Related papers: Lecture on Branched Polymers and Dimensional Reduc…
The Brydges-Imbrie dimensional reduction formula relates the pressure of a $d$-dimensional gas of hard spheres to a model of $(d+2)$-dimensional branched polymers. Brydges and Imbrie's proof was non-constructive and relied on a…
Building on and from the work of Brydges and Imbrie, we give an elementary calculation of the volume of the space of branched polymers of order $n$ in the plane and in 3-space. Our development reveals some more general identities, and…
We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie, and Kenyon and Winkler to any hyperplane arrangement A. The volume of the…
Due to the recent renewal in the interest for embedded surfaces we provide a list of commented references of interest.
I will use this opportunity on the one hand to comment upon some of the many interesting results that have been presented at this meeting, on the other hand to discuss some new features that we have recently learned on the structure and…
The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
A hierarchy of differential equations on a Banach Lie-Poisson space related to the restricted Grassmannian is studied. Flows on the groupoid of partial isometries and on the restricted Grassmannian are described, and a momentum map picture…
We present a brief tutorial on the nuts and bolts computation of a multisymplectic particle-in-cell algorithm using the discretized Lagrangian approach. This approach, originated by Marsden, Shadwick, and others, brings the benefits of…
This paper contains the material discussed in the series of three lectures that I gave during the workshop of the ICRA 2018 in Prague. I will introduce the reader to some of the techniques used in the study of the geometry of quiver…
We study an ensemble of branched polymers which are embedded on other branched polymers. This is a toy model which allows us to study explicitly the reaction of a statistical system on an underlying geometrical structure, a problem of…
We reframe linear dimensionality reduction as a problem of Bayesian inference on matrix manifolds. This natural paradigm extends the Bayesian framework to dimensionality reduction tasks in higher dimensions with simpler models at greater…
This is a short introduction to affine and convex spaces, written especially for physics students. It summarizes different elementary presentations available in the mathematical literature, and blends analytic- and geometric-flavoured…
This paper summarizes the results in Integral Biomathics obtained to this moment and provides an outlook for future research in the field.
This is the draft of lecture notes for Phd students in Sichuan University. In this notes we expand Li-Ruan's paper with much more detailed explanations and calculations.
The Branched Polymer Growth Model (BPGM) has been employed to study the kinetic growth of ramified polymers in the presence of impurities. In this article, the BPGM is revisited on the square lattice and a subtle modification in its…
In this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n+1)-dimensional contact manifold and the…
These lectures on the combinatorics and geometry of 0/1-polytopes are meant as an \emph{introduction} and \emph{invitation}. Rather than heading for an extensive survey on 0/1-polytopes I present some interesting aspects of these objects;…
Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any…
This is a set of introductory lectures on the behaviour of a directed polymer in a random medium. Both the intuitive picture that helps in developing an understanding and systematic approaches for quantitative studies are discussed.