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Now showing items 781-790 of 1850
Exceptional collections, and the Néron–Severi lattice for surfaces
(ElsevierAdvances in Mathematics, 2017-01-10)
We work out properties of smooth projective varieties X over a (not necessarily algebraically closed) field $\textit{k}$ that admit collections of objects in the bounded derived category of coherent sheaves D$^{b}$(X) that ...
$\textit{K}$-Theory of Fermat Curves
(Department of Pure Mathematics and Mathematical Statistics, University of CambridgeUniversity of CambridgeChurchill College, 2017-01-10)
I investigate the $K_2$ groups of the quotients of Fermat curves given in projective coordinates by the equation $F_n:X^n+Y^n=Z^n$. On any quotient where the number of known elements is equal to the rank predicted by ...
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$_{2}$ ...