This week Professor Dominic Vella will talk about wrinkling  

In this talk I will provide an overview of recent work on the wrinkling of thin elastic objects. In particular, the focus of the talk will be on answering questions that arise in recent applications that seek not to avoid, but rather, exploit wrinkling. Such applications usually take place far beyond the threshold of instability and so key themes will be the limitations of “standard” instability analysis, as well as what analysis should be performed instead. I will discuss the essential ingredients of this ‘Far-from-Threshold’ analysis, as well as outlining some open questions.  

Abstract

This talk will provide an overview of mathematical modelling applied to the behaviour of ice sheets and their role in the climate system.  I’ll provide some motivation and background, describe simple approaches to modelling the evolution of the ice sheets as a fluid-flow problem, and discuss some particular aspects of the problem that are active areas of current research.  The talk will involve a variety of interesting continuum-mechanical models and approximations that have analogues in other areas of applied mathematics.

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The many facets of community detection on networks 

Community detection, the decomposition of a graph into essential building blocks, has been a core research topic in network science over the past years. Since a precise notion of what consti- tutes a community has remained evasive, community detection algorithms have often been com- pared on benchmark graphs with a particular form of assortative community structure and classified based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different goals and rea- sons for why we want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community detection. This problem-driven classification is useful in applied network science, where it is important to select an appropriate algorithm for the given purpose. Moreover, highlighting the different facets of community detection also delineates the many lines of research and points out open directions and avenues for future research.

How long does it take for a pandemic to stop spreading? When modelling an infection process, especially these days, this is one of the main questions that comes to mind. In this talk, we consider this question in the bootstrap percolation setting.

Graph-bootstrap percolation, also known as weak saturation, was introduced by Bollobás in 1968. In this process, we start with initial "infected" set of edges $E_0$, and we infect new edges according to a predetermined rule. Given a graph $H$ and a set of previously infected edges $E_t \subseteq E(Kn)$, we infect a non-infected edge $e$ if it completes a new copy of $H$ in $G=([n] , E_t \cup \{e\})$. A question raised by Bollobás asks for the maximum time the process can run before it stabilizes. Bollobás, Przykucki, Riordan, and Sahasrabudhe considered this problem for the most natural case where $H=K_r$. They answered the question for $r \leq 4$ and gave a non-trivial lower bound for every $r \geq 5$. They also conjectured that the maximal running time is $o(n^2)$ for every integer $r$. We disprove their conjecture for every $r \geq 6$ and we give a better lower bound for the case $r=5$; in the proof we use the Behrend construction. This is a joint work with József Balogh, Alexey Pokrovskiy, and Tibor Szabó.

In some ways the theory of mapping class groups of 4-manifolds is in 2020 at the same place where the theory of mapping class groups of 2-manifolds was in 1973, before Thurston changed everything.  In this talk I will describe some first steps in an ongoing joint project with Eduard Looijenga where we are trying to understand mapping class groups of certain algebraic surfaces (e.g. rational elliptic surfaces, and also K3 surfaces) from the Thurstonian point of view.