Title: Equidistribution of Short Mesh Patterns

Date: Wednesday 30th September 2065, 1.00pm

Venue: LT908

Abstract:  

Mesh patterns are a powerful generalization of classical permutation patterns that encompass vincular, consecutive, and bivincular patterns. Introduced in 2011, they have become an important tool in the study of permutation statistics and pattern avoidance. In this talk, I will briefly introduce mesh patterns and the notions of distribution, equidistribution, and Wilf equivalence. The focus will be on short patterns, mainly of lengths 2 and 3, and on the use of symmetries, bijections, and enumerative techniques to establish distributional equivalences.

I will survey recent progress on the classification of short mesh patterns into equidistribution and Wilf-equivalence classes over several families of permutations, including all permutations, alternating permutations, layered permutations, and involutions.

I hope to see many of you.

Title: Patterns in Multi-dimensional Permutations

Date: Thursday 2nd October 2025, 2.00pm

Venue: LT907

Abstract:  In this talk, I will present a general framework that extends the theory of permutation patterns to higher dimensions and unifies several combinatorial objects studied in the literature. The approach introduces the concept of a level for an element in a multi-dimensional permutation, which can be defined in various ways. I will discuss two natural definitions of level, each establishing connections to combinatorial sequences listed in the Online Encyclopedia of Integer Sequences (OEIS).

Our framework provides combinatorial interpretations for numerous OEIS sequences, many of which previously lacked such interpretations. As a notable example, we offer an elegant interpretation of the Springer numbers: they count weakly increasing 3-dimensional permutations under a level definition based on maximal entries.

This is joint work with Shaoshi Chen, Hanqian Fang, and Candice X.T. Zhang, all from the Chinese Academy of Sciences.

Title: Essential spectra of Sturm-Liouville operators and their indefinite counterpart

Date: Thursday 9th October 2025, 2.00pm

Venue: LT907

Abstract:  The difference to classical Sturm-Liouville expressions is here that the weight may change its sign.  In this situation the associated maximal operators become self-adjoint with respect to indefinite inner products and their spectral properties differ essentially from the Hilbert space situation.  We investigate the essential spectra and accumulation properties of nonreal and real discrete eigenvalues.

Title: Counting cycles in planar graphs

Date: Tuesday 21st October 2025, 3.00pm

Venue: LT907

Prof. Ryan Martin - Editor-in-Chief of the Journal "Order") https://faculty.sites.iastate.edu/rymartin/ 

Abstract: Basic Tur\'an theory asks how many edges a graph can have, given certain restrictions such as not having a large clique. A more generalized Tur\'an question asks how many copies of a fixed subgraph $H$ the graph can have, given certain restrictions. There has been a great deal of recent interest in the case where the restriction is planarity. In this talk, we will discuss some of the general results in the field, primarily the asymptotic value of ${\bf N}_{\mathcal P}(n,H)$, which denotes the maximum number of copies of $H$ in an $n$-vertex planar graph. In particular, we will focus on the case where $H$ is a cycle.

It was determined that ${\bf N}_{\mathcal P}(n,C_{2m})=(n/m)^m+o(n^m)$ for small values of $m$ by Cox and Martin and resolved for all $m$ by Lv, Gy\H{o}ri, He, Salia, Tompkins, and Zhu. The case of $H=C_{2m+1}$ is more difficult and it is conjectured that ${\bf N}_{\mathcal P}(n,C_{2m+1})=2m(n/m)^m+o(n^m)$. 

We will discuss recent progress on this problem, including verification of the conjecture in the case where $m=3$ and $m=4$ and a lemma which reduces the solution of this problem for any $m$ to a so-called ``maximum likelihood'' problem. The maximum likelihood problem is, in and of itself, an interesting question in random graph theory.

This is joint work with Emily Heath and Chris (Cox) Wells.

Title: The Early History of Knowledge Exchange in Mathematics: a personal perspective

Date: Monday 5th October 2026, 1.00pm

Venue: LT907

Abstract:  Arguably, Knowledge exchange in mathematics dates from the Lighthill report in 1968 which, among other recommendations, stated that, ”Postgraduate mathematicians should be exposed to real practical problems.”

