School of Physical Sciences

Inspired by the classical Poincaré and Korn inequalities in analysis, the “Poincaré-Korn” inequalities were introduced in 2020 by Carrapatoso et al. In that paper, the authors conjectured that among a suitable class of reference measures, the standard Gaussian measure uniquely achieves the smallest sharp constant in the Poincaré-Korn inequality. In this talk, I’ll establish a quantitative stability result for the Poincaré-Korn inequalities, affirmatively resolving the question by Carrapatoso et al. The argument involves a combination of Stein’s method and variational techniques. Time permitting, I’ll also mention recent work on stability of Klartag’s improved Lichnerowicz bound, which is one of the main ingredients behind current best-progress on the KLS conjecture. Everything is joint work with Max Fathi.

• Speaker: Prof Thomas Courtade, UC Berkeley
• Wednesday 08 May 2024, 14:00-15:00
• Venue: MR5, CMS Pavilion A.
• Series: Information Theory Seminar; organiser: Dr Varun Jog.

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In this talk, we discuss a notion of exact solution of the Wiener–Hopf factorisation problem for matrix polynomials. By the exact solution, we understand the fulfilment of the following two conditions: 1) the input data belongs to the Gaussian field Q(i) of complex rational numbers and 2) all (finite) steps of the explicit algorithm can be performed in the rational arithmetic. Since the factorisation is generally speaking unstable with respect to small perturbation, those requirements are crucial to guarantee that the instability issue does not arise. Unfortunately, even the conditions 1) – 2) are not sufficient for the exact solution to exist. We have proven the following necessary and sufficient condition: a matrix polynomial over the field of Gaussian rational numbers admits the exact Wiener–Hopf factorisation if and only if its determinant is exactly factorable. For the factorisation, we use the explicit algorithm based on the method of essential polynomials. It has been proven already its efficiency (it provides both left and right factorisation simultaneously) but is rather technical. To help possible users, we develop its realisation within an ExactMPF package in Maple Software. We illustrate its performance presenting several examples.

WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method

• Speaker: Natalia Adukova (Aberystwyth University)
• Friday 05 July 2024, 14:00-14:30
• Venue: Seminar Room 1, Newton Institute.
• Series: Isaac Newton Institute Seminar Series; organiser: nobody.

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ADIW03 - Climate Applications of Layering

• Speaker: Leif Thomas (Stanford University)
• Thursday 23 May 2024, 14:00-15:00
• Venue: Seminar Room 1, Newton Institute.
• Series: Isaac Newton Institute Seminar Series; organiser: nobody.

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Abstract not available

• Speaker: Mark Whitehead (Glasgow)
• Tuesday 14 May 2024, 11:00-12:00
• Venue: Ryle Seminar Room.
• Series: Cavendish HEP Seminars; organiser: Dr Steve Dennis.

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Abstract not available

• Speaker: Mark Whitehead (Glasgow)
• Tuesday 14 May 2024, 11:00-12:00
• Venue: Ryle Seminar Room.
• Series: Cavendish HEP Seminars; organiser: Dr Steve Dennis.

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Abstract: We study the deformation theory of Hilbert schemes of points on surfaces by looking more broadly at the deformation theory of their derived categories, which is controlled by the Hochschild cohomology. In this way, we recover, unify, and extend the previous works of Fantechi, Hitchin, and Boissière. One interesting finding is that the Hochschild cohomology of a Hilbert scheme of a surface not only depends on that of the surface, but also on the more generally bigraded cohomology theory called Hochschild-Serre cohomology of the surface. Our method computes the Hochschild-Serre cohomology of the symmetric stack [X^n/S_n] in terms of the Hochschild-Serre cohomology of X. This is based on a joint work with Pieter Belmans and Andreas Krug, arXiv:2309.06244.

• Speaker: Lie Fu (University of Strasbourg)
• Tuesday 07 May 2024, 10:00-11:00
• Venue: Seminar Room 1, Newton Institute.
• Series: Isaac Newton Institute Seminar Series; organiser: nobody.

