Related papers: Branched Polymers Re-Revisited

Branch points of a real 2-surface S in a 4-manifold M generalize the branch points of complex curves in complex surfaces: for example, they can occur as singularities of minimal surfaces. We investigate such a branch point p when S is…

We introduce non-trivial two-point functions of the super Schur polynomials in the ABJM matrix model and study their exact values with the Fermi gas formalism. We find that, although defined non-trivially, these two-point functions enjoy…

Double Hurwitz numbers enumerate branched covers of $\mathbb{CP}^1$ with prescribed ramification over two points and simple ramification elsewhere. In contrast to the single case, their underlying geometry is not well understood. In…

Let F be a foliation of codimension 2 on a compact manifold with at least one non-compact leaf. We show that then F must contain uncountably many non-compact leaves. We prove the same statement for oriented p-dimensional foliations of…

It is shown how twisted N=2 (k=1) provides for the first time a complete conformal field theory description of the usual geometrical phase transitions in two dimensions, like polymers, percolation or brownian motion. In particular, four…

We discuss the geometry and arithmetic of higher-dimensional analogues of Ch\^atelet surfaces; namely, we describe the structure of their Brauer and Picard groups and show that they can violate the Hasse principle. In addition, we use these…

Building on techniques from complex analysis and topology, we establish a remarkable property of branched covers and formulate a complete criterion for the existence of specific types of branched covers between 2-spheres. Our results extend…

We provide new branched covering representations for bounded and/or non-compact 4-manifolds, which extend the known ones for closed 4-manifolds. Assuming $M$ to be a connected oriented PL 4-manifold, our main results are the following: (1)…

We construct branched double coverings by certain direct products of manifolds for connected sums of copies of sphere bundles over the 2-sphere. As an application we answer a question of Kotschick and Loeh up to dimension five. More…

We study a one dimensional directed polymer model in an inverse-gamma random environment, known as the log-gamma polymer, in three different geometries: point-to-line, point-to-half line and when the polymer is restricted to a half space…

Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest neighbour attraction. The bias corresponds to opposite forces applied to the first…

We consider the problem of undirected polymers (tied at the endpoints) in random environment, also known as the unoriented first passage percolation on the hypercube, in the limit of large dimensions. By means of the multiscale refinement…

While stretching of most polymer chains leads to rather featureless force-extension diagrams, some, notably DNA, exhibit non-trivial behavior with a distinct plateau region. Here we propose a unified theory that connects force-extension…

We identify branched coverings (continuous open surjections p:Y->X of Hausdorff spaces with uniformly bounded number of pre-images) with Hilbert C*-modules C(Y) over C(X) and with faithful unital positive conditional expectations…

In the 1980's, Almgren developed a theory of multi-valued Dirichlet energy minimizing functions on $n$ dimensional domains and used it, in an essential way, to bound the Hausdorff dimension of the singular sets of area minimizing…

We prove multiplier theorems on rank one noncompact symmetric spaces which improve aspects of existing results. A common theme of our main results is that we partially drop specific assumptions on the multiplier function such as a…

We study theoretically the scattering imprint of a number of branched supramacromolecular architectures, namely, polydisperse stars and dendrimeric, hyperbranched structures. We show that polydispersity and nature of branching highly…

We analyse new exact enumeration data for self-avoiding polygons, counted by perimeter and area on the square, triangular and hexagonal lattices. In extending earlier analyses, we focus on the perimeter moments in the vicinity of the…

We consider flexible branched polymer, with quenched branch structure, and show that its conformational entropy as a function of its gyration radius $R$, at large $R$, obeys, in the scaling sense, $\Delta S \sim R^2/(a^2L)$, with $a$ bond…

We study dimensions of strange non-chaotic attractors and their associated physical measures in so-called pinched skew products, introduced by Grebogi and his coworkers in 1984. Our main results are that the Hausdorff dimension, the…