The Oxford Study groups with Industry (OSGI) were conceived as a direct result of this report. We shall discuss some of the early meetings, the problems and the benefits to both academia and industry. As time went by, it became apparent that computational solutions were often required and this led Professor Fox acquiring SRC funding for the University Consortium for industrial Numerical Analysis (UCINA). In1979 I was appointed Project Coordinator with the remit to go out to Industry and find interesting problems. After three years we set up what was essentially a non-profit making company whereby Industry paid an annual subscription to cover my salary, my secretary and my expenses. However, in 1986 I was head-hunted by one of my clients, Unilever Research, to be head of Mathematics and Statistics with a roving consultant role. At the same time eleven Europeans (including myself) founded the European Consortium for Mathematics in Industry (ECMI) whose mission statement was influenced by that of UCINA’s. ECMI is still flourishing; indeed, this year is the 50th anniversary of ECMI.

This talk will be light on mathematical detail but instead will focus on the areas of science and technology which gave rise to the hundreds of mathematical problems.

There will also be anecdotes about the many players involved in these early days.

Title: Modelling drying porous media 

Date: Monday 12th October 2026, 1.00pm

Venue: LT907

Abstract: TBC

Title: Lean & AI for applied mathematicians 

Date: Monday 19th October 2026, 1.00pm

Venue: LT907

Abstract: TBC

Title: From microscopic to macroscopic laws of transport of yield-stress fluids in porous media.

Date: Monday 26th October 2026, 1.00pm

Venue: LT907

Abstract: TBC

Title: TBC

Date: Tuesday 3rd November 2026, 1.00pm

Venue: LT907

Abstract: TBC

Title: Dissecting Deep Neural Networks

Date: Tuesday 10th November 2026, 1.00pm

Venue: LT907

Abstract: TBC

Title: TBC

Date: Tuesday 24th November 2026, 1.00pm

Venue: LT907

Abstract: TBC

Title: Modern Optimisation Techniques and Deep Learning 

Date: Friday 29th May 2026, 8.45am

Venue: LT908

Abstract:  The proposed workshop targets the increasingly important interface between optimisation and deep learning, with imaging and vision as a central application domain. Modern deep learning models in imaging and vision give rise to massive optimisation problems, often involving millions of variables even for conceptually small tasks. There is growing recognition that further progress will require optimisation methods that go beyond standard gradient-based approaches, motivating the development of more efficient, scalable, and mathematically rigorous algorithms. This also enables a small, focused event in which early-career researchers and PhD students can interact closely with internationally recognised experts. This is an opportunity that is rarely feasible at large conferences.

ALL ARE WELCOME. The event is free to attend but registration is necessary to ensure the room is adequate.

Title: A Sliding Window Survival Model for Shock Processes with a General Stochastic Intensity  

Date: Wednesday 28th October 2026, 3.30pm

Venue: LT908

Abstract: A system is subject to external point events (e.g., shocks) arriving in accordance with a general orderly point process. Within a classical 𝛿-shock model and its generalizations that consider only specific point processes, a failure occurs when the next event is too close to the previous one. However, for many systems, isolated close pairs (or more than two close events) of shocks can be practically harmless, whereas failures are caused by an excessive concentration of shocks in a finite observation window. This motivates development of a new approach for failures that occur when the number of shocks in a window of length 𝛿 exceeds some threshold for the first time. The survival probability of a system for this model is obtained and analysed for general orderly point processes. The specific cases of the renewal process, the NHPP and the generalized Polya process are considered, and some relevant stochastic comparisons are discussed. The corresponding numerical illustrations are provided. 

Keywords: Stochastic intensity; delta-shock model; survival probability; integral equations of the Volterra type; clustering. 

Title: Modelling the impact of fishing on the biological carbon pump in shelf-ecosystems with StrathE2E

Date: Wednesday 14th October 2026, 2.00pm

Venue: LT907

Abstract: With StrathE2E, our in-house end-to-end shelf-ecosystem model, we wanted to investigate the impact of fishing on carbon sequestration. Initially, StrathE2E simulates nitrogen fluxes throughout coastal ecosystems, from dissolved inorganic forms (ammonia and nitrate), through plankton, benthos and fish, to marine mammals and birds, including recycling through excretion and remineralisation in the water column and sediment. The model also simulates fishing activities for different gears, including trawling effect on seabed habitats and benthos. Since StrathE2E outputs are in nitrogen, we first developed an algorithm to translate nitrogen fluxes into carbon by considering dynamic stoichiometry between consumers and their food. This work required to compile a global dataset of carbon-nitrogen ratios (C:N) from literature and open-access datasets, covering most functional groups of the marine food web. After fitting our algorithm to C:N data, we were able to compute carbon fluxes for different regional implementations of StrathE2E and to test different fishing scenarios.