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Heat and particle transport across the nested magnetic surfaces of tokamak plasmas is mainly governed by turbulence. Several underlying instabilities coexist, but the most virulent bear similarity with the Rayleigh-Bénard instability in neutral fluids. In addition, drift waves are also present, the plasma analogue of Rossby waves in rotating atmospheric turbulence. Sheared flows efficiently contribute to their saturation. As will be shown, turbulence self-organization in magnetized plasmas tends to develop localized regions of shear flow layers with fronts propagating in between. This results in the local storage of turbulent energy into corrugations, leading to a staircase pattern of the pressure profile. The segregation of these complementary structures – fronts and layers – is believed to be key to the achieve good confinement properties. One of the issues deals with their possible role in triggering bifurcations towards the macroscopic transport barriers which are observed experimentally. By means of a reduced flux driven nonlinear model that captures “fluctuations – mean” interactions, we explore some of the characteristics of layering and transport. Layering dynamics turns out to depend on the turbulent regime. Flow layer nucleation will be shown to involve phase curvature dynamics and to require the positive feedback loop with the pressure profile. Implications will be discussed.

ADI - Anti-diffusive dynamics: from sub-cellular to astrophysical scales

• Speaker: Yanick Sarazin (CEA, Cadarache)
• Tuesday 07 May 2024, 11:30-12:30
• Venue: Seminar Room 1, Newton Institute.
• Series: Isaac Newton Institute Seminar Series; organiser: nobody.

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Dark matter below electronvolt masses remains strikingly unexplored. Axions and dark photons are sought-after targets requiring unconventional techniques for direct detection. Traditional cavity haloscopes decisively probe microwave frequencies but face longstanding obstructions at higher masses. This motivates novel instrumentation including the Broadband Reflector Experiment for Axion Detection (BREAD). BREAD recently pioneered its first science results with pilot runs at Chicago surpassing astrophysical bounds on dark photons by two orders of magnitude. This milestone using just one month of room-temperature data opens a new dark matter discovery program bridging astroparticle physics with quantum technology.

• Speaker: Dr Jesse Liu (University of Cambridge)
• Tuesday 07 May 2024, 11:00-12:00
• Venue: Ryle Seminar Room.
• Series: Cavendish HEP Seminars; organiser: Dr Bill Balunas.

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This talk will discuss the component of the K-moduli space of Fano threefolds of anticanonical degree 24 associated to smooth divisors of multidegree (1,1,1,1) in a product of four projective lines.    This is joint work with Ivan Cheltsov, Maksym Fedorchuk and Kento Fujita.   

EMGW04 - K-stability and moment maps

• Speaker: Anne-Sophie Kaloghiros (Brunel University)
• Thursday 16 May 2024, 11:45-12:45
• Venue: Seminar Room 1, Newton Institute.
• Series: Isaac Newton Institute Seminar Series; organiser: nobody.

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Given a closed hyperbolic manifold M, are there lower bounds on the number of k-cells c_k(M) in a cell decomposition in terms of the geometry of the manifold? Gromov showed that if the manifold has injectivity radius at least 10^6 times (n log n), then there are at least n 1-cells, and conjectured that injectivity radius const times log n should be enough. In this talk I will describe a result providing a lower bound on the number of k-cells for each 0 < k < dim (M). The main input is a freedom theorem for ideals in group rings of hyperbolic groups, which also has other applications. Joint work with Thomas Delzant.

• Speaker: Grigori Avramidi (MPIM)
• Wednesday 08 May 2024, 16:00-17:00
• Venue: MR13.
• Series: Differential Geometry and Topology Seminar; organiser: Oscar Randal-Williams.

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The Cosmic Dawn marks the first star formations and preceded the Epoch-of-Reionization, when the Universe underwent a fundamental transformation propelled by the radiation from these first stars and galaxies. Interferometric 21-cm experiments aim to probe redshifted neutral hydrogen signals from these periods, constraining the conditions of the early Universe. The SKA -LOW instrument of the Square Kilometre Array telescope is envisaged to be the largest and most sensitive radio telescope at m and cm wavelengths. In this talk we present a full SKA pipeline that consist of forward modelling and data analysis that were also tested in the SKA Science Data Challenge 3a: Epoch of Reionisation (SKA SDC3a) to process the novel data products expected from the SKA . The forward modelling enables simulation of the astrophysical signals from the Epoch of Reionization and chosen systematic effects of the SKA -LOW. In the analysis part we implement predictive foreground and Bayesian Gaussian Process Regression models alongside a foreground avoidance strategy to isolate the 21-cm signal from that of the astrophysical radio frequency (RF) foregrounds. Together these will determine whether a successful 21-cm detection is possible with the envisaged SKA .

