Extending the Reshetikhin-Turaev TQFT
Abstract
A d-dimensional TQFT is a topological invariant which assigns (d-1)-dimensional manifolds to vector spaces and d-dimensional cobordisms to linear maps. In the early 90s, Reshetikhin and Turaev constructed examples of these in the case d=3, using the data of certain types of linear categories. In this talk, I will provide an overview of this construction, and then explore how this might be meaningfully extended downwards to assign 1-manifolds to "2-vector spaces". Minimal knowledge of category theory assumed!
14:00
The canonical dimension: a different approach to investigate the wavefront set
Abstract
An important invariant in the complex representation theory of reductive p-adic groups is the wavefront set, because it contains information about the character of such a representation. In this talk, Mick Gielen will introduce a new invariant called the canonical dimension, which can be said to measure the size of a representation and which has a close relation to the wavefront set. He will then state some results he has obtained about the canonical dimensions of compactly induced representations and show how they teach us something new about the wavefront set. This illustrates a completely new approach to studying the wavefront set, because the methods used to obtain these results are very different from the ones usually used.
OCIAM TBC
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Dr Marcelo A. Dias is a Reader in Structural Engineering at the University of Edinburgh. His research spans theoretical structural mechanics, soft condensed matter, and materials modelling. He focuses on understanding how the mechanical behaviour of elastic bodies emerges from the interplay between material composition and carefully designed internal geometry. His work has applications across shape formation in nature, biomechanics, materials and structural mechanics, and the controlled design and functionality of thin plates and shells. You can find some wonderful examples of this research on his research site: https://mazdias.wordpress.com/research/
OCIAM TBC
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Dr Edwina Yeo is an applied mathematician working at the interface of continuum mechanics and mathematical biology. She specialises in developing mathematical models for biological and biomedical fluid-mechanics processes, with research spanning regenerative medicine, nanotechnology, microbiology and geology. Her recent work includes models of bacterial adhesion in fluid flow, Von Willebrand Factor dynamics in arterial flows, and microscale contaminant behaviour extracted from imaging data.
Her publications appear in journals such as Biomechanics and Modelling in Mechanobiology, Advanced Materials, and Royal Society Interface, alongside recent collaborative preprints. She is currently an EPSRC National Fellow in Fluid Dynamics at UCL and a visiting research fellow in OCIAM.