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This talk will contain no new algorithms or methods for computation in groups. Instead, I will describe my (ab)using of existing algorithms (in Magma) to help study the structure of exceptional algebraic groups, their Lie algebras and the exceptional finite groups of Lie type. Such computational methods have guided me and often formed part of the argument in lots of my work, including joint projects with Tim Burness, Alastair Litterick and David Stewart. These applications have included representation theory, especially calculating cohomology groups, intersection of subgroups and construction of subgroups. The talk will include many open-ended (and impossible-to-answer) questions about the finite groups of Lie type machinery and related algorithms, which will hopefully be helpful to other users in the audience.

I will describe practical methods for the construction of ordinary representations of a finite group G via the extension of existing representations defined on a proper subgroup of G. I will also describe how, using an implementation of this algorithm within Magma, I was able to construct for the first time minimal-degree faithful ordinary representations of most of the large sporadic simple groups, such as the Baby Monster.

Disordered proteins play an essential role in a wide variety of biological processes. One such protein is Histone H1, which condenses chromatin – the complex of genomic DNA and its packaging proteins – in a way that is still poorly understood, despite decades of research. While the textbooks tell us that the endpoint of this condensation process is a 30 nm fibre, the fibre is elusive in vivo. Instead, the latest super-resolution methods reveal a heterogeneous, dynamic and liquid-like assembly, and the growing evidence, from us and others, points to liquid-liquid phase separation as a mechanism that could produce a compact but dynamic ‘ground state’ of H1-bound chromatin. The hypothesis is compelling, since a liquid condensate is a more plausible means by which chromatin could respond quickly to environmental stimuli.

The region of H1 that is responsible for chromatin condensation is its long, highly disordered C-terminal tail. However, the tail is all but invisible in the best cryo-EM structures of chromatin to date, implying some degree of disorder remains. We have developed a model system that is amenable to NMR and other biophysical techniques. The model allows us to study the nature of this disordered state at high resolution. In addition, it recapitulates the condensing behaviour of chromatin, forming phase-separated liquid condensates, while allowing capture of the thermodynamics underpinning the various processes. Before condensation, we find the protein, despite its high affinity for DNA, does not undergo a disorder-to-order transition on binding, but forms a ‘fuzzy complex’. We can also use the model to study the phase-separated state, which under certain conditions contains higher-order structure. The condensate is also highly sensitive to the phosphorylation state of the protein. These ‘bottom-up’ findings are broadly consistent with the current in vivo picture. They also provide insights into how tight binding need not be driven by disorder-to-order transitions, and how condensation and higher-order structuring can be dynamic and thus exquisitely sensitive to perturbation by post-translational modifications, broadening the repertoire of mechanisms that might regulate chromatin and presumably other macromolecular assemblies.

Turner AL, Watson M, Wilkins OG, Cato L, Travers A, Thomas JO, Stott K. “Highly disordered histone H1-DNA model complexes and their condensates.” Proc Natl Acad Sci U S A. (2018) doi: 10.1073/pnas.1805943115.
Associated commentary: https://doi.org/10.1073/pnas.1816936115

Abstract not available

There are various methodological choices that can be made for (TD)DFT simulations, some of which impact on the calculations to be carried out to a greater or lesser extent. This talk will discuss the implications for the atomic forces of a moving basis set as used in the SIESTA code.

Since the work of Dynkin the reductive subalgebras of a semisimple complex Lie algebra are divided in two groups: those that are contained in a proper regular subalgebra, and those that are not (these are called S-subalgebras). I will describe computational methods to obtain real forms of the complex embeddings of reductive Lie algebras in semisimple subalgebras. There is one algorithm for the regular subalgebras and one for the S-subalgebras. Recently we have used these to obtain the maximal reductive subalgebras of the simple real Lie algebras of ranks up to 8. This is joint work with Heiko Dietrich, Paolo Faccin and Alessio Marrani.

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In March 2016, DeepMind’s computer program AlphaGo surprised the world by defeating the world-champion Go player, Lee Sedol. AlphaGo has a novel, surprising and valuable style of play, and has been recognized as ‘creative’ by the AI and Go communities. This paper examines whether AlphaGo engages in creative problem solving according to the standards of comparative psychology. I conclude that although AlphaGo lacks one important aspect of creative problem solving found in animals (domain generality) it exhibits a different capacity for creativity: namely, the ability to transform a conceptual space through something akin to instrumental conditioning. This analysis has consequences for how we think about creativity in humans and AI.

