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Microstructural Kinetics Group

Department of Materials Science & Metallurgy
 
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This is a superlist combining all those seminars on talks.cam taking place in one of the Departments of the School of Physical sciences, plus occasional other talks which would be of significant interest to researchers in the School. If you would like your talk or list included please contact Duncan (drs45)
Updated: 3 min 50 sec ago

Tue 08 Oct 19:15: Title to be confirmed

Mon, 05/02/2024 - 09:42
Title to be confirmed

Abstract not available

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Tue 06 Feb 15:30: Distances on the CLE(4), critical Liouville quantum gravity and 3/2-stable maps

Sun, 04/02/2024 - 23:28
Distances on the CLE(4), critical Liouville quantum gravity and 3/2-stable maps

Random planar maps with high degrees are expected to have scaling limits related to the conformal loop ensemble (CLE) equipped with an independent Liouville quantum gravity (LQG). In the dilute case, where informally the degrees have finite expectations, Bertoin, Budd, Curien and Kortchemski established the scaling limit of the distances to the root. However, the scaling limit does not have an interpretation as a distance from the loops to the boundary in terms of LQG . I will focus on the critical case where the probability that a vertex has degree k is of order k^-2. In this case, the distances from the root to the high degree vertices satisfy a scaling limit, and this scaling limit is related to a quantum distance to the boundary on a CLE -decorated critical LQG introduced by Aru, Holden, Powell and Sun. Finally, I will draw a connection with a conformally invariant distance to the boundary on the CLE from Werner and Wu.

  • Speaker: Emmanuel Kammerer (Ecole Polytechnique)
  • Tuesday 06 February 2024, 15:30-16:30
  • Venue: MR12.
  • Series: Probability; organiser: Jason Miller.

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Mon 12 Feb 14:30: The many faces of global hyperbolicity

Sat, 03/02/2024 - 15:22
The many faces of global hyperbolicity

The notion of global hyperbolicity was introduced by Jean Leray in 1952 to obtain global uniqueness of solutions to nonlinear wave equations. Globally hyperbolic spacetimes subsequently turned out to be the right geometric setting not only for the well-posedness of the initial value formulation for the Einstein equations in General Relativity but also for the singularity theorems of Penrose and Hawking and several splitting results in Lorentzian geometry. After reviewing the rich history and omnipresence of global hyperbolicity in General Relativity, I discuss recent geometric insights in settings with a timelike boundary and in low regularity, and present our new characterization via metric completeness.

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Wed 07 Feb 16:30: Jordan correspondence and block distribution of characters.

Fri, 02/02/2024 - 14:29
Jordan correspondence and block distribution of characters.

Given a finite group G and a prime p, the set of complex valued irreducible characters of G is naturally partitioned into families called p-blocks. The p-block distribution of characters plays a central role in the modular representation theory of finite groups and giving an explicit description of this distribution for finite (quasi)-simple groups has been a long ongoing endeavour. I will talk about recent joint work with Gunter Malle on the p-block distribution of characters of finite quasi-simple exceptional groups of Lie type and on an application to a conjecture of G.R. Robinson on defects of characters.

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Thu 08 Feb 17:00: How to prove Fermat's Last Theorem Online

Fri, 02/02/2024 - 13:51
How to prove Fermat's Last Theorem

The statement of Fermat’s Last Theorem would have been comprehensible to Diophantus, who lived nearly 2000 years ago. The question was explicitly raised by Fermat in the 1600s, and was resolved by Wiles and Taylor in the 1990s, when I was a PhD student of Taylor. In 2023 I got an EPSRC grant to begin formalising the proof in the Lean theorem prover.

In my talk I’ll start with a history of the problem, and say something about the contributions made by computers in the pre-Wiles era. Without going into details, I’ll then say a little bit about the proof (due to Taylor) which I’m going to formalise, how it differs from Wiles’ original approach (it is broadly but not exactly the same), and what factors influenced the choice of route to the top. I’ll finish by talking about the infrastructure which I’ll be using in order to run the project as an open source multi-author collaborative experiment.

It is probably worth stressing that this talk is suitable for a general audience familiar with the idea of formalisation but with no background in modern number theory, and in particular it will not be a technical explanation of the route we’re taking.

