Below are the future seminars organised by the School of Mathematics.
Please note that only some seminar series are advertised here.
Results 301 to 310 of 370
No! (Okay, it’s slightly more complicated than that). Inspired by a recent expository paper on arXiv of the same name, my talk will give the necessary set theoretic background to consider questions about the independence of measurability of certain functions from ZFC. If time permits, I’ll give further results using large cardinal assumptions and in the context of o-minimality.
Assuming X is a random vector and A a non-invertible matrix, one sometimes need to perform inference while only having access to samples of Y=AX. The corresponding likelihood is typically intractable. One may still be able to perform exact Bayesian inference using a pseudo-marginal sampler, but this requires an unbiased estimator of the intractable likelihood. We propose saddlepoint Monte Carlo, a method for obtaining an unbiased estimate of the density of Y with very low variance, for any model belonging to an exponential family. Our method relies on importance sampling and characteristic functions, with insights brought by the standard saddlepoint approximation scheme with exponential tilting. We show that saddlepoint Monte Carlo makes it possible to perform exact inference on particularly challenging problems and datasets. We focus on the ecological inference problem, where one observes only aggregates at a fine level. We present in particular a study of the carryover of votes between the two rounds of various French elections, using the finest available data (number of votes for each candidate in about 60,000 polling stations over most of the French territory).
Joint work with Théo Voldoire, Nicolas Chopin, and Guillaume Rateau. Preprint: https://arxiv.org/abs/2410.18243
In this talk, I will show how the theory of rough stochastic differential equations (rough SDEs) — introduced by Friz, Hocquet, and Lê in 2021 — helps to establish the existence, uniqueness, or smoothness of solutions to certain rough partial differential equations (rough PDEs).
A key motivation comes from stochastic filtering, where the Zakai equation, an SPDE describing the unnormalized conditional density, can be reformulated as a rough PDE using rough path theory.
I will present results from [1], where we develop a solution theory for linear rough PDEs and derive a Feynman–Kac-type representation via rough SDEs. If time permits, I will briefly discuss how we extend Hörmander’s theory to the rough setting in [2] using Malliavin calculus.
[1] F.B., Peter K. Friz, Wilhelm Stannat, Parameter dependent rough SDEs with applications to rough PDEs, 2024 (arXiv:2409.11330)
[2] F.B., Michele Coghi, Torstein K. Nilssen, Malliavin calculus for rough stochastic differential equations, 2024 (arXiv:2402.12056)
Impacts by icy bodies likely played a key role in shaping the composition of solar systems objects, including the Earth's habitability. Hence, it is likely that they play a similar role in exoplanetary systems. Here I discuss how an impact from a comet affects the atmospheric chemistry, climate, and composition of two Earth-like terrestrial exoplanets with differing orbital configurations: a short (6 days), tidally-locked, orbit and an Earth-analogue orbit with a diurnal cycle.
To investigate this, I coupled a cometary impact model, which includes thermal ablation and pressure-drive breakup, with the 3D Earth-System-Model WACCM6/CESM2, quantifying the impact of a 2.5 km radius pure water ice comet. This revealed how both the impact-delivered water and thermal energy together affect the planetary atmosphere, including changing i) the cloud greenhouse effect, ii) the planetary albedo, iii) and the overall atmospheric composition. For the latter, we generally find an increase in the abundance of oxygen-bearing molecules with one key exception: ozone, the abundance of which is highly sensitive to products of the photodissociation of water, e.g OH.
My models also revealed how the response of the planetary atmosphere to the impact is shaped by the orbital configuration, and hence circulation regime of the planet. I find that the global atmospheric circulation may play a key role in setting the potential observability of individual massive impacts in future observations of exo-Earths. On the other hand, longer term changes to atmospheric composition appear less sensitive to orbital configuration, suggesting that sustained bombardment, or multiple large impacts, have the potential to measurably change the composition, and hence the habitability, of terrestrial exo-Earths.
In summary we find that cometary impacts may play an important role in shaping terrestrial exoplanetary atmospheres, and that to fully understand their impact we must also understand the underlying atmosphere they interact with.
Dependent Choice (DC) is one the most useful choice principles with many equivalents (including the Downward Löwenheim–Skolem and the Baire Category Theorem). When we violate the Axiom of Choice via symmetric extensions we often want to preserve at least that much. In this talk we will discuss a few older results about the preservation of DC in generic and symmetric extensions, and we will present a recent breakthrough from a work-in-progress with Jonathan Schilhan.
Chalk and talk.
An opportunity to meet and discuss research ideas.
Dependent Choice (DC) is one the most useful choice principles with many equivalents (including the Downward Löwenheim–Skolem and the Baire Category Theorem). When we violate the Axiom of Choice via symmetric extensions we often want to preserve at least that much. In this talk we will discuss a few older results about the preservation of DC in generic and symmetric extensions, and we will present a recent breakthrough from a work-in-progress with Jonathan Schilhan.
The open core of a structure is the reduct generated by the open definable sets. Tame topological structures (e.g. o-minimal) are inter-definable with their open core. Structures such as M = (ℝ, <, +, ℚ) are wild in the sense that they define a dense co-dense set. Still, M is NIP and its open core is o-minimal. In this talk we push forward the thesis that the open core of an NTP2 (a generalization of NIP) topological structure is tame. Our main result is that, under suitable conditions, the open core has quantifier elimination, and its definable functions are generically continuous.
Nearly Kähler manifolds are Riemannian 6-manifolds admitting real Killing spinors. They are the cross-sections of Riemannian cones with holonomy G2. Like the Einstein equation, the nearly Kähler condition has a variational interpretation in terms of volume functionals, first introduced by Hitchin in 2001.
The existence problem for nearly Kähler manifolds is poorly understood, and the only currently known inhomogeneous examples were found in 2017 by Foscolo and Haskins using cohomogeneity one methods. For one of their examples, we establish non-trivial bounds on the coindex of the Hitchin-type and Einstein functionals. We do this by analysing the eigenvalue problem for the Laplacian on coclosed primitive (1,1)-forms under a cohomogeneity-one symmetry assumption.
Fundamental to the practice of logic is the dogma regarding the first order/second order logic distinction, namely that it is ironclad. Was it always so? The emergence of the set theoretic paradigm is an interesting test case. Early workers in foundations generally used higher order systems in the form of type theory; but then higher order systems were gradually abandoned in favor of first order set theory—a transition that was completed, more or less, by the 1930s.
As for logic in general, the concept of a logic being first order is not only about whether the variables range over the elements of a given domain, or over sets of elements, or over sets of sets of elements, and so on; it is also, I suggest, about the context.
Of course, set theory is a theory and second order logic is a logic, at least that is the common understanding. However if one cares to view set theory as a logic—and if we do think of set theory as a logic, it is a logic with the cumulative hierarchy 𝑉 as its standard (class) model—then set theory turns out to be a stronger logic than second order logic. This is perhaps as it should be, given that the latter restricts the domain of quantifiable objects to those generated by (at most) a single iteration of the power set operation, while set theory allows for arbitrary iterations of the power set operation.
This talk is based on the forthcoming paper "How first order is first order logic?" by J. Kennedy and Jouko Väänänen for The Oxford Handbook of Philosophy of Logic. Editors: Elke Brendel, Massimiliano Carrara, Filippo Ferrari, Ole Hjortland, Gil Sagi, Gila Sher, Florian Steinberger, Oxford University Press.