Gene regulatory evolution provides a significant source of material for phenotypical change. However, there is only a limited understanding of what paths are possible for regulatory evolution, as most evidence is limited to either standing variation or biased perturbations of transcriptional enhancers. Using a synthetic mutation library for a developmental enhancer in Drosophila melanogaster, and an automated robotics pipeline, we show that most nucleotide mutations in a minimal enhancer cause changes in gene expression. These changes include transcription levels, probability, timing, and spatial patterns. We demonstrate that this pipeline can be used to identify novel transcription factor binding sites. Based on these sites, we present evidence for transcriptional cooperativity that makes the enhancer sensitive to nucleotide polymorphisms. We find that sets of mutations often simultaneously change levels and locations of expression. Together, our results suggest that the parameters of gene expression are not independent variables but rather convolved within an enhancer, and this codependency can constrain the evolvability of developmental enhancers.

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Two loop Feynman diagrams give rise to interesting cubic hypersurfaces in n variables, where n is the number of edges. When n=3, the cubic is obviously an elliptic curve. (In fact, a family of elliptic curves parametrized by physical parameters like momentum and masses.) Remarkably, elliptic curves appear also for suitable graphs with n=5 and n=7, and conjecturally for an infinite sequence of graphs with n odd. I will describe the algebraic geometry involved in proving this. Physically, the amplitudes associated to one-loop graphs are known to be dilogarithms. Time permitting, I will speculate a bit about how the presence of elliptic curves might point toward relations between two-loop amplitudes and elliptic dilogarithms.   

This is joint work with C. Doran, P. Vanhove, and M. Kerr.   

Because of a long history of intergroup conflict, humans evolved to be tribal. These tribal tendencies can lead individuals to sacrifice sound reasoning and judgmental accuracy in order to conform to and defend the views of their ingroup. Political tribes are one of the most salient forms of modern tribal identity, and so politics likely triggers these tribal tendencies, leading to ideologically distorted information processing. My work has shown that these ideological biases exist in similar degrees in liberals and conservatives, but certain sacred concerns can lead to stronger biases in one group than in the other. Liberals have sacred concerns about traditionally conceived disadvantaged groups, and thus liberals are more biased than conservatives when evaluating information with significance to such groups. And because social scientists are overwhelmingly liberal, these sacred concerns may have biased and may continue to bias the conclusions drawn by social scientists.

_Cory Clark received her PhD in Social Psychology from University of California, Irvine in 2014, and she is currently an Assistant Professor of Social Psychology at Durham University. She has two main programs of research, examining (1) how punitive desires shape beliefs about human agency and moral responsibility, and (2) how political biases influence evaluations of science. She also co-hosts a podcast, Psyphilopod, which covers psychology, philosophy, politics, and academic culture._

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We know well that ice is a crystal where molecules are arranged in a regular pattern, while water is a liquid where molecules have a disordered arrangement. Also, water flows, while ice is a solid. There is a natural physical theory that links the crystalline order of ice to its solid properties. However, this theory fails for materials like window glass, which manage to be physically solid, without crystalline order. Some modern theories aim to explain this by the concept of “amorphous order” — they say that glass is an ordered material, but the order is not apparent to our eye. Other theories argue that the relevant order can only be seen if one looks at the system in space-time, instead of regular space. This remains a controversial area of science, despite the fact that glassy materials have been used by humans for thousands of years.

I use these examples to discuss some unusual types of Order in physical theories, and how this can be quantified.

About the Speaker: Dr Robert Jack is an interdisciplinary Lecturer with a joint appointment between the Dept of Chemistry and DAMTP. His research uses the theory of statistical mechanics to understand the behaviour of complex systems including biomolecules, glassy liquids, and soft matter. In particular, he is interested in co-operative dynamics: for example, how do molecules move in crowded environments? What are the co-operative mechanisms for colloidal self-assembly, and the folding of biomolecules?

Chevalley proved that the image of an algebraic morphism between algebraic varieties is a constructible set. Examples are orbits of algebraic group actions. A constructible set in a topological space is a finite union of locally closed sets and a locally closed set is the difference of two closed subsets. Simple examples show that even if the source and target of the morphism are affine varieties the image may neither be affine nor quasi-affine. In this talk, I will present a Gröbner-basis-based algorithm that computes the constructible image of a morphism of affine spaces, along with some applications.