Related papers: Lecture on Branched Polymers and Dimensional Reduc…
In this contribution I discuss recent and ongoing progress on the inclusion of resummation effects in the fit of parton distributions.
A class of trigonometric interpolation splines depending on parameter vectors, selected convergence factors and interpolation factors is considered. The concept of crosslink grids and interpolation grids is introduced; these grids can match…
Comment: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]
Comment: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]
Comment: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]
These notes have been prepared as reading material for the mini-course given by the author at the "2019 Graduate Summer School" at Park City Mathematics Institute - Institute for Advanced Study. We begin by introducing Higgs bundles and…
We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any…
We present an array of new calculations in Lagrangian Floer theory which demonstrate observations relating to symplectic reduction, grading periodicity, and the closed-open map. We also illustrate Perutz's symplectic Gysin sequence and the…
Intrinsic volumes are fundamental geometric invariants generalizing volume, surface area, and mean width for convex bodies. We establish a unified Laplace-Grassmannian representation for intrinsic and dual volumes of convex polynomial…
The decomposition of polynomial spaces on unions of Grassmannians $\mathcal G_{{k_1},d}\cup\ldots\cup \mathcal G_{{k_r},d}$ into irreducible orthogonally invariant subspaces and their reproducing kernels are investigated. We also generalize…
This paper presents the integral(or differential) form of G-BSDEs, gives some kind of apriori estimates of their solutions, and under a very strong condition, proves the G-martingale representation theorem, and the existence and uniqueness…
This work is devoted to the variational derivation of a reduced model for brittle membranes in finite elasticity. The main mathematical tools we develop for our analysis are: (i) a new density result in $GSBV^{p}$ of functions satisfying a…
We develop a new, dynamical field theory of isotropic randomly branched polymers, and we use this model in conjunction with the renormalization group (RG) to study several prominent problems in the physics of these polymers. Our model…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
Book Chapter from "Coarse-Grained Modeling of Biomolecules" part of the submitted "Series in Computational Biophysics"
Using the Plucker map between grassmannians, we study basic aspects of classic grassmannian geometries. For `hyperbolic' grassmannian geometries, we prove some facts (for instance, that the Plucker map is a minimal isometric embedding) that…
This is a pedagogical introduction into theories with branes and extra dimensions. We first discuss the construction of such models from an effective field theory point of view, and then discuss large extra dimensions and some of their…
An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions…
In this survey article we gather classical as well as recent results on minimal geodesics of Riemannian or Finsler metrics, giving special attention to the two-dimensional case. Moreover, we present open problems together with some first…
The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined…