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Increasingly high-profile research is being undertaken into the socio-environmental challenges associated with the over-production and consumption of food from animals. Transforming food systems to mitigate climate change and hidden hunger, ensure food security and good health all point to reducing animal-based foods as a key lever. Moving beyond animal-based food systems is a societal grand challenge requiring coordinated international research by the social sciences and humanities. A ‘selective openness’ to this range of disciplines has been observed within multi-discipline research programmes designed to address societal grand challenges including those concerned with the sustainability of food systems, inhibiting the impact of social sciences and humanities. Further, existing research on animal-based foods within these disciplines is largely dispersed and focused on particular parts of food systems. Inspired by the ‘Sutherland Method’ this paper discusses the results of an iterative research prioritisation process carried out to enhance capacity, mutual understanding and impact amongst European social sciences and humanities researchers. The process produced 15 research questions from an initial list of 100 and classified under the following five themes: 1) Debating and visioning food from animals; 2) Transforming agricultural spaces; 3) Framing animals as food; 4) Eating practices and identities; 5) Governing transitions beyond animal-based food systems. These themes provide an important means of making connections between research questions that invite and steer research on key challenges in moving beyond animal-based food systems. The themes also propose loci for future transdisciplinary research programmes that join researchers from the natural sciences, social sciences and humanities and stakeholders from beyond academia to develop cooperative research and implementation initiatives. The experiences gained from the prioritisation process draw attention to the value of spending time to discuss and collaboratively steer research inquiry into emergent and controversial matters of concern. Fundamental, ethical questions around the continuation or complete cessation of the use of animals for food was a key tension. The positioning of research towards these questions affects not only the framing of the research area but also the partners with whom the research can be carried out and for whom it may be of benefit.

Statistical analysis of tibiotarsus distal breadth measurements shown in Figure 3. Measurements are in mm. Univariate statistics are presented in the upper register of the table. The test (U) statistics (top right of the lower register) and p-values (bottom left of the lower register) of a non-parametric Mann-Whitney pairwise comparison are presented. Mann-Whitney analysis is commonly used in zooarchaeological studies to test temporal changes to animal bone measurements77, 78. Statistically-significant p-values are highlighted in grey. The null hypothesis, that there is no difference in median tibiotarsus distal breadth measurements over time, can be rejected for chicken bones younger than 1340-1450C.E. Modern broiler tibiotarsi are significantly larger than those from all other periods.

The Anthropocene provides a useful way to think through all manner of human-environment processes and challenges. This is especially pronounced in relation to food and farming, which are heavily implicated in changes to the earth’s biophysical and chemical processes. Yet, despite burgeoning interest in the Anthropocene as a concept, it is comparatively absent from recent developments in food geography. This is surprising given the profound impacts of food and agriculture on biogeochemical flows and geographical strata, and given future predictions regarding ‘Anthropogenic climate change’. The objective of this Theme Issue therefore, and the five papers that comprise it, is to redress this by directly connecting and drawing together social science scholarship that examines food geographies ‘in’, ‘of’ and ‘for’ the Anthropocene. The Theme Issue papers engage with different aspects of the Anthropocene as spatial phenomenon and here we integrate relevant arguments from each, alongside wider agri-food geographical scholarship, to explain what we mean by food geographies ‘in’, ‘of’ and ‘for’ the Anthropocene. In doing so, we respond to Tsing et al.’s (2019) call for a spatial as well as temporal treatment of the Anthropocene. These spatial expressions are also key to the proliferation of terms that have accompanied developments in Anthropocene scholarship. We conclude by offering up some brief reflections on a future research agenda. An important first step is to conceptualise food geographies ‘in’, ‘of’ and ‘for’ the Anthropocene, including accounts that ground and potentially unsettle food and the Anthropocene as Capitalocene (Moore, 2016) and food and the Anthropocene as more-than-human (Haraway, 2016). A second step is to address key contemporary Anthropogenic agri-food relations, especially those that are already in flux or transition. A final priority for future research is to deepen and extend the ethics of care and moral food geographies of the Anthropocene imperative.

In the first part of this thesis, we give a survey of the conjugacy problem in the braid group, describing the solution provided by Garside theory, and outlining the progress that has been made towards a polynomial time solution in recent years using refinements of Garside's solution, and the Thurston-Nielsen classification of braids, which reduces the problem to the case of pseudo-Anosov braids. Using the faithful Lawrence-Krammer-Bigelow representation of the braid groups, we consider how the eigenspaces of pseudo-Anosov braids can under certain conditions yield invariants of their conjugacy class and thus lead us towards a polynomial time solution of the conjugacy problem.\ud \ud In the second part we introduce Bessis-Garside groups, a generalisation of the methods used by Bessis in his papers on dual braid monoids. We consider the groups given by taking the quotient of the free group by the orbits of its generators under the action of some subgroup of the braid group, and find that in many cases this construction can give us a group with a Garside structure. By means of introduction we review the simple rank 2 case, and summarise examples of such groups already known to admit Garside structures, in particular due to the work of Digne. We then go on to give all those of such groups which can be found as quotients of affine and spherical Artin groups of rank 3. We show that all such groups may be given a cycle presentation, or equivalently may be given as labelled-oriented-graph presented groups, and give conditions on such presentations that are equivalent to the group admitting a `dual' Garside structure. Restricting by the cycle lengths occurring in such presentations we give all Bessis-Garside groups of rank 3 which have all cycles length at most 4, and discuss the case of Bessis-Garside groups with uniform cycle length.