Seminars in Mathematical Sciences

May 11 (Mon)

13:00 MJC_2004 ApplFrancesca Scarabel (Leeds): Bistability and complex dynamics in an infectious disease model with waning and boosting of immunity

In this talk, I will present some results motivated by a model for transmission of an infectious disease with temporary immunity. The model is formulated in the literature either as a partial differential equation or, equivalently, as a delay differential equation (DDE) with distributed delay. Focusing on the DDE formulation, I will present an overview of the pseudospectral discretization approach to approximate a DDE with a system of ordinary differential equations. This method has recently been implemented in a DDE importer for the software package MatCont, allowing users to perform numerical bifurcation analysis of DDEs via the MatCont graphical user interface. I will show how waning and boosting of immunity give rise to very complex dynamics at the population level, including regions of parameters where multiple attractors exist (an equilibrium and a limit cycle or two stable limit cycles). Bistability phenomena can be particularly important to explain for instance the resurgence of pertussis cases after the COVID-19 pandemic, to levels different than pre-pandemic. I will then present some recent ongoing work to investigate the basins of attraction of DDEs.

Venue: MJC_2004 (Mountjoy Centre)

13:00 MCS2068 StatNarayanaswamy Balakrishnan (McMaster University): Joint Prediction and Associated Results

Prediction of future failures has been discussed rather extensively in the life-testing and reliability literature. Most of these developments center on prediction of one future failure. In this talk, I will introduce the joint prediction of future failures, specifically joint best linear unbiased prediction, and then establish several interesting properties associated with it. I will present some illustrative examples to highlight the established results.

Venue: MCS2068

May 13 (Wed)

11:00 MCS2050 E&PAndrew Krause and Denis Patterson (Durham): Lessons from Teaching Computational Mathematics: Creativity and Self-Directed Study in Undergraduate Education

We will discuss the initial motivations and our design philosophy for the Computational Mathematics II module, as well as how it was received by students. This will include expected and unexpected problems, especially in designing a coursework-only assessment structure in the age of AI. We will also highlight some incredible work by the students, and some lessons about creativity and student independence that we think are relevant to broader departmental discussions around group work, projects, and the future of our degree programmes.

Venue: MCS2050

Online: https://teams.microsoft.com/l/meetup-join/19%3ameeting_NjI5NjY1ZWUtZjNjNC00MTRjLWJlZmMtYWQ0YWEyMTYxNmY0%40thread.v2/0?context=%7b%22Tid%22%3a%227250d88b-4b68-4529-be44-d59a2d8a6f94%22%2c%22Oid%22%3a%226cb8930b-1559-4659-8c60-d0b762855115%22%7d

May 14 (Thu)

13:00 MCS2068 G&TVictoria Pelayo Alvaredo (Universidad Autónoma de Madrid/ICMAT): Beyond Dvoretzky's Theorem

Dvoretzky's theorem states that in real normed spaces there exist subspaces of sufficiently high dimension that are nearly Euclidean. Equivalently, every high-dimensional symmetric convex body has a section of dimension on the order of log(n) that is close to a Euclidean ball.

We study a functional version of this phenomenon in terms of radial functions on the sphere. We also give versions of Dvoretzky's Theorem in complex and quaternionic normed spaces. Finally, using the Hopf fibration, which lifts positive functions on complex or quaternionic projective spaces to radial functions on the sphere, we obtain functional versions of these extensions.

Venue: MCS2068

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• Amplitudes and Correlators

Contact: arthur.lipstein@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Analysis and PDE

Usual Venue: MCS2068

Contact: yohance.a.osborne@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Applied Mathematics

Usual Venue: MCS3070