Angus Matthews (University of Leeds) – Exponential polynomials by algebraic methods
We will discuss how Chow varieties can be used to control the large-scale behaviour of certain systems of exponential polynomials. This is a work-in-progress talk.
Seminars
Below are the future seminars organised by the School of Mathematics.
Please note that only some seminar series are advertised here.
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Results 41 to 50 of 370
Ivan Miranda de Almeida (IMPA, Brazil) – On the existence of non-compact CMC hypersurfaces with finite index
Let $X$ be a six-dimensional Riemannian manifold with nonnegative sectional curvature that is a Riemannian product of a closed manifold with an Euclidean factor. We prove that every complete, finite index, non-minimal CMC hypersurface immersed in $X$ is compact. This answers affirmatively a question of do Carmo for this class of ambient Riemannian spaces, extending known lower dimensional results.
As a consequence, we complete the classification of two-sided, complete weakly stable CMC hypersurfaces immersed in the space forms of positive curvature in dimension six.
We also show that a complete, finite index CMC hypersurface immersed in the hyperbolic space $\mathbb{H}^6$ with mean curvature $|H|>7$ is compact. This gives a partial answer to a question posed by Chodosh in his survey for the ICM.
Dicle Mutlu Sozer (University of Leeds) – Types and Definable Groups in Henselian Valued Fields
Henselian valued fields have a central place in model theory: they provide natural examples of tame theories in the sense of classification theory, while also offering a rich setting in which to study complexity phenomena in model theory. In this talk, I will survey some fundamental model-theoretic results on Henselian valued fields and present new results from joint work with Paul Wang, in which we generalize results from the algebraically closed valued field setting to the broader Henselian context.
Fernando Mendez Mendez (University of Leeds) – An Introduction to Frobenius Lie Algebras
Abstract: In 1968, N. Jacobson proposed the problem of characterizing finite-dimensional Lie algebras that have a primitive universal enveloping algebra. Later, in 1976, A. Ooms demonstrated that these can be characterized exactly as Frobenius Lie algebras. In this talk, I will provide an introduction to this class of Lie algebras. We will discuss their fundamental properties and explore their connections with other algebraic structures, such as contact Lie algebras and pre-Lie structures.
Duncan Lee (University of Glasgow) – A spatial random forest algorithm for population-level epidemiological risk assessment
A key objective in spatial epidemiology is to identify the drivers of elevated disease risks at a population level, using non-overlapping areal unit level data that comprise the total numbers of disease cases, exposures of interest and known confounders. The spatial pattern in disease risk is likely to be influenced by unmeasured confounders, whose omission induces spatial autocorrelation into the residuals from the chosen epidemiological model. A Poisson log-linear model fitted in a Bayesian paradigm is typically used for inference, which incorporates the known confounders with a linear or additive regression component and the unmeasured confounders via a set of spatially autocorrelated random effects. While such a model correctly allows for the inherent autocorrelation in the data, confounder interactions and the shapes of their functional relationships with disease risk have to be specified in advance rather than being directly learned from the data. Therefore this paper proposes the SPAR-Forest-ERF algorithm for population-level epidemiological risk assessment, which is the first fusion in this context of random forests for capturing non-linear and interacting confounder-response effects with Bayesian spatial autocorrelation models that can estimate interpretable exposure response functions (ERF) with full uncertainty quantification. Methodologically, we extend existing methods set in a prediction context by correctly propagating uncertainty between both the ML and statistical models, developing a new stopping criteria designed to ensure the stability of the primary inferential target, and incorporating a range of different ERFs for maximum model flexibility. This methodology is motivated by a new study of the impact of air pollution concentrations on self-rated health in Scotland, using data from the recently released 2022 national census.
Ruby Nixson (University of Oxford) – Parameter Identifiability Under Limited Experimental Data in Age-Structured Models of the Cell Cycle
NOTES: unusual hour, etc (remove this line if not necessary).
The mitotic cell cycle governs DNA replication and cell division. The effectiveness of radiotherapy and chemotherapy depends on cell-cycle position, with increased resistance during DNA replication and mitosis. Thus, accurate mathematical models of the cell cycle are essential for understanding and predicting treatment response. However, mathematical modellers often face the problem of a lack of publicly available, sufficiently resolved, time-series datasets for parametrising models. In this work, we consider how the ability to collate population summary measurements across the literature, from different cell lines and/or experimental set ups, affects identifiability of parameters for a cell cycle model.
