Below are the future seminars organised by the School of Mathematics.
Please note that only some seminar series are advertised here.
Results 1 to 10 of 49
This conference will put together researchers in the field of set-theoretical solutions of the Yang-Baxter equation, and related areas (in the broad sense), and discuss some of their different perspectives and incarnations, recent developments, applications, and future directions.
Inhalational anthrax, caused by the bacterium Bacillus anthracis, is a disease with very high fatality rates. Due to the significant risk posed if the bacterium was to be intentionally used as a bioweapon, it is important to be able to defend against such an attack and to make optimal decisions about treatment strategies. Mechanistic mathematical models can help to quantify and improve understanding of the underlying mechanisms of the infection. In this talk, I will present a multi-scale mathematical model for the infection dynamics of inhalational anthrax. This approach involves constructing individual models for the intracellular, within-host, and population-level infection dynamics, to define key quantities characterising infection at each level, which can be used to link dynamics across scales. I will begin by introducing a model for the intracellular infection dynamics of B. anthracis, which describes the interaction between B. anthracis spores and host cells. The model can be used to predict the distribution of outcomes from this host-pathogen interaction. For example, it can be used to estimate the number of bacteria released upon rupture of an infected phagocyte, as well as the timing of phagocyte rupture and bacterial release. Next, I will show how these key outputs can be used to connect the intracellular model to a model of the infection at the within-host scale. The within-host model aims to provide an overall understanding of the early progression of the infection, and is parametrised with infection data from studies of rabbits and guinea pigs. Furthermore, this model allows the probability of infection and the time to symptoms to be calculated. Building a model that offers a realistic mechanistic description of different animal responses to the inhalation of B. anthracis spores is an important step towards eventually extrapolating the model to describe the dynamics of human infection. This would enable predictions of how many individuals would become infected in different exposure scenarios and also on what timescale this would occur.
One of the strongest known large cardinal axioms is I3, positing the existence of a non-trivial elementary embedding $j$ from $V_λ$ to $V_λ$ for some $λ$. Given two such embeddings $j$ and $k$ for the same lambda, there is a natural "application" operation to yield a third, $j*k$, and elementarity shows that this operation is left self-distributive: $j*(k*l)=(j*k)*(j*l)$. Structures with such an operation are called LD-algebras or shelves. Laver showed that the algebra of embeddings generated by a single such $j$ under $*$ is in fact the free LD-algebra on 1 generator; and the set-theoretic context around this concrete (once you've assumed I3) instantiation of the free LD-algebra gives rise to various theorems about LD-algebras that are only known under this very strong large cardinal assumption. Given I3, there will be many other embeddings from $V_λ$ to $V_λ$, and it is natural to ask if one can obtain from amongst them a free LD-algebra on more than one generator. In joint work with Scott Cramer and Sheila Miller, we show that the answer is positive if one assumes a little more: from I2 we get a free 2-generator LD-algebra of embeddings. This talk will focus on set-theoretic aspects of the proof; a week later I will be giving a talk in the ARTIN conference on the same topic, focusing more on the algebraic aspects.
Given a (Dynkin) quiver $Q$ one can associate both a simple Lie algebra 𝔤 and the category of representations $Rep(Q)$ of $Q$. Early on it was realised that both associated objects are related, as for example beautifully illustrated by Gabriel's theorem. In this talk we will consider two associated categories of representations: (i) (some quotient of) the derived category $D^b(Rep(Q))$ and (ii) the finite dimensional representations of the quantum loop algebra $U_q(L𝔤)$. Although both look quit differently, we will delve into wished to be understood ties. The presented story will be one of categorifications of a common algebra with a rich combinatorial structure: a cluster algebra. The category (i) yields a so-called additive categorification and (ii) a monoidal one. In the first half of the talk we will give a gentle and minimalistic introduction to the various objects and concepts mentioned. In the second half we will give an intuitive overview of recent conjectural connections and then finish by (very briefly) mentioning some ongoing contributions.
