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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, ...
High-dimensional change point estimation via sparse projection
Changepoints are a very common feature of Big Data that arrive in the form of a data stream. In this paper, we study high-dimensional time series in which, at certain time points, the mean structure changes in a sparse ...
Critical surface of the 1-2 model
The 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either 1 or 2. There are three edge directions, and three corresponding parameters a, b, c. It ...
Homological stability for moduli spaces of high dimensional manifolds. I
We prove a homological stability theorem for moduli spaces of simply connected manifolds of dimension 2n > 4, with respect to forming connected sum with S$^{n}$ x S$^{n}$ . This is analogous to Harer's stability theorem ...
Level lines of the Gaussian free field with general boundary data
We study the level lines of a Gaussian free field in a planar domain with general boundary data F. We show that the level lines exist as continuous curves under the assumption that F is regulated (i.e., admits finite left ...
Fractional Calabi-Yau Categories from Landau-Ginzburg Models
We give criteria for the existence of a Serre functor on the derived category of a gauged Landau-Ginzburg model. This is used to provide a general theorem on the existence of an admissible (fractional) Calabi-Yau subcategory ...
Pro-p subgroups of profinite completions of 3-manifold groups
We completely describe the finitely generated pro-$p$ subgroups of the profinite completion of the fundamental group of an arbitrary 3-manifold. We also prove a pro-$p$ analogue of the main theorem of Bass–Serre theory for ...
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 $\mathrm{Symp}(X, L)$ ...