Browsing Department of Pure Mathematics and Mathematical Statistics (DPMMS) by Title
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The classification of maps between the classifying spaces of Lie groups
(University of CambridgeGonville and Caius CollegeDepartment of Pure Mathematics and Mathematical Statistics, 19740801)

The contact property for magnetic flows on surfaces
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity College, 20150106)This work investigates the dynamics of magnetic flows on closed orientable Riemannian surfaces. These flows are determined by triples (M, g, σ), where M is the surface, g is the metric and σ is a 2form on M . Such dynamical ...

The Fourier transform for certain hyperKähler fourfolds
(American Mathematical SocietyThe Fourier transform for certain hyperKähler fourfolds, 20151118)Using a codimension1 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 ...

The Fukaya category, exotic forms and exotic autoequivalences
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20120410)A symplectic manifold is a smooth manifold M together with a choice of a closed nondegenerate twoform. Recent years have seen the importance of associating an A∞category to M, called its Fukaya category, in helping ...

The geodesic Xray transform with a $GL(n,\mathbb{C})$connection
We derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of such all transforms in a neighbourhood of constant ...

The greedy basis equals the theta basis: A rank two haiku
(ElsevierJournal of Combinatorial Theory Series A, 20160826)We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee–Li–Zelevinsky and the theta basis of Gross–Hacking–Keel–Kontsevich.

The half plane UIPT is recurrent
(SpringerProbability Theory and Related Fields, 20170307)We prove that the half plane version of the uniform infinite planar triangulation (UIPT) is recurrent. The key ingredients of the proof are a construction of a new full plane extension of the half plane UIPT, based on a ...

The monotone wrapped Fukaya category and the openclosed string map
(SpringerSelecta Mathematica, 20160809)We build the wrapped Fukaya category $\textit{W}$($\textit{E}$)for any monotone symplectic manifold $\textit{E}$, convex at infinity. We define the openclosed and closedopen string maps, OC : HH$_{*}$($\textit{W}$($\textit{E}$)) ...

The Planar Ising Model and Total Positivity
(SpringerJournal of Statistical Physics, 20170101)A matrix is called totally positive (resp. totally nonnegative) if all its minors are positive (resp. nonnegative). Consider the Ising model with free boundary conditions and no external field on a planar graph G. Let ...



The symplectic arc algebra is formal
(Duke University PressDuke Mathematical Journal, 20160128)We prove a formality theorem for the Fukaya categories of the symplectic manifolds underlying symplectic Khovanov cohomology over fields of characteristic zero. The key ingredient is the construction of a degreeone ...

The topology of terminal quartic 3folds
(University of Cambridge, 20070620)Let Y be a quartic hypersurface in P^4 with terminal singularities. The GrothendieckLefschetz theorem states that any Cartier divisor on Y is the restriction of a Cartier divisor on P^4 . However, no such result holds ...

The Triviality problem for profinite completions
(SpringerInventiones Mathematicae, 20150224)We prove that there is no algorithm that can determine whether or not a finitely presented group has a nontrivial finite quotient; indeed, this property remains undecidable among the fundamental groups of compact, ...

The work of Lucio Russo on percolation
The contributions of Lucio Russo to the mathematics of percolation and disordered systems are outlined. The context of his work is explained, and its ongoing impact on current work is described and amplified.

The Xray transform for connections in negative curvature
(SpringerCommunications in Mathematical Physics, 20151123)We consider integral geometry inverse problems for unitary connections and skewHermitian Higgs fields on manifolds with negative sectional curvature. The results apply to manifolds in any dimension, with or without boundary, ...

Three viewpoints on semiabelian homology
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticisEmmanuel College, 20091117)The main theme of the thesis is to present and compare three different viewpoints on semiabelian homology, resulting in three ways of defining and calculating homology objects. Any two of these three homology theories ...

Threedimensional manifolds
(University of CambridgeFaculty of MathematicsTrinity College, 19600803)In the postwar years, the theory of 3dimensional manifolds has developed tremendously. On the one hand, Bing and Moise have proved that 3manifolds can be triangulated, and that the Hauptvermutung (that any two triangulations ...

Topics in arithmetic combinatorics
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20071023)This thesis is chiefly concerned with a classical conjecture of Littlewood's regarding the L^1norm of the Fourier transform, and the closely related idempotent theorem. The vast majority of the results regarding these ...

Topological cycle matroids of infinite graphs
(ElsevierEuropean Journal of Combinatorics, 20170201)We prove that the topological cycles of an arbitrary infinite graph together with its topological ends form a matroid. This matroid is, in general, neither finitary nor cofinitary.