Initially synchronised cell populations gradually desynchronise over successive cycles, converging to balanced exponential growth (BEG) which is characterised by exponential population growth and steady, time-independent phase proportions. These proportions can be obtained from fluorescence-activated cell sorting (FACS) data. The increasing use of the Fluorescent Ubiquitination-based Cell Cycle Indicator (FUCCI) provides higher-resolution information on phase dynamics, such as minimum phase durations and variability.
We present an age-structured PDE model in which cell-cycle phase progression follows a delayed gamma distribution. We derive analytical expressions for BEG phase proportions and other FUCCI-observable quantities, and use them to assess how data availability influences parameter identifiability. When parameters are not uniquely identifiable, we determine identifiable parameter groupings, thereby determining the minimum amount of data that must be available for successfully fitting structured population models of the cell cycle.
Çağın Ararat (University of Leeds) – Superhedging under Proportional Transaction Costs in Continuous Time
We revisit the well-studied superhedging problem under proportional transaction costs in continuous time using the recently developed tools of set-valued stochastic analysis. By relying on a simple Black-Scholes-type market model for mid-prices and using continuous trading schemes, we define a dynamic family of superhedging sets in continuous time and express them in terms of set-valued integrals. We show that these sets, defined as subsets of Lebesgue spaces at different times, form a dynamic set-valued risk measure with multi-portfolio time-consistency. Finally, we transfer the problem formulation to a path-space setting and introduce approximate versions of superhedging sets that will involve relaxing the superhedging inequality, the superhedging probability, and the solvency requirement for the superhedging strategy with a predetermined error level. In this more technical framework, we are able to relate the approximate superhedging sets at different times by means of a set-valued Bellman’s principle. We conjecture that this pathwise principle can be used to obtain a set-valued differential structure that characterizes the superhedging sets. Joint work with Atiqah Almuzaini and Jin Ma.
Kevin Houston (University of Leeds) – How to Tell the Public About Your Research Without Losing Them
NOTES: Unusual Location.
Explaining your research to other specialists is hard enough. Explaining it to the general public -- people who may not share your enthusiasm for notation, definitions, and carefully stated lemmas -- can be even more challenging. Yet public engagement is an important part of academic life, and mathematicians now have many opportunities to share their work beyond the university.
In this talk I’ll discuss practical ways to tell the public about your research without losing them somewhere around the first equation. We’ll look at how to find the hook in your work, how to replace technical detail with intuition and examples, and how to turn abstract mathematics into something people can actually picture.
Ideally, by the end you’ll have a few techniques for explaining your research to non-mathematicians -- whether in a public lecture, an article, or when someone innocently asks what you do.
Timothy Moy (University of Cambridge) – Joyce structures from quadratic differentials on the sphere
Let M be a moduli space of quadratic differentials on the sphere with poles of fixed odd orders. Such a space has a concrete realisation as a space of rational functions. In this talk, I will explain an elementary construction that gives rise to a meromorphic hyper-Kähler metric on the algebraic torus bundle that is the quotient of TM by the natural period lattice. We will meet the theory of isomonodromic deformations, the geometry of Riemann surfaces and, crucially, twistor theory. All of this is motivated by the wall-crossing behaviour of Donaldson-Thomas invariants under the variation of Bridgeland stability conditions but the technical prerequisites to understand this particular construction should be minimal. This talk is partly based on joint work with Maciej Dunajski.
Erik Walsberg (University of Vienna) – The model theory of large fields
NOTES: Unusual time 16:00. Part of workshop on "Tame Geometry and Combinatorics".
Large fields are an interesting class of fields first introduced by Pop in the 90's for Galois-theoretic reasons. They have subsequently been studied for a variety of reasons. As logicians we are interested in large fields because essentially all known logically tame fields are large. I will discuss recent work on the model theory of large fields, joint with Will Johnson, Chieu-Minh Tran, and Jinhe Ye. Only minimal background in algebra will be assumed.