Related papers: On Polyakov's basic variational formula for loop s…

We establish foundational properties of fractional operators on Lie groups of homogeneous type. We prove embedding theorems for the associated Sobolev-type spaces.

We construct and study universal spaces for birational invariants of algebraic varieties over algebraic closures of finite fields.

The present note contains a review of $p$-energies and Sobolev spaces on metric measure spaces that carry a strongly local regular Dirichlet form. These Sobolev spaces are then used to generalize some basic results from the calculus of…

The purpose of this paper is to discuss a number of issues that crop up in the computation of Poisson brackets in field theories. This is specially important for the canonical approaches to quantization and, in particular, for loop quantum…

We study the Polyakov loop and the correlator of two Polyakov loops at finite temperature in the weak-coupling regime. We calculate the Polyakov loop at order g^4. The calculation of the correlator of two Polyakov loops is performed at…

We give an elementary proof of the Hurewicz theorem relating homotopy and homology groups of a cubical Kan complex. Our approach is based on the notion of a loop space of a cubical set, developed in a companion paper ``Homotopy groups of…

We introduce loom spaces, a generalisation of both the leaf spaces associated to pseudo-Anosov flows and the link spaces associated to veering triangulations. Following work of Gu\'eritaud, we prove that there is a locally veering…

We extend Carleson's formula to radially polynomially weighted Dirichlet spaces.

A method for constructing homogeneous Lyapunov functions of degree 1 from polynomial invariant sets is presented for linear time varying systems, homogeneous dynamic systems and the class of nonlinear systems that can be represented as…

This paper uses differential spaces to obtain some new results in integrable Hamiltonian systems

We compute the homology of the space of equivariant loops on the classifying space of a simplicial monoid $M$ with anti-involution, provided $\pi_0 (M)$ is central in the homology ring of $M$. The proof is similar to McDuff and Segal's…

We give an different proof of our result computing the stable homology of dihedral group Hurwitz spaces. This proof employs more elementary methods, instead of higher algebra.

We introduce the notion of Hamiltonian spaces for Manin pairs over manifolds, using the so-called generalized Dirac structures. As an example, we describe Hamiltonian spaces of a quasi-Lie bialgebroid using this general framework. We also…

In this paper, we establish an analogue of the Fundamental Theorem of Algebra for polynomial matrix equations, where both the coefficient matrices and the unknown matrix are $Q$-circulant matrices. This result generalizes Abramov's result…

We prove a homological stability theorem for certain complements of symmetric spaces. This is a variant of a conjecture by Vakil and Matchett Wood for subspaces of $\mathrm{Sym}^n(X)$ where $X$ is an open manifold admitting a boundary. To…

The manuscript is an overview of the motivations and foundations lying behind Voevodsky's ideas of constructing categories similar to the ordinary topological homotopy categories. The objects of these categories are strictly related to…

We present the area and coarea formulas for Lipschitz maps, valid for general volume densities. As applications, we give a short, "euclidean" proof of the anisotropic Sobolev inequality and describe an anisotropic tube formula for…

We find an elementary proof for Voiculescu's theorem on the polar decomposition of circular variables.

In a previous article by the author, it was shown that one could effectively give a variational formulation to non-conservative mechanical systems by starting with the first variation functional instead of an action functional. In this…

We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…