Below are the future seminars organised by the School of Mathematics.
Please note that only some seminar series are advertised here.
Results 351 to 360 of 370
Lie algebras have an interesting relationship with model companions: Whether a given theory has a model companions depends nontrivially on the chosen language and restrictions on the Lie algebras. We will discuss several of these results, and how they can be applied to answer a question of Mennuni.
Martin's Conjecture is a proposed classification of Turing-invariant functions under the Axiom of Determinacy. Whether the classification holds for the ostensibly smaller class of order-preserving functions is open, but more tractable. In this talk, we’ll explain an approach to proving Martin’s Conjecture for order-preserving functions and discuss how far we can go. This is joint work with Patrick Lutz.
The Antarctic Ice Sheet can undergo non-linear dynamics due to the Marine Ice Sheet Instability (MISI). Observations of ocean-driven grounding line retreat in the Amundsen Sea Embayment in Antarctica raise the question of an imminent collapse of the West Antarctic Ice Sheet due to MISI. This would raise global sea levels by more than three metres, impacting coastal regions and communities worldwide. A collapse would be caused by irreversible retreat of the ice sheet’s grounding lines – the positions where the formerly grounded ice starts to float. Here we analyse whether Antarctic grounding lines are undergoing a Marine Ice Sheet Instability in their current position. Furthermore, we investigate the committed evolution of Antarctic grounding lines under present-day ocean and atmospheric conditions and put this into past context, in order to understand the stability of the (West) Antarctic Ice Sheet.
In this talk, I will present a complete classification of finite bijective set-theoretic solutions to the Pentagon Equation, uncovering a surprising connection with matched pairs of groups. We will introduce all necessary definitions, including the notion of irretractable solutions, and explore how these solutions correspond with matched pairs of groups. Finally, I will show how each irretractable solution lifts to provide the full classification of all bijective solutions.
NOTES: extra seminar this week on an unusual day (Friday); no seminar next week.
Unrefinable partitions, arising quite unexpectedly in a combinatorial problem in group theory, represent a special subset of integer partitions into distinct parts, constrained by an additional additive relationship between the parts. Despite being a natural combinatorial object, they remain relatively unexplored in the literature, with only a few known properties and results.
In this talk, we explore the foundational aspects of unrefinable partitions, showing some of their initial properties. We will present an algorithm designed to efficiently test for unrefinability in a given partition. By establishing a bound on the largest part in such partitions, we introduce the concept of maximal unrefinable partitions, a subclass with its own distinctive structure. We will show how to count such maximal unrefinable partitions using explicit bijections, providing a clearer understanding of their combinatorial structure.
Swirling flows induced by the combination of rotation and shear in orthogonal directions are ubiquitous in various natural phenomena, such as tornadoes and tropical cyclones, meandering rivers, vortex rings with swirl, and geophysical and astrophysical flows. These flows also occur in trailing vortices of aircraft wingtips and in branching junctions of everyday piping systems and physiological flows, where identifying instabilities that lead to vortex breakdown is of paramount importance. Swirling flows are present in industrial processes, such as filtration or purification of wastewater, isotope separation through centrifugation, and oil-drilling systems. They are also characteristic of convective flows with rotation, associated with cooling or lubrication of rotating machinery, crystal growth, and solidification of metals.
From a hydrodynamic perspective, the base state of a swirling flow has azimuthal and axial velocity components in either open or confined geometries. The open flow configuration is typical of swirling jets in natural phenomena, while the confined one is more common in engineering. A convenient setup to study swirling flows, both theoretically and experimentally, confines the fluid in a cylindrical annulus with differentially rotating cylinders, creating the classical circular Couette-Taylor flow. The axial component in this setup can be induced by an external pressure gradient, as in Spiral Poiseuille flow (SPF), by sliding inner cylinder, as in Spiral Couette flow (SCF), or by a radial temperature gradient, as in baroclinic Couette flow (BCF).
