We study versions of homological mirror symmetry for hypersurface cusp singularities and the three hypersurface simple elliptic singularities. We show that the Milnor fibres of each of these carries a distinguished Lefschetz ...

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, ...

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 ...

We prove a homological stability theorem for moduli spaces of manifolds of dimension 2$\textit{n}$, for attaching handles of index at least $\textit{n}$, after these manifolds have been stabilised by countably many copies ...

© 2017, Mathematical Sciences Publishers. All rights reserved.We study the space of oriented genus-g subsurfaces of a fixed manifold M and, in particular, its homological properties. We construct a “scanning map” which ...

We study the space of oriented genus $\textit{g}$ subsurfaces of a fixed manifold $\textit{M}$, and in particular its homological properties. We construct a “scanning map” which compares this space to the space of sections ...

In communicating chronic risks, there is increasing use of a metaphor that can be termed ‘effective-age’: the age of a ‘healthy’ person who has the same risk profile as the individual in question. Popular measures include ...

My thesis focuses on the parameterisation and estimation of graphical models, based on the concept of hyper and meta Markov properties. These state that the parameters should exhibit conditional independencies, similar to ...

We develop a notion of containment for independent sets in hypergraphs. For every r-uniform hypergraph G, we find a relatively small collection C of vertex subsets, such that every independent set of G is contained within ...

We establish existence and uniqueness for Gaussian free field flow lines started at interior points of a planar domain. We interpret these as rays of a random geometry with imaginary curvature and describe the way distinct ...

This note presents families of inequalities for the Gaussian measure of convex sets which extend the recently proven Gaussian correlation inequality in various directions.

We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature ...

We construct almost toric fibrations (ATFs) on all del Pezzo surfaces, endowed with a monotone symplectic form. Except for CP$^{2}$#CP$^{2}$, CP$^{2}$#2CP$^{2}$, we are able to get almost toric base diagrams (ATBDs) of ...

Smooth manifolds have been always understood intuitively as spaces that are infinitesimally linear at each point, and thus infinitesimally affine when forgetting about the base point. The aim of this thesis is to develop ...

Let (M, g) be an analytic, compact, Riemannian manifold with boundary, of dimension n≥2. We study a class of generalized Radon transforms, integrating over a family of hypersurfaces embedded in M, satisfying the Bolker ...

In this paper we consider the Gaussian thermostat ray transforms on both closed Riemannian surfaces and compact Riemannian surfaces with boundary. We establish certain results on the injectivity of the thermostat ray ...

We establish an equivalence principle between the solenoidal injectivity of the geodesic ray transform acting on symmetric $\textit{m}$-tensors and the existence of invariant distributions or smooth first integrals with ...

In the recent articles [PSU13, PSU14c], a number of tensor tomography results were proved on two-dimensional manifolds. The purpose of this paper is to extend some of these methods to manifolds of any dimension. A central ...

The U 2 norm gives a useful measure of quasirandomness for realor complex-valued functions defined on finite (or, more generally, locally compact) groups. A simple Fourier-analytic argument yields an inverse theorem, which ...

In this paper we solve the hedge fund manager’s optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager’s payoff at the end of the year will ...