, more generally, intersection numbers on moduli of parabolic bundles. Enriching the problem with a parabolic structure gives access to powerful tools, such as wall-crossing, Hecke transforms and Weyl symmetry. If time allows, I will explain how this approach gives a new proof of (a generalization to the parabolic setting of) a vanishing result conjectured by Newstead and proven by Earl and Kirwan.

• Speaker: Miguel Moreira, MIT
• Wednesday 29 January 2025, 14:15-15:15
• Venue: CMS MR13.
• Series: Algebraic Geometry Seminar; organiser: Dhruv Ranganathan.

Add to your calendar or Include in your list

Abstract not available

• Speaker: Juan Cruz-Martinez (CERN)
• Friday 21 March 2025, 16:00-17:00
• Venue: MR19 (Potter Room, Pavilion B), CMS.
• Series: HEP phenomenology joint Cavendish-DAMTP seminar; organiser: Terry Generet.

Add to your calendar or Include in your list

Abstract not available

• Speaker: Steven Abel (Durham U., IPPP)
• Friday 24 January 2025, 16:00-17:00
• Venue: MR19 (Potter Room, Pavilion B), CMS.
• Series: HEP phenomenology joint Cavendish-DAMTP seminar; organiser: Terry Generet.

Add to your calendar or Include in your list

The modern study of knots and links has important roots in the theory of algebraic curves, where links encode subtle features of singularities. The interaction between links in 3-dimensional manifolds and algebraic curves in complex surfaces continues to be a rich source of interesting mathematics. In this talk I will survey the subject, from its seeds in the work of Newton to advances which have occurred in the past decade.

• Speaker: Matthew Hedden (Michigan State University)
• Wednesday 29 January 2025, 16:00-17:00
• Venue: MR13.
• Series: Differential Geometry and Topology Seminar; organiser: Oscar Randal-Williams.

Add to your calendar or Include in your list

The modern study of knots and links has important roots in the theory of algebraic curves, where links encode subtle features of singularities. The interaction between links in 3-dimensional manifolds and algebraic curves in complex surfaces continues to be a rich source of interesting mathematics. In this talk I will survey the subject, from its seeds in the work of Newton to advances which have occurred in the past decade.

• Speaker: Matthew Hedden (Michigan State University)
• Wednesday 22 January 2025, 16:00-17:00
• Venue: MR13.
• Series: Differential Geometry and Topology Seminar; organiser: Oscar Randal-Williams.

Add to your calendar or Include in your list

Self-assembly, a spontaneous process driven by thermal agitation and intermolecular interactions, is crucial for the formation and folding of complex macromolecules, with profound implications for chemistry and biology. While extensively studied at the molecular level, capillary-driven self-assembly has emerged as a promising approach for constructing structures at the mesoscopic scale, bridging the gap between classical bottom-up and top-down fabrication methods. Operating between 10 micrometers to 10 millimeters, this approach has, over two decades, largely produced regular or simplistic structures. This work leverages experimental and statistical physics to unveil methodologies for controlling subtle capillary interactions, enabling the design of intricate and highly complex structures. We demonstrate how these mesoscopic systems act as analogs for molecular phenomena, such as folding, lock-and-key mechanisms, and crystallization processes. Furthermore, by incorporating magnetic actuation, we explore the dynamic self-assembly of functional micromachines. These micromachines present potential applications in interface cleaning, particle sorting, and targeted transport, underscoring the transformative possibilities of capillary-driven systems for soft robotics and materials science.

• Speaker: Professor Nicolas Vandewalle, University of Liège
• Friday 31 January 2025, 16:00-17:00
• Venue: MR2.
• Series: Fluid Mechanics (DAMTP); organiser: Professor Grae Worster.

Add to your calendar or Include in your list

Lubrication theory is adapted to incorporate the large normal stresses that occur for order-one Deborah numbers, $De$, the ratio of the relaxation time to the residence time.

Comparing with the pressure drop for a Newtonian viscous fluid with a viscosity equal to that of an Oldroyd-B fluid in steady simple shear, we find numerically a reduced pressure drop through a contraction and an increased pressure drop through an expansion, both changing linearly with $De$ at high $De$. For a constriction there is a smaller pressure drop that plateaus at high $De$. Much of the change in pressure drop occurs in the stress relaxation in a long exit channel.

An asymptotic analysis for high $De$, based on the idea that normal stresses are stretched by an accelerating flow in proportion to the square of the velocity, reveals that the large linear changes in pressure drop are due to higher normal stresses pulling the fluid through the narrowest gap. A secondary cause of the reduction is that the elastic shear stresses do not have time to build up to their steady state equilibrium value while they accelerate through a contraction.

And experiments find differently!

• Speaker: Professor John Hinch, DAMTP
• Friday 28 February 2025, 16:00-17:00
• Venue: MR2.
• Series: Fluid Mechanics (DAMTP); organiser: Professor Grae Worster.

Add to your calendar or Include in your list

I’ll be giving a broad overview of the decision procedures we have been building for bitvector reasoning in Lean, with both fixed and infinite width. Time permitting, I shall sketch the design and mechanization strategy of the infinite width decision procedure, since the core involves verifying a cute model checking algorithm (k-induction), with games to be played to hook in a SAT solver into the tactic loop.

Note: work done in collaboration with the wider Lean community, and effort led by the Lean FRO : Henrik Boving, Kim Morrison, and Leo de Moura.

=== Hybrid talk ===

Join Zoom Meeting https://cam-ac-uk.zoom.us/j/87143365195?pwd=SELTNkOcfVrIE1IppYCsbooOVqenzI.1

Meeting ID: 871 4336 5195

Passcode: 541180

• Speaker: Siddharth Bhat (University of Cambridge)
• Thursday 23 January 2025, 17:00-18:00
• Venue: MR14 Centre for Mathematical Sciences.
• Series: Formalisation of mathematics with interactive theorem provers ; organiser: Anand Rao Tadipatri.

Add to your calendar or Include in your list