In this talk I present a universal theory of instabilities in swirling flows, occurring in both natural settings and industrial applications. The theory encompasses a wide range of open and confined flows, including spiral isothermal flows and baroclinic flows driven by radial temperature gradients and natural gravity in rotating fluids. By employing short-wavelength local analysis, the theory generalizes previous findings from numerical simulations and linear stability analyses of specific swirling flows, such as spiral Couette flow, spiral Poiseuille flow, and baroclinic Couette flow. A general criterion, extending and unifying existing criteria for instability to both centrifugal and shear-driven perturbations in swirling flows is derived, taking into account viscosity and thermal diffusion and guiding experimental and numerical investigations in the otherwise inaccessible parameter regimes.
Brauer graph algeras are finite dimensional algebras constructed from the combinatorial data of a graph called a Brauer graph. Kauer proved that derived equivalences of Brauer graph algebras can be obtained from the move of one edge in the corresponding Brauer graph. Moreover, this derived equivalence is entirely described thanks to a tilting object which can be interpreted in terms of silting mutation. In this talk, I will be interested in skew Brauer graph algebras which generalize the class of Brauer graph algebras. These algebras are constructed from the combinatorial data of a Brauer graph where some edges might be "degenerate". I will explain how Kauer's results can be generalized for the move of multiple edges and to the case of skew Brauer graph algebras.
The icy ocean worlds (e.g., Enceladus, Europa) are promising astrobiological targets since they potentially have regions with active water-rock interaction and hydrothermal activity at present-day. However, these habitable environments are typically overlain by a thick (>10 km) ocean and ice shell. Thus, to interpret surface observations, we need to understand the efficiency and the timescale over which fluids and particles get transported from the ocean-- core to the surface. In this study, we use high-resolution (~ 40-80m grid resolution) fluid dynamical simulations to analyze hydrothermal plume dynamics in an icy ocean world context. Our results significantly expand upon previous work by Goodman et al. (2004, 2012) by considering a larger range of: (i) hydrothermal heat fluxes (in particular lower heat fluxes < 100 W/m2 - consistent with estimates from tidal dissipation models), (ii) planetary rotation rates, and (iii) plume latitudes (polar to equatorial). We also consider the possibility of rapid vertical transport by bubble rich plumes.
We find that, in contrast to typical terrestrial hydrothermal plumes, baroclinic eddies play a critical role in the rotational plume dynamics in a deep icy ocean worlds in presence of minimal ocean stratification. The eddies efficiently transport heat laterally away from the vent location on a timescale faster than plume rise timescale. Consequently, a buoyant rotating plume rises much more slowly compared to a non-rotating plume. Using scaling results calibrated with the simulations, we find that the transit time across Enceladus's ocean for highest 1% of hydrothermal plume particles is at least ~ 100 yrs, if not significantly longer. This timescale significantly exceeds the months-to-a-few-years estimate based on a core hydrothermal activity model for silica nanoparticles observed in Enceladus’s plume. Thus, alternative models for silica nanoparticle formation need to be considered given the physical implausibility of fast transit times. Although bubbles can provide additional plume buoyancy, we find that unrealistically large bubbles are needed for rapid across-ocean transit. Our results also have significant implications for interpreting the measured geyser fluid compositions (e.g., methane, hydrogen, CO2) in the context of seafloor habitability.
Henselian valued fields are a class of structures whose model theory has been much investigated. After an introduction to this area, I will present recent joint work with Anscombe and Jahnke in the finitely ramified setting. Prior knowledge of valued fields will not be assumed.
The positive integers that come up in the solutions of the Diophantine equation $x^2+y^2+z^2=3xyz$ are called Markov numbers. They play an important role in the theory of rational expansions and come with a 100+ year old open problem called the Uniqueness conjecture. Recently discovered connections to cluster algebras have revitalized the theory, leading to generalizations and deformations motivated by the cluster model. In this talk, we will use oriented posets to construct a combinatorial model for $q$-deformed Markov numbers. We will also discuss future directions and further avenues of research.