• Speaker: Yuchen Liu and Oscar O'Hara (Cavendish Astrophysics)
• Tuesday 07 May 2024, 11:15-12:00
• Venue: Coffee area, Battcock Centre.
• Series: Hills Coffee Talks; organiser: Charles Walker.

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(Joint with Ziquan Zhuang) The concept of local volume of a klt singularity, which is the infimum of normalized volumes of all valuations centered at the singularity, plays a central role in the local stability theory. The Stable Degeneration Theorem says any klt singularity admits a volume preserved degeneration to a K-semistable log Fano cone singularity. In this talk, I will show that all K-semistable log Fano cone singularities with volume bounded from below are bounded. As a consequence, this implies that the set of normalized volumes of all klt singularities has 0 as its only accumulation point.  

EMGW04 - K-stability and moment maps

• Speaker: Chenyang Xu (Princeton University)
• Friday 17 May 2024, 11:45-12:45
• Venue: Seminar Room 1, Newton Institute.
• Series: Isaac Newton Institute Seminar Series; organiser: nobody.

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In this talk, we construct Kaehler metrics with constant scalar curvature on the projectivisation of certain holomorphic vector bundles. When the vector bundle is slope-stable and the base admits a constant scalar curvature metric, it is a classical result of Hong that the total space of the projectivisation admits a constant scalar curvature metric in adiabatic classes. We extend their result to slope-semistable vector bundles: we show that if E → B is slope-semistable and the total space of the projectivisation is K-polystable then it admits a constant scalar curvature metric in adiabatic classes. This is joint work with L.M. Sektnan.

EMGW04 - K-stability and moment maps

• Speaker: Annamaria Ortu (Göteborgs Universitet)
• Monday 13 May 2024, 11:45-12:45
• Venue: Seminar Room 1, Newton Institute.
• Series: Isaac Newton Institute Seminar Series; organiser: nobody.

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Consider a crowd sourcing problem where we have n experts and d tasks. The average ability of each expert for each task is stored in an unknown matrix M, from which we have incomplete and noise observations. We make no (semi) parametric assumptions, but assume that the experts can be perfectly ordered: so that if an expert A is better than an expert B, the ability of A is higher than that of B for all tasks. We either assume the same for the task, or not, depending on the scenario. This implies that if the matrix M, up to permutations of its rows and columns, is either isotonic, or bi-isotonic.

We focus on the problem of recovering the optimal ranking of the experts and/or of the tasks, in l2 norm. We will consider this problem with some side-information — i.e. when the ordering of the tasks (if it exists) is known to the statistician – or not. In other words, we aim at estimating the suitable permutation of the rows of M. We provide a minimax-optimal and computationally feasible method for this problem in three scenarios of increasing difficulty: known order of the task, unknown order of the tasks, no order of the tasks. The algorithms we provide are based on hierarchical clustering, PCA , change-point detection, and exchange of informations among the clusters.

This talk is based on a joint ongoing work with Emmanuel Pilliat, Maximilian Graf and Nicolas Verzelen.

• Speaker: Alexandra Carpentier, University of Potsdam
• Friday 17 May 2024, 14:00-15:00
• Venue: MR12, Centre for Mathematical Sciences.
• Series: Statistics; organiser: Dr Sergio Bacallado.

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WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method

• Speaker: Grigori Giorgadze (Tbilisi State University), Samaneh Moeini (INL- International Iberian Nanotechnology Laboratory), Stanislav Maslovski (Universidade de Aveiro), Kseniia Kniazeva (Moscow State University), Yu Fu (Aberystwyth University)
• Monday 01 July 2024, 15:30-16:30
• Venue: Seminar Room 1, Newton Institute.
• Series: Isaac Newton Institute Seminar Series; organiser: nobody.

