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Homological stability for automorphism groups
(Academic PressAdvances in Mathematics, 2017-10-01)
Given a family of groups admitting a braided monoidal structure (satisfying mild assumptions) we construct a family of spaces on which the groups act and whose connectivity yields, via a classical argument of Quillen, ...
The Calderón problem for connections
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity College, 2017-10-03)
This thesis is concerned with the inverse problem of determining a
unitary connection $A$ on a Hermitian vector bundle $E$ of rank $m$ over
a compact Riemannian manifold $(M, g)$ from the Dirichlet-to-Neumann
(DN) ...
Symmetry in monotone Lagrangian Floer theory
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity College, 2017-10-01)
In this thesis we study the self-Floer theory of a monotone Lagrangian submanifold $L$ of a closed symplectic manifold $X$ in the presence of various kinds of symmetry. First we consider the group $\mathrm{Symp}(X, L)$ ...
Brownian motion correlation in the peanosphere for κ >8
(ElsevierAnnales de l'institut Henri Poincare (B) Probability and Statistics, 2017-11-01)
The peanosphere (or "mating of trees") construction of Duplantier, Miller, and Sheffield encodes certain types of $\gamma$-Liouville quantum gravity (LQG) surfaces ($\gamma \in (0,2)$) decorated with an independent ...
Bounded Height in Families of Dynamical Systems
(Oxford University PressInternational Mathematics Research Notices, 2017-08-29)
Let a, b ∈ $\bar{\mathbb{Q}}$ be such that exactly one of a and b is an algebraic integer, and let f$_{t}$(z) := z$^{2}$ + t be a family of polynomials parameterized by t ∈ $\bar{\mathbb{Q}}$. We prove that the set of all ...
Fano Varieties in Mori Fibre Spaces
(International Mathematics Research Notices, 2016-01-01)
Simplified models for multi-criteria decision analysis under uncertainty
(2010)
When facilitating decisions in which some performance evaluations are uncertain, a decision must be taken about how this uncertainty is to be modelled. This involves, in part, choosing an uncertainty format {a way of ...
Software Support for Podcasting Mobile Lecture Content for Education in Sub-Sahara African Universities
(2013-11)
Podcasting is fast gaining traction in developing regions as a means to augment classroom instruction. Commercial podcasting tools such as Apple’s Leopard Server, Tele-task and OpenEya, despite being successfully used in ...
Designing Ummeli a case for mediated design, a participatory approach to designing interactive systems for semi-literate users
(2013)
This dissertation documents a journey into the design of Ummeli with a community of semi‐literate job seekers in Khayelitsha, Cape Town whose primary access to the internet was through their mobile phones. Working closely ...
Video quality requirements for South African Sign Language communications over mobile phones.
(2012)
This project aims to find the minimum video resolution and frame rate that supports intelligible cell phone based video communications in South African Sign Language.