Coastal vegetation has a well-known effect of attenuating waves; however, quantifiable measures of attenuation for general wave and vegetation scenarios are not well known. On the plant scale, there are extensive studies in predicting the dynamics of a single plant in an oscillatory flow. On the coastal scale however, there are yet to be compact models which capture the dynamics of both the flow and vegetation, when the latter exists in the form of a dense canopy along the bed. In this talk, we will discuss the open questions in the field and the modelling approaches involved. In particular, we investigate how micro-scale effects can be homogenised in space and how periodic motions can be averaged in time.

 Author of Alan Turing: The Enigma, sharing his academic path and experience as activist for LGBTQ+ rights

Seeking income during World War II, Piet Hein created the game now called Hex, marketing it through the Danish newspaper Politiken.  The game was popular but disappeared in 1943 when Hein fled Denmark.

The game re-appeared in 1948 when John Nash introduced it to Princeton's game theory group, and became popular again in 1957 after Martin Gardner's column --- "Concerning the game of Hex, which may be played on the tiles of the bathroom floor" --- appeared in Scientific American.

I will survey the early history of Hex, highlighting the war's influence on Hein's design and marketing, Hein's mysterious puzzle-maker, and Nash's fascination with Hex's theoretical properties.

Cluster Adjacency is a geometric principle which defines a subclass of multiple polylogarithms with analytic properties compatible with that of scattering amplitudes and Feynman loop integrals. We use this principle to a priori remove the redundances in the perturbative bootstrap approach and efficiently compute the four-loop NMHV heptagon. Moreover, cluster adjacency is naturally applied to the space of $A_n$ polylogarithms and generates numerous structures therein to be explored further.

I will review the fishnet model, which is an integrable scalar QFT, obtained by an extreme gamma deformation of N=4 super Yang-Mills. The theory has a peculiar perturbative expansion in which many quantities at a fixed loop order are given by a single Feynman diagram. This feature allows the reinterpretation of Feynman loop integrals as integrable systems.

It is known that every continuum X is a weakly confluent image of a continuum Y which is hereditarily indecomposable and of covering dimension one.  We use the ultracoproduct construction to gain information about the number of composants of Y.  For example, in ZFC, we can ensure that this number is arbitrarily large.  And if we assume the GCH, we can arrange for Y to have as many composants at it has points.

Abstract:   Let $f$ be a continuous surjection from the compact metric space $X$ to itself. 

We say that the dynamical system $(X,f)$ has shadowing if for every $\epsilon>0$ there is a $\delta>0$ such that every $\delta$-pseudo orbit is $\epsilon$-shadowed.  Here a sequence $(x_n)$ is a $\delta$-pseudo orbit provided the distance from $f(x_n)$ to $x_{n+1}$ is less than $\delta$ and $(x_n)$ is $\epsilon$-shadowed if there is a point $z$ such that the distance from $x_n$ to $f^n(z)$ is less than $\epsilon$.  

If $f$ is a homeomorphism, $(X,f)$ is said to be expansive if there is some $c>0$, such that if the distance from $f^n(x)$ and $f^n(y)$ is less than $c$ for all $n\in \mathbb Z$, then $x=y$.

In his proof that a homeomorphism that is expansive and has shadowing is stable, Walters shows that in an expansive system with shadowing, a pseudo orbit is shadowed by exactly one point.  It turns out that the converse is also true: if the system has unique shadowing (in the above sense), then it is expansive.

In this talk, which is joint work with Joel Mitchell and Joe Thomas, we explore this notion of unique shadowing.