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It is well known that solvability of the complex Monge- Ampere (CMA) equation on compact Kaehler manifolds is related to the positivity of certain intersection numbers. In fact, this follows from combining Yau’s resolution of the Calabi conjecture, with Demailly and Paun’s generalization of the classical Nakai-Mozhesoin criteria. This correspondence was recently extended to a broad class of complex non-linear PDEs including the J-equation and the deformed Hermitian-Yang-Mills (dHYM) equations by the work of Gao Chen and others. A natural question to ask is whether solutions (necessarily singular) exist in any reasonable sense if the Nakai criteria fails. A motivating example is that of CMA equations in big classes. In this talk, I will provide an overview of a program for constructing such singular solutions for the J equation and the dHYM equations, and state some conjectures and problems. Analogous to the characterization of volumes of big classes, a key point is to define a minimal slope using birational models. Finally, I will outline how to resolve some of these questions on Kahler surfaces and some manifolds with large symmetry groups. This is joint work with Ramesh Mete and Jian Song. 

EMGW04 - K-stability and moment maps

• Speaker: Ved Datar (Indian Institute of Science)
• Wednesday 15 May 2024, 10:15-11:15
• Venue: Seminar Room 1, Newton Institute.
• Series: Isaac Newton Institute Seminar Series; organiser: nobody.

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In my talk I will discuss the notion of normalised volume for singularities. For the special case of toric singularities this turns out to be closely related to the notions of Mahler volume and Santaló point in convex geometry. I will explain how well-known facts from convex geometry can be utilised to deduce non-trivial statements about toric singularities. I will also speculate about algebro-geometric interpretations of the well-known Mahler conjecture in convex geometry. This is joint work with Joaquín Moraga.

EMGW04 - K-stability and moment maps

• Speaker: Hendrik Süß (Friedrich-Schiller-Universität Jena)
• Thursday 16 May 2024, 15:30-16:30
• Venue: Seminar Room 1, Newton Institute.
• Series: Isaac Newton Institute Seminar Series; organiser: nobody.

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Many approaches to machine learning have struggled with applications that possess complex process dynamics. In contrast, human intelligence is adapted, and – arguably – built to deal with complex dynamics. The current theory holds that human brain achieves that by constantly rebuilding a model of the world based on the feedback it receives. I will describe an approach to machine learning of dynamical systems based on Koopman Operator Theory (KOT) that also produces generative, predictive, context-aware models amenable to (feedback) control applications. KOT has deep mathematical roots and I will discuss its basic tenets. I will also present computational methods that enable lean computation. A number of examples will be discussed, including use in fluid dynamics, soft robotics, and game dynamics.

• Speaker: Igor Mezic, UC Santa Barbara
• Friday 10 May 2024, 16:00-17:00
• Venue: MR2.
• Series: Fluid Mechanics (DAMTP); organiser: Professor Grae Worster.

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Condensed sets form a topos, and hence admit an internal type theory. In this talk I will describe a list of axioms satisfied by this particular type theory. In particular, we will see two predicates on types, that single out a class CHaus of “compact Hausdorff” types and a class ODisc of “overt and discrete” types, respectively. A handful of axioms describe how these classes interact. The resulting type theory is spiritually related Taylor’s “Abstract Stone Duality”.

As an application I will explain that ODisc is naturally a category, and furthermore, every function ODisc → ODisc is automatically functorial. This axiomatic approach to condensed sets, including the functoriality result, are formalized in Lean 4. If time permits, I will comment on some of the techniques that go into the proof.

Joint work with Reid Barton.

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WATCH ONLINE HERE : https://www.microsoft.com/en-gb/microsoft-teams/join-a-meeting?rtc=1 Meeting ID: 370 771 279 261 Passcode: iCo7a5

• Speaker: Johan Commelin (Utrecht University)
• Thursday 02 May 2024, 17:00-18:00
• Venue: Live-streamed at MR14 Centre for Mathematical Sciences.
• Series: Formalisation of mathematics with interactive theorem provers ; organiser: Jonas Bayer.

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Mathematicians have opportunities to work collaboratively on wide ranging topics. In this talk, I will share examples from my research where I study the spatial and temporal dynamics of biological systems, ranging from bacterial chemotaxis, cancer cell motility and phytoplankton in turbulence, to cell-signalling pathways and drug transport. I will also share some music influenced by this research and invite reflection on the creative process.

• Speaker: Professor Rachel Bearon, Professor of Mathematical Biology and Executive Dean of the Faculty of Natural, Mathematical & Engineering Sciences, KCL
• Thursday 16 May 2024, 12:00-13:00
• Venue: Centre for Mathematical Sciences MR2, CMS.
• Series: Rouse Ball Lectures; organiser: Sarah Jefferys.

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