In this talk, I will present our algorithm and how it was successful at reproducing the C:N variation observed in marine food webs. Then, I will talk about the importance to choose dynamic over fixed stoichiometry when converting nitrogen outputs into carbon. Finally, I will discuss the impact of fishing, especially trawling, on carbon sequestration and benthic fluxes, comparing results from different fishing scenarios and from two different regions, the Celtic Sea and the Brazilian Shelf.

Title: Two problems in biological fluids: bacterial locomotion and microtubules in embryos

Date: Wednesday 21st October 2026, 2.00pm

Venue: LT907

Abstract: In this talk, I will discuss two topics: swimming bacteria near surfaces and cytoplasmic streaming in egg cells. Flagellated bacteria are hydrodynamically attracted to rigid walls, yet experiments show a 'hovering' state where they swim stably at a finite height above surfaces. We use numerics and theory to reveal the physical origin of hovering. Simulations show that hovering requires an elongated cell body and results from a tilt away from the wall. Theoretical models identify two essential asymmetries: the response of width-asymmetric cells to active flows created by length-asymmetric cells. A minimal model reconciles near and far-field hydrodynamics, capturing all key features of hovering. The latter part focuses on the fluid dynamics of Drosophila oocytes (egg cells), which exhibit a rotating flow known as cytoplasmic streaming during a maturation stage. This process is crucial for establishing polarity and promoting cytoplasmic mixing. These flows are generated by flexible microtubules inside the cells. The minus ends of microtubules are anchored at the oocyte cortex, and kinesin-cargo complexes move along these microtubules, generating streaming flows in the viscous cytoplasmic fluid. I will show how a fluid-structure elastohydrodynamic instability of these microtubules explains cytoplasmic streaming.

Title: Local Thermal Regimes Structure Community-Level Phenology of Tintinnids

Date: Wednesday 4th November 2026, 2.00pm

Venue: LT907

Abstract: Surface seawater temperature varies seasonally across latitudes, shaping the temporal organization of plankton communities. However, the phenology of microzooplankton at the community level remains poorly understood, largely due to insufficient temporal resolution in most monitoring programs. In this study, we conducted a high-frequency (three times per week) year-round survey of tintinnids in Qingdao coastal waters, a site characterized by one of the largest annual temperature ranges among global coastal systems. Thirty tintinnid species were identified, and all were neritic taxa. Based on their annual occurrence patterns, the community was classified into four phenological types: cold-water type, temperate type I, temperate type II, and warm-water type, each exhibiting distinct seasonal peaks and thermal performance ranges. These four phenological types constitute the community-level phenological pattern of tintinnids in Qingdao coastal waters. The effective breadths of thermal performance range for each type were 5–8 ℃, and the number of phenological types increased with the site’s annual temperature range, from two in Hong Kong to three in Ningbo and four in Qingdao. Cold-associated types exhibited positively skewed thermal performance curves, indicating higher sensitivity to temperature fluctuations at low temperatures, whereas warm-associated types followed the typical negatively skewed pattern. By linking phenological types to distinct thermal niches, this study provides a framework for understanding how local thermal regimes structure microzooplankton community-level phenology and seasonal succession.

Title: TBA

Date: Wednesday 18th November 2026, 2.00pm

Venue: LT907

Abstract: TBA

Title: Future Fish and Oceans With and Without the Atlantic Overturning Circulation

Date: Wednesday 25th November 2026, 2.00pm

Venue: LT907

Abstract: TBA

Date: 3.00pm Tuesday 3rd November 2026

Venue: LT907

Title:  Stability and componentwise accuracy in multilinear PageRank

Abstract:    We study the stability with respect to perturbations and the accuracy of numerical algorithms for computing solutions to the multilinear PageRank problem $x=(1-\alpha)v+\alpha Px^{m-1}$. Our results reveal that the solution can be less sensitive to perturbations and numerical errors than what stated by the classical bounds for nonlinear systems of equations (based on the norm of the Jacobian). In detail, one can obtain bounds for the minimal solution which ignore the singularity of the problem for $\alpha=1/{(m-1)}$, and one can show that the limiting accuracy of the Newton method depends not on the norm of the Jacobian but on a quantity that can be much smaller, thanks to the nonnegativity structure of the equation. For the minimal solution, we also suggest subtraction-free modifications to the existing algorithms to achieve componentwise stability.

