Browsing Department of Pure Mathematics and Mathematical Statistics (DPMMS) by Title

Now showing items 209-228 of 248

  • The classification of maps between the classifying spaces of Lie groups 

    Mahmud, Zafer (University of CambridgeGonville and Caius CollegeDepartment of Pure Mathematics and Mathematical Statistics, 1974-08-01)

  • The contact property for magnetic flows on surfaces 

    Benedetti, Gabriele (University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity College, 2015-01-06)
    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 2-form on M . Such dynamical ...

  • The Fourier transform for certain hyperKähler fourfolds 

    Shen, Mingmin; Vial, Charles Louis (American Mathematical SocietyThe Fourier transform for certain hyperKähler fourfolds, 2015-11-18)
    Using a codimension-1 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 

    Harris, Richard (University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2012-04-10)
    A symplectic manifold is a smooth manifold M together with a choice of a closed non-degenerate two-form. Recent years have seen the importance of associating an A∞-category to M, called its Fukaya category, in helping ...

  • The geodesic X-ray transform with a $GL(n,\mathbb{C})$-connection 

    Monard, François; Paternain, Gabriel Pedro
    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 

    Cheung, Man Wai; Gross, Mark; Muller, Greg; Musiker, Gregg; Rupel, Dylan; Stella, Salvatore; Williams, Harold (ElsevierJournal of Combinatorial Theory Series A, 2016-08-26)
    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 

    Angel, O; Ray, Gourab (SpringerProbability Theory and Related Fields, 2017-03-07)
    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 open-closed string map 

    Ritter, Alexander F; Smith, Ivan (SpringerSelecta Mathematica, 2016-08-09)
    We build the wrapped Fukaya category $\textit{W}$($\textit{E}$)for any monotone symplectic manifold $\textit{E}$, convex at infinity. We define the open-closed and closed-open string maps, OC : HH$_{*}$($\textit{W}$($\textit{E}$)) ...

  • The Planar Ising Model and Total Positivity 

    Lis, Marcin (SpringerJournal of Statistical Physics, 2017-01-01)
    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 Rohde--Schramm theorem, via the Gaussian free field 

    Berestycki, Nathanael Edouard; Jackson, Henry

  • The structure of limit groups over hyperbolic groups 

    Groves, Daniel; Wilton, Henry John

  • The symplectic arc algebra is formal 

    Abouzaid, Mohammed; Smith, Ivan (Duke University PressDuke Mathematical Journal, 2016-01-28)
    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 degree-one ...

  • The topology of terminal quartic 3-folds 

    Kaloghiros, Anne-Sophie (University of Cambridge, 2007-06-20)
    Let Y be a quartic hypersurface in P^4 with terminal singularities. The Grothendieck-Lefschetz 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 

    Bridson, Martin R; Wilton, Henry John (SpringerInventiones Mathematicae, 2015-02-24)
    We prove that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this property remains undecidable among the fundamental groups of compact, ...

  • The work of Lucio Russo on percolation 

    Grimmett, Geoffrey Richard
    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 X-ray transform for connections in negative curvature 

    Guillarmou, Colin; Paternain, Gabriel Pedro; Salo, Mikko; Uhlmann, Gunther (SpringerCommunications in Mathematical Physics, 2015-11-23)
    We consider integral geometry inverse problems for unitary connections and skew-Hermitian Higgs fields on manifolds with negative sectional curvature. The results apply to manifolds in any dimension, with or without boundary, ...

  • Three viewpoints on semi-abelian homology 

    Goedecke, Julia (University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticisEmmanuel College, 2009-11-17)
    The main theme of the thesis is to present and compare three different viewpoints on semi-abelian homology, resulting in three ways of defining and calculating homology objects. Any two of these three homology theories ...

  • Three-dimensional manifolds 

    Epstein, David Alper (University of CambridgeFaculty of MathematicsTrinity College, 1960-08-03)
    In the post-war years, the theory of 3-dimensional manifolds has developed tremendously. On the one hand, Bing and Moise have proved that 3-manifolds can be triangulated, and that the Hauptvermutung (that any two triangulations ...

  • Topics in arithmetic combinatorics 

    Sanders, Tom (University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2007-10-23)
    This thesis is chiefly concerned with a classical conjecture of Littlewood's regarding the L^1-norm of the Fourier transform, and the closely related idempotent theorem. The vast majority of the results regarding these ...

  • Topological cycle matroids of infinite graphs 

    Carmesin, Johannes (ElsevierEuropean Journal of Combinatorics, 2017-02-01)
    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.