When managing a breeding programme, we want to maximize the selection of desirable traits (such as health or yield). At the same time, we know that related plants or animals are more likely to share traits, so we also need to incorporate minimizing inbreeding and its associated risks. This can be modelled as a bi-objective optimization problem, which happens to have a similar structure to portfolio theory from financial mathematics.
Collaborating with researchers at the Roslin Institute in the Royal (Dick) School of Veterinary Studies, we examined how a range of mathematical tools can be used to explore this problem more accurately and efficiently than the state of the art. These were tested with simulated breeding programmes and led to the creation of an open-source tools for practitioners.
An element $x$ in a group $G$ is a left Engel element if for each $x ∈ G$ there exists a positive integer $n = n(x)$ such that $[[[g,x],x],··· ,x] = 1$ ($n$ times). If $n = n(x)$ can be chosen independently of $x$, then we say that $x$ is a left $n$-Engel element. There are some connections to groups of prime power exponent and for example, every element in a group of exponent 3 is a left 2-Engel element. Whereas it is easy to see that the normal closure of a left 2-Engel element is abelian, it is still an open question whether the normal closure of a left 3-Engel element is locally nilpotent. We will give some overview of this problem, focusing on advances in recent years.
We take a look at several random geometric graphs (RGG) with increasing levels of complexity, starting from the classical Gilbert disc model with fixed radius and up to the weight-dependent random connection model. At each step, we discuss the heuristics of what the newly added complexity changes in the behaviour of the models and how it affects the criticality of the largest connected component and the typical distance between two points of this component.
In this talk, I will show that a ring morphism $p:A ⟶ B$ satisfying certain mild assumptions induces a derived endomorphism of $A$ and a derived endomorphism of $B$, which are closely related. In fact, the derived endomorphism of $A$ is the twist around the restriction of scalars functor, and the derived endomorphism of $B$ is the corresponding cotwist. These endomorphisms are autoequivalences in certain settings, one of which is that of Frobenius exact categories. More precisely, assume that $A$ is the endomorphism algebra of an object in a Frobenius exact category satisfying mild assumptions and B is the corresponding stable endomorphism algebra. Then, if $B$ is "$n$-relatively spherical", I will show that both the twist and cotwist are equivalences. In fact, when $B$ is finite dimensional, "3-relatively spherical" is equivalent to self-injective, and the cotwist turns out to be a shift of the Nakayama autoequivalence of $B$. This technology can be used to construct new derived autoequivalences for very singular varieties.
Type Ia supernova are known to be thermonuclear explosions in a carbon-oxygen white dwarf that has acquired a helium envelope by accretion from a close companion star. The consensus model is that a flame starts at the centre of such a star and then becomes a detonation. This only works if the star is close to its maximum possible mass, the Chandrakhar mass (~ 1.4 solar masses).
I will discuss an alternative model in which a detonation in the helium envelope triggers a detonation the carbon-oxygen core. Recent work has shown that such a model could explain all "normal" type Ia supernovae, but there are disparities in length scales that make direct numerical simulations extremely difficult. The talk will consider some alternative techniques, such as front tracking using level set methods.
Lagrangian multiforms were introduced in 2009 together with a new variational principle that was suitable for describing the phenomenon of multidimensional consistency (MDC) within a variational framework. MDC is the key integrability aspect of families of simultaneous equations that can be imposed on one and the same dependent variable in a space of independent variables of in principle arbitrary dimension.
In Lagrangian multiform theory, not only the equations of motion are derived from one cohesive principle, but also the Lagrangian components themselves, of what has now become no longer a scalar object ("the Lagrangian of a theory") but a differential or difference form in a (multi-time) space of arbitrary dimension.
In the talk I will explain the principle, and present examples of Lagrangian 1-forms (compatible systems of ODEs), 2-forms (hierarchies of PDEs or partial difference equations) and 3-forms, both in the discrete as well as continuous realm. In the latter cases I will make a connection with topological field theory and an infinite-dimensional Chern-Simons theory.
(This comprises work with many collaborators).