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Computations in monotone Floer theory
(Department of Pure Mathematics and Mathematical Statistics, University of CambridgeUniversity of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2016-06-28)
Floer theory is a rich collection of tools for studying symplectic manifolds and their Lagrangian submanifolds with the help of holomorphic curves. Its origins lie in estimating the numbers of equilibria in Hamiltonian ...
L-space intervals for graph manifolds and cables
(Cambridge University PressCompositio Mathematica, 2017-05)
We present a graph manifold analog of the Jankins–Neumann classification of Seifert fibered spaces over $S^2$ admitting taut foliations, providing a finite recursive formula to compute the L-space Dehn-filling interval for ...
Spectral gap in the group of affine transformations over prime fields
(University of ToulouseAnnales de la Faculte des Sciences de Toulousehttp://afst.cedram.org/item?id=AFST_2016_6_25_5_969_0, 2016-11-01)
We study random walks on the groups $\Bbb F^d_p \rtimes$ SL$_d$($\Bbb F_p$). We estimate the spectral gap in terms of the spectral gap of the projection to the linear part SL$_d$($\Bbb F_p$). This problem is motivated by ...
INVARIANT DISTRIBUTIONS AND THE GEODESIC RAY TRANSFORM
(Mathematical Science PublishersAnalysis & PDE, 2016-12-11)
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 ...
Freiman homomorphisms on sparse random sets
(Oxford University PressQuarterly Journal of Mathematics, 2017-02-03)
A result of Fiz Pontiveros shows that if $A$ is a random subset of $\mathbb{Z}_N$ where each element is chosen independently with probability $N^{-1/2+o(1)}$, then with high probability every Freiman homomorphism defined ...
Tubular free by cyclic groups act freely on CAT(0) cube complexes
(Canadian Mathematical SocietyCanadian Mathematical Bulletin, 2017-03-01)
We identify when a tubular group (the fundamental group of a finite graph of groups with $\mathbb{Z}$$^{2}$ vertex and $\mathbb{Z}$ edge groups) is free by cyclic and show, using Wise's equitable sets criterion, that every ...
Exploring Random Geometry with the Gaussian Free Field
(University of CambridgeDPMMSPeterhouse, 2016-10-01)
This thesis studies the geometry of objects from 2-dimensional statistical physics in the continuum.
Chapter 1 is an introduction to Schramm-Loewner evolutions (SLE). SLEs are the canonical family of non-self-intersecting, ...
Total Positivity in Markov Structures
(Institute of Mathematical StatisticsAnnals of Statistics, 2017-06)
We discuss properties of distributions that are multivariate totally positive of order two (MTP$_{2}$) related to conditional independence. In particular, we show that any independence model generated by an MTP$_{2}$ ...
Pairwise Markov properties for regression graphs
(WileyStat, 2016-11-13)
With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ...
Bayesian Nonparametric Ordination for the Analysis of Microbial Communities
(Taylor & FrancisJournal of the American Statistical Association, 2017-07-10)
Human microbiome studies use sequencing technologies to measure the abundance of bacterial species or Operational Taxonomic Units (OTUs) in samples of biological material. Typically the data are organized in contingency ...