Related papers: Endpoint formulation and Molien--Weyl structure fo…
We construct a three dimensional toy systems with two types of fermions forming a composite boson. They are hold in a harmonic potential. The basis functions are constructed from an internal and an external Gauss function. All integrals…
The Landau-Lifshitz equation describes the dynamics of magnetization in ferromagnetic materials. Due to the essential nonlinearity and nonconvex constraint, it is typically solved numerically. In this paper, we developed a finite volume…
We study the statistical mechanics of a multicomponent two-dimensional Coulomb gas which lives on a finite surface without boundaries. We formulate the Debye--Huckel theory for such systems, which describes the low-coupling regime. There…
These are lecture notes of lectures presented at the 1993 Trieste Summer School, dealing with two classes of two-dimensional field theories, (topological) Yang-Mills theory and the G/G gauged WZW model. The aim of these lectures is to…
The exact nonequilibrium steady state solution of the nonlinear Boltzmann equation for a driven inelastic Maxwell model was obtained by Ben-Naim and Krapivsky [Phys. Rev. E 61, R5 (2000)] in the form of an infinite product for the Fourier…
We consider the quartic analogue of the Kontsevich model, which is defined by a measure $\exp(-{N}\,\mathrm{Tr}(E\Phi^2+(\lambda/4)\Phi^4)) d\Phi$ on Hermitian ${N}\times{N}$-matrices, where $E$ is any positive matrix and $\lambda$ a…
In this paper, we investigate the multilinear boundedness properties of the higher ($n$-th) order Calder\'on commutator for dimensions larger than two. We establish all multilinear endpoint estimates for the target space…
The Moyal--Weyl description of quantum mechanics provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in $\hbar$. Its semiclassical expansion…
In 4 dimensions, general relativity can be formulated as a constrained $BF$ theory; we show that the same is true in 2 dimensions. We describe a spinfoam quantization of this constrained BF-formulation of 2d riemannian general relativity,…
We revisit the problem of bounding the expected supremum of a canonical Gaussian process indexed by a convex set $T \subset \mathbf{R}^d$. We develop two decompositions for the Gaussian width, based on the geometry of the index set