6 research outputs found
Boundary and defect CFT: Open problems and applications
A review of Boundary and defect conformal field theory: open problems and applications, following a workshop held at Chicheley Hall, Buckinghamshire, UK, 7–8 Sept. 2017. We attempt to provide a broad, bird’s-eye view of the latest progress in boundary and defect conformal field theory in various sub-fields of theoretical physics, including the renormalization group, integrability, conformal bootstrap, topological field theory, supersymmetry, holographic duality, and more. We also discuss open questions and promising research directions in each of these sub-fields, and combinations thereof
Approximation Theory and Related Applications
In recent years, we have seen a growing interest in various aspects of approximation theory. This happened due to the increasing complexity of mathematical models that require computer calculations and the development of the theoretical foundations of the approximation theory. Approximation theory has broad and important applications in many areas of mathematics, including functional analysis, differential equations, dynamical systems theory, mathematical physics, control theory, probability theory and mathematical statistics, and others. Approximation theory is also of great practical importance, as approximate methods and estimation of approximation errors are used in physics, economics, chemistry, signal theory, neural networks and many other areas. This book presents the works published in the Special Issue "Approximation Theory and Related Applications". The research of the world’s leading scientists presented in this book reflect new trends in approximation theory and related topics
Bridge between worlds: relating position and disposition in the mathematical field
Using ethnographic observations and interview based research I document the
production of research mathematics in four European research institutes,
interviewing 45 mathematicians from three areas of pure mathematics: topology,
algebraic geometry and differential geometry. I use Bourdieu's notions of habitus,
field and practice to explore how mathematicians come to perceive and interact
with abstract mathematical spaces and constructions. Perception of mathematical
reality, I explain, depends upon enculturation within a mathematical discipline. This
process of socialisation involves positioning an individual within a field of
production. Within a field mathematicians acquire certain structured sets of
dispositions which constitute habitus, and these habitus then provide both
perspectives and perceptual lenses through which to construe mathematical
objects and spaces.
I describe how mathematical perception is built up through interactions
within three domains of experience: physical spaces, conceptual spaces and
discourse spaces. These domains share analogous structuring schemas, which are
related through Lakoff and Johnson's notions of metaphorical mappings and image
schemas. Such schemas are mobilised during problem solving and proof
construction, in order to guide mathematicians' intuitions; and are utilised during
communicative acts, in order to create common ground and common reference frames. However, different structuring principles are utilised according to the
contexts in which the act of knowledge production or communication take place.
The degree of formality, privacy or competitiveness of environments affects the
presentation of mathematicians' selves and ideas. Goffman's concept of interaction
frame, front-stage and backstage are therefore used to explain how certain
positions in the field shape dispositions, and lead to the realisation of different
structuring schemas or scripts.
I use Sewell's qualifications of Bourdieu's theories to explore the multiplicity
of schemas present within mathematicians' habitus, and detail how they are given
expression through craftwork and bricolage. I argue that mathematicians'
perception of mathematical phenomena are dependent upon their positions and
relations. I develop the notion of social space, providing definitions of such spaces
and how they are generated, how positions are determined, and how individuals
reposition within space through acquisition of capital