Some of the theoretical results we obtain are interesting even outside the scope of this problem: bounds for more general multilinear vector equations, and a partial inverse for M-matrices which remains bounded when the M-matrix approaches singularity.

Date: 3.00pm Tuesday 6th October 2026

Venue: LT907

Title:  A finite element method for a non-Newtonian dilute polymer fluid

Abstract:    We propose a finite element discretisation of a three-dimensional non-Newtonian flow whose dynamics are described by an Upper Convected Maxwell model.  First, a one-directional simplification of the UCM problem is made, so the main variables are velocity, pressure, and one vector which acts as the "square root" of the stress tensor. For this model a finite element method is proposed and analysed.

Date: 3.00pm Tuesday 15th September 2026

Venue: LT907

Title:  A robust, simple, and efficient time-stepping scheme for Two-phase dense granular flows with pressure-dependent rheology.

Abstract:   Granular flows have attracted increasing attention in recent decades due to their relevance across a wide range of natural and industrial settings. They are key to understanding natural hazards (landslides, avalanches, debris flows) and to modeling industrial operations in mining (crushing, grinding, sorting), pharmaceuticals (powder mixing, tablet formation), and food processing (e.g., rice, barley, and malt handling). 

Title: Long time behavior for SIS model driven by pure-jump noise with Markov switching  

Wednesday 17th September 2025, 3.00-4.00pm

Venue: LT907

Abstract: In this talk, we focus on long time behavior for SIS epidemic model driven by an alpha-stable process with Markov switching. Necessary and sufficient conditions for recurrence or extinction have been established. To analyze the ergodic behavior, we establish the well-posedness of a nonlocal Dirichlet problem with regime switching and derive a strong maximum principle. Our results disclose heavy-tailed fluctuations and stationary distribution of Markov chain significantly affect the epidemic threshold and asymptotic dynamics. 

Title: A Journey Through Academia: Some Personal Reflections as a Member of an Under-Represented Group(s)

Date: Wednesday 29th October 2025, 3.00pm

Venue: LT908

Abstract: In this talk I will present a brief overview of my career, discussing why I became interested in Statistics and how this led to my academic journey to date, including several critical turning points. I will present personal reflections in the context of being an individual from an under-represented group through different career stages and in particular how this has subsequently informed how I now approach situations and in particular decision-making. I will also aim to discuss some aspects of leadership (at least as I see it) including some challenges this brings, as well as opportunities to support diversity. 

Title: From Pure Maths to AI via Computer Science — One Woman’s Journey

Date: Wednesday 27th May 2026, 3.00pm

Venue: LT908

Abstract: In this talk I will offer some reflections on my personal journey from an undergraduate degree in pure mathematics, through to serving as the Head of School in the largest Computer Science/Artificial Intelligence department in the UK, the School of Informatics at the University of Edinburgh in the period 2018-2023.  During the talk as well as giving a high-level description of my research and how it evolved, I will also talk about the changing EDI landscape, highlighting both challenges and opportunities.

Title: What can you do? - Recommendations for Improving Gender Allyship in STEM

Date: Thursday 22nd October 2026, 12.45pm

Venue: LT908

Abstract: Oftentimes those in STEM research can have good intentions about improving gender diversity, but do not necessarily know where to begin or the resources that are already available.

During my time as a PhD student, I co-hosted a workshop for postgraduate research students within the College of Engineering and Physical Sciences at the University of Birmingham entitled “How to be an Ally”. The workshop aimed to collaboratively create a definition for what we as postgraduate research students believe to be an ally, with a focus on gender equity. We also planned to generate a broad set of actions to promote and develop allyship across the college ranging from individual to institutional level change.

In this talk, I will discuss the importance of allyship, the objectives of the “How to be an Ally” workshop and discuss some of the actions suggested by attendees. Last year, we created a booklet entitled “What can you do?” (in collaboration with the Piscopia Initiative) which incorporates the suggestions from the workshop alongside thoughts from academics across the UK and the Piscopia community. I will highlight some of the themes found across the recommendations, including the concept of the “invisible workload”, myth-busting an academic career and contextualising the mathematics that we teach.

The talk is supported by funding received from the University of Strathclyde’s Research, Knowledge Exchange and Innovation Network Culture Network - Collaborative Cultures Development Funding (RKEI), supported by the Wellcome Trust (Wellcome Trust grant reference number 228116/Z/23/Z (‘Cultures of Collaborative Research in a Socially Progressive Technological University’). ) .