We study the winding mode sector of recently discovered string theories, which were, until now, believed to describe only conventional field theories in target space. We discover that upon compactification winding modes allows the string to acquire an oscillator spectrum giving rise to an infinite tower of massive higher-spin modes. We study the spectra, S-matrices, T-duality and high-energy behaviour of the bosonic and supersymmetric models. In the tensionless limit, we obtain formulae for amplitudes based on the scattering equations. The windings decouple from the scattering equations but remain in the integrands. The existence of this winding sector shows that these new theories do have stringy aspects and describe non-conventional field theories.  This talk is based on https://arxiv.org/abs/1710.01241.

A wide range of chronic degenerative diseases of mankind result from the accumulation of altered forms of self proteins, resulting in cell toxicity, tissue destruction and chronic inflammatory processes in which the body’s immune system contributes to further cell death and loss of function. A hallmark of these conditions, which include major disease burdens such as Alzheimer’s Disease and type II diabetes, is the formation of long fibrillar polymers that are deposited in expanding tangled masses called plaques. Recently, similarities between these pathological accumulations and physiological mechanisms for organising intracellular space have been recognised, and formal demonstrations that amyloid accumulations form hydrogels have confirmed this link. We are interested in the pathological consequences of amyloid hydrogel formation and in order to study these processes we combine modelling of the assembly process with biophysical measurement of gelation and its cellular consequences.

Please see https://www.eventbrite.co.uk/e/qbiox-colloquium-dunn-school-seminar-hil…

for further details

T cells stimulation by antigen (peptide-MHC, pMHC) initiates adaptive immunity, a major factor contributing to vertebrate fitness. The T cell antigen receptor (TCR) present on the surface of T cells is the critical sensor for the recognition of and response to “foreign" entities, including microbial pathogens and transformed cells. Much is known about the complex molecular machine physically connected to the TCR to initiate, propagate and regulate signals required for cellular activation. However, we largely ignore the physical distribution, dynamics and reaction energetics of this machine before and after TCR binding to pMHC. I will illustrate a few basic notions of TCR signalling and potent quantitative in-cell approaches used to interpret TCR signalling behaviour. I will provide two examples where mathematical formalisation will be welcome to better understand the TCR signalling process.

Please see https://www.eventbrite.co.uk/e/qbiox-colloquium-dunn-school-seminar-hil… for further details.

In this talk, we propose a model describing the growth of tree stems and vine, taking into account also the presence of external obstacles. The system evolution is described by an integral differential equation which becomes discontinuous when the stem hits the obstacle. The stem feels the obstacle reaction not just at the tip, but along the whole stem. This fact represents one of the main challenges to overcome, since it produces a cone of possible reactions which is not normal with respect to the obstacle. However, using the geometric structure of the problem and optimal control tools, we are able to prove existence and uniqueness of the solution for the integral differential equation under natural assumptions on the initial data.

An interval exchange transformation is a map  of an 
interval to 
itself that rearranges a finite number of intervals by translations.  They 
appear among other places in the 
subject of rational billiards and flows of translation surfaces. An 
interesting phenomenon is that an IET may have dense orbits that are not 
uniformly distributed, a property known as non unique ergodicity.  I will 
talk about this phenomenon and present some new results about how common 
this is. Joint work with Jon Chaika.

The structure of the state of art of scientific research is an important object of study motivated by the understanding of how research evolves and how new fields of study stem from existing research. In the last years complex networks tools contributed to provide insights on the structure of research, through the study of collaboration, citation and co-occurrence networks, in particular keyword co-occurrence networks proved useful to provide maps of knowledge inside a scientific domain. The network approach focuses on pairwise relationships, often compressing multidimensional data structures and inevitably losing information. In this paper we propose to adopt a simplicial complex approach to co-occurrence relations, providing a natural framework for the study of higher-order relations in the space of scientific knowledge. Using topological methods we explore the shape of concepts in mathematical research, focusing on homological cycles, regions with low connectivity in the simplicial structure, and we discuss their role in the understanding of the evolution of scientific research. In addition, we map authors’ contribution to the conceptual space, and explore their role in the formation of homological cycles.

Authors: Daniele Cassese, Vsevolod Salnikov, Renaud Lambiotte
 

The number of solutions of a given algebro-geometric configuration, when it is finite, does not change upon a small perturbation of the parameters; this persists 
even upon specializations that change the topology.    The precise formulation of this principle of Poncelet and Schubert   required, i.a., the notions of   algebraically closed fields, flatness, completenesss, multiplicity.     I will explain a model-theoretic version, presented in   quite different terms.  It applies notably to difference equations involving the Galois-Frobenius automorphism $x^p$, uniformly in a prime $p$.   In fixed positive characteristic, interesting technical problems arise that I will discuss if time permits.  

We are all familiar with the need for continuum mechanics-based models in physical applications. In this case, we are interested in large-scale water-wave problems, such as coastal flows and dam breaks.
When modelling these problems, we inevitably wish to solve them on a finite domain, and require boundary conditions to do so. Ideally, we would recreate the semi-infinite nature of a coastline by allowing any generated waves to flow out of the domain, as opposed to them reflecting off the far-field boundary and disrupting the remainder of our simulation. However, applying an appropriate boundary condition is not as straightforward as we might think.
In this talk, we aim to evaluate alternatives to so-called 'active boundary condition' absorption. We will derive a toy model of a shallow-water wavetank, and consider the implementation and efficacy of two 'passive' absorption techniques.