Sep 29 (Tue)
14:00 MCS2068 APDELyonell Boulton (Heriot-Watt University): Norm-ideal perturbations of one-parameter semigroups and applications
The notion of equivalence classes of generators of one-parameter semigroups based on the convergence of the Dyson expansion can be traced back to the seminal work of Hille and Phillips, who in Chapter XIII of the 1957 edition of their Functional Analysis monograph, developed the theory in minute detail. Following their approach of regarding the Dyson expansion as a central object, in the first part of this talk we examine a general framework for perturbation of generators relative to the Schatten-von Neumann ideals on Hilbert spaces. This allows us to develop a graded family of equivalence relations on generators, which refine the classical notion and provide stronger-than-expected properties of convergence for the tail of the perturbation series. We then show how this framework realises in the context of non-self-adjoint Schrödinger operators.
Venue: MCS2068
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These events are hosted in and/or organised by members of the Department (follow links for details):
Sep 23 [MCS0001] Research Day 2026
online: https://teams.microsoft.com/meet/340405727128006?p=ux5aXCYxyqUJBIZc8b
Venue: MCS0001 at/from 09:30
Link: here
Click on series to expand.
Usual Venue: MCS2068
Contact: yohance.a.osborne@durham.ac.uk
Sep 29 14:00 Lyonell Boulton (Heriot-Watt University): Norm-ideal perturbations of one-parameter semigroups and applications
The notion of equivalence classes of generators of one-parameter semigroups based on the convergence of the Dyson expansion can be traced back to the seminal work of Hille and Phillips, who in Chapter XIII of the 1957 edition of their Functional Analysis monograph, developed the theory in minute detail. Following their approach of regarding the Dyson expansion as a central object, in the first part of this talk we examine a general framework for perturbation of generators relative to the Schatten-von Neumann ideals on Hilbert spaces. This allows us to develop a graded family of equivalence relations on generators, which refine the classical notion and provide stronger-than-expected properties of convergence for the tail of the perturbation series. We then show how this framework realises in the context of non-self-adjoint Schrödinger operators.
Venue: MCS2068
Oct 06 14:00 Catherine Drysdale (Lancaster University): The Mathematics of Depression
In this talk, I will talk about the research that motivated my fellowship that brings together brain network and hormones in the case of the mental illness depressions. In my approach, I consider brain networks as directed graphs and hormone networks as systems of DDEs that are linked via the hippocampus. I give examples where techniques such as pseudospectra can be used to understand perturbations of biological rhythms. I will also speak to the challenges of data-integration and mapping together different brain imaging modalities.
Venue: MCS2068
Oct 13 14:00 Phoebe Valentine (University of Warwick): Characterising 1-rectifiable metric spaces via connected tangent spaces
Characterising rectifiability using the existence of tangents is a very classical technique in GMT and positive results can be found even when using very weak notions of a tangent. This work goes further to only require that tangents are supported on a connected set. Despite this weak requirement, we can still prove that 1-rectifiability in complete metric spaces is implied by the existence of connected tangents almost everywhere. This, combined with prior results of Bate, establishes a characterisation of 1-rectifiability in complete metric spaces, which is in particular also new for Euclidean space. Inspired by geometric ideas from Besicovitch in the plane, we achieve our result by exploiting the inherent gappiness of purely 1-unrectifiable sets. To this end, we will give rigorous meaning to this 'gappiness' and show how it may be quantified.
Venue: MCS2068
Oct 20 14:00 Ofelia Bonesini (London School of Economics): Continuous-time persuasion by filtering
We frame dynamic persuasion in a partial observation stochastic control Leader-Follower game with an ergodic criterion. The Receiver controls the dynamics of a multidimensional unobserved state process. Information is provided to the Receiver through a device designed by the Sender that generates the observation process. The commitment of the Sender is enforced. We develop this approach in the case where all dynamics are linear and the preferences of the Receiver are linear-quadratic. We prove a verification theorem for the existence and uniqueness of the solution of the HJB equation satisfied by the Receiver's value function. An extension to the case of persuasion of a mean field of interacting Receivers is also provided. We illustrate this approach in two applications: the provision of information to electricity consumers with a smart meter designed by an electricity producer; the information provided by carbon footprint accounting rules to companies engaged in a best-in-class emissions reduction effort. In the first application, we link the benefits of information provision to the mispricing of electricity production. In the latter, we show that even in the absence of information cost, it might be optimal for the regulator to blur information available to firms to prevent them from coordinating on a higher level of carbon footprint to reduce their cost of reaching a below average emission target. This is a joint work with René Aïd, Giorgia Callegaro and Luciano Campi.
Venue: MCS2068
Usual Venue: MCS3070
Contact: andrew.krause@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: OC218
Contact: mohamed.anber@durham.ac.uk
For more information, see HERE.
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS3052
Contact: andrew.krause@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS2068
Contact: martin.p.kerin@durham.ac.uk
Oct 09 14:00 Adam Barber (Durham): TBA
Oct 23 14:00 Yuri Santos Rego (Lincoln): TBA
Nov 27 14:00 Emily Roff (Edinburgh): TBA
Jan 29 14:00 Marco Radeschi (Torino): TBA
Usual Venue: MCS2068
Contact: tyler.helmuth@durham.ac.uk,oliver.kelsey-tough@durham.ac.uk
Oct 05 13:00 Xusheng Zhang (Durham (CS)): Low temperature random Cluster Model on Trees and Random Graphs
In this talk, I will discuss the low-temperature random-cluster model on trees and tree-like random graphs, a dependent percolation model closely related to the Ising and Potts models. I will describe a second uniqueness threshold on the wired regular tree, resolving a conjecture of Haggstrom from 1996, and explain how this threshold is tied to decay of correlations under wired boundary conditions. I will then discuss consequences for dynamics: near-optimal mixing of random-cluster Glauber dynamics on wired trees, and on random regular graphs in the low temperature uniqueness regime. These results give efficient sampling algorithms for the random-cluster and Potts models on treelike graphs. Based on joint work with A. Blanca, R. Gheissari, and H. Park.
Venue: MCS2068
Usual Venue: MCS3070
Contact: joe.thomas@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
