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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)
Severe depression is associated with increased microglial quinolinic acid in subregions of the anterior cingulate gyrus: Evidence for an immune-modulated glutamatergic neurotransmission?
(2011-08-10)
Abstract Background Immune dysfunction, including monocytosis and increased blood levels of interleukin-1, interleukin-6 and tumour necrosis factor α has been observed during acute episodes of major depression. These ...
The Fourier transform for certain hyperKähler fourfolds
(American Mathematical SocietyThe Fourier transform for certain hyperKähler fourfolds, 2015-11-18)
Using a codimension-1 algebraic cycle obtained from the Poincar e line bundle, Beauville de ned the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition ...
Multiple functionally divergent and conserved copies of alpha tubulin in bdelloid rotifers
(2012-08-17)
AbstractBackgroundBdelloid rotifers are microscopic animals that have apparently survived without sex for millions of years and are able to survive desiccation at all life stages through a process called anhydrobiosis. ...
A Quantum Paradox of Choice: More Freedom Makes Summoning a Quantum State Harder
(American Physical SocietyPhysical Review A, 2016)
The properties of quantum information in space-time can be investigated by studying operational tasks, such as ‘summoning’, in which an unknown quantum state is supplied at one point, and a call is made at another for it ...