—-

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

Online

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Wed 07 Feb 14:00: Enabling Fast, Robust, and Personalized Federated Learning

Fri, 02/02/2024 - 09:12
Enabling Fast, Robust, and Personalized Federated Learning

In many large-scale machine learning applications, data is acquired and processed at the edge nodes of the network such as mobile devices, users’ devices, and IoT sensors. While distributed learning at the edge can enable a variety of new applications, it faces major systems bottlenecks that severely limit its reliability and scalability including system and data heterogeneity and communication bottleneck. In this talk, we focus on federated learning which is a new distributed machine learning approach, where a model is trained over a set of devices such as mobile phones, while keeping data localized. We first present a straggler-resilient federated learning scheme that uses adaptive node participation to tackle the challenge of system heterogeneity. We next present a robust optimization formulation for federated learning that enables us to address the data heterogeneity challenge in federated learning. We finally talk about a new algorithm for personalizing the learned models for different users.

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Fri 16 Feb 14:00: Compressed sensing for the sparse Radon transform

Thu, 01/02/2024 - 14:21
Compressed sensing for the sparse Radon transform

Compressed sensing allows for the recovery of sparse signals from a limited number of measurements, which is proportional – up to logarithmic factors – to the sparsity of the unknown signal. The classical theory mostly considers either random linear measurements or subsampled isometries. In particular, the case with the subsampled Fourier transform finds applications to undersampled magnetic resonance imaging. In this talk, I will show how the theory of compressed sensing can also be rigorously applied to the sparse Radon transform, in which only a finite number of angles are considered. One of the main novelties consists in the fact that the Radon transform is associated to an ill-posed inverse problem, and the result follows from a new theory of compressed sensing for abstract inverse problems.

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Wed 14 Feb 16:30: Integral line bundles of weight -1 on the Drinfeld half-plane and De Rham representations

Thu, 01/02/2024 - 00:48
Integral line bundles of weight -1 on the Drinfeld half-plane and De Rham representations

The study of the l-adic cohomology of the Drinfeld symmetric space and its coverings was central to exhibit geometric realizations of the classical local Langlands and Jacquet-Langlands correspondences. On the other hand, inspired by the paper of Dospinescu-Le Bras, the study of the coherent cohomology of equivariant vector bundles should allow us to realize some aspects of the p-adic local Langlands correspondence. More precisely, we will explain a work in progress which exhibits a class of equivariant line bundles “of weight -1” that should provide a geometric realization of some de Rham Galois representations of Hodge-Tate weights (0,0).

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Fri 02 Feb 15:45: Quantum entanglement of top quarks

Thu, 01/02/2024 - 00:06
Quantum entanglement of top quarks

The ATLAS Collaboration recently reported the observation of quantum entanglement between top quarks. This constitutes the first observation of entanglement in a pair of quarks, and the observation of entanglement at the highest energy to date. Prompted by these results, I will illustrate recent developments in the field of quantum information theory in collider experiments, as this measurement paves the way to use colliders as a laboratory to study quantum information and other foundational properties of quantum mechanics. Furthermore, other similar measurements such as measuring quantum discord, reconstructing the quantum steering ellipsoid, and even establishing a violation of Bell inequalities, may be achievable at the LHC in the near future. From a high-energy physics perspective, borrowing concepts from quantum information theory inspires new approaches and observables that can be used to search new phenomena that may have escaped detection so far.

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Wed 14 Feb 16:00: Title to be confirmed

Wed, 31/01/2024 - 18:04
Title to be confirmed

Abstract not available

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Tue 21 May 16:00: Title to be confirmed

Wed, 31/01/2024 - 14:03
Title to be confirmed

Abstract not available

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Mon 13 May 16:00: Title to be confirmed

Wed, 31/01/2024 - 14:03
Title to be confirmed

Abstract not available

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Thu 01 Feb 11:00: Thermodynamic Integration, fermion sign problem, and real-space renormalization

Wed, 31/01/2024 - 10:03
Thermodynamic Integration, fermion sign problem, and real-space renormalization

As non-specialists in renormalization, we have tried to understand Sect VI of the famous 1975 Review of Modern Physics by K. G. Wilson that has remained cryptic to many. I will discuss a practical and un-biased Monte Carlo algorithm that we have implemented for the two-dimensional Ising model. Inspired by the original numerical method, it integrates modern twists in sampling, and that might be useful in other contexts (work with K. Sathwik).

*disclaimer!

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Thu 22 Feb 17:00: Experiences with Isabelle/HOL: Formalising Real Algebraic Geometry

Tue, 30/01/2024 - 22:36
Experiences with Isabelle/HOL: Formalising Real Algebraic Geometry

The Isabelle/HOL interactive theorem prover has multiple frameworks for formalising abstract algebra: one library which relies on typeclasses, and another, better suited to formalising algebra, which makes no use of them. In this talk, we discuss the experience of formalising material in real algebraic geometry – real closed fields, Thom encoding and Puiseux series – in the latter framework. We explore the strengths and weaknesses of the available automation, as well as the feasibility of transferring results from one library to the other.

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Fri 09 Feb 13:00: The Evolving Relative Role of Stratospheric Ozone and Greenhouse Gasses in Modifying the Southern Ocean Carbon Sink from 1950-2100

Tue, 30/01/2024 - 16:47
The Evolving Relative Role of Stratospheric Ozone and Greenhouse Gasses in Modifying the Southern Ocean Carbon Sink from 1950-2100

Southern Ocean winds have strengthened and moved poleward in the latter half of the 20th century, which has been attributed to the depletion of stratospheric ozone and to climate warming from rising greenhouse gas concentrations. Both ozone recovery and changing greenhouse gas concentrations are expected to continue modulating wind structure throughout the 21st century. Here, we quantify the relative roles of ozone and greenhouse gases on Southern Ocean wind structure from 1950-2100 using the UK Earth System Model (UKESM1) model output, with a combination of three scenarios of ozone and two scenarios of greenhouse gas evolution. Both ozone depletion and increases in greenhouse gas concentration act to increase wind speed over the Southern Ocean. The influence of ozone is predominant in summer winds, while the influence of greenhouse gases acts in all seasons. We show that wind speeds return close to their original levels by the end of the 21st century under a low-greenhouse gas scenario with ozone recovery. The influence of ozone on wind speed was dominant in the 1950-2000 time-period, but not in the 21st Century when the influence of greenhouse gases becomes two to three times larger than that of ozone, even in the low emissions scenario. We find significant effects of both ozone scenario and greenhouse gas emissions on physical-oceanographic variables (sea surface temperature, mixed layer depth, and overturning circulation). Finally, we quantify the relative contributions of these physical changes to the evolving carbon sink of the Southern Ocean, and discuss how wind-induced physical changes can alter ecosystem processes and the associated carbon export to the deep ocean.

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Wed 07 Feb 14:30: Homotopy methods for convex optimization

Tue, 30/01/2024 - 14:10
Homotopy methods for convex optimization

Convex optimization concerns the problem of finding the maximum of a linear function over a convex set. This class covers many optimization problems in quantum information, portfolio optimization, and machine learning.

In this talk, we will introduce a new approach to solving convex optimization problems via a homotopic approach. In this approach, we deform an optimization problem with a trivial solution into the target problem and keep track of the solutions along the homotopy. This is motivated by the field of numerical algebraic geometry, which solves systems of polynomial equations using a similar idea.

We show that our method applies to certain convex optimization problems, including Semidefinite Programs, Hyperbolic Programs, and convex optimization problems with a single convexity constraint. Moreover, we present several benchmark problems in which this method outperforms known methods.

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Thu 01 Feb 11:00: Thermodynamic Integration, fermion sign problem, and real-space renormalization

Tue, 30/01/2024 - 12:14
Thermodynamic Integration, fermion sign problem, and real-space renormalization

As non-specialists in renormalization, we have tried to understand Sect VI of the famous 1975 Review of Modern Physics by K. G. Wilson that has remained cryptic to many. I will discuss a practical and un-biased Monte Carlo algorithm that we have implemented for the two-dimensional Ising model. Inspired by the original numerical method, it integrates modern twists in sampling, and that might be useful in other contexts (work with K. Sathwik). *disclaimer!

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Fri 02 Feb 13:00: Towards reconciling Cosmology, GR and QFT through non-perturbative Stochastic Inflation

Tue, 30/01/2024 - 11:21
Towards reconciling Cosmology, GR and QFT through non-perturbative Stochastic Inflation

In the context of inflation, we show how to account for quantum modes in general and numerical relativity on scales bigger than the Hubble radius, from where they behave classically and can grow non-perturbatively.

We provide a formulation of Stochastic Inflation in full general relativity that goes beyond the slow-roll and separate universe approximations. Starting from the initial conditions problem in numerical relativity, we show how gauge invariant Langevin source terms can be obtained for the complete set of Einstein equations in their ADM formulation by providing a recipe for coarse-graining the spacetime in any small gauge. These stochastic source terms are defined in terms of the only dynamical scalar degree of freedom in single-field inflation and all depend simply on the first two time derivatives of the coarse-graining window function, on the gauge-invariant mode functions that satisfy the Mukhanov-Sasaki evolution equation, and on the slow-roll parameters.

We validate the efficacy of these Langevin dynamics directly using an example in uniform field gauge, obtaining the stochastic e-fold number without the need for a first-passage-time analysis. As well as investigating the most commonly used gauges in cosmological perturbation theory, we also derive stochastic source terms for the coarse-grained first-order BSSN formulation of Einstein’s equations, which enables a well-posed implementation for 3+1 numerical relativity simulations.

Based on https://arxiv.org/abs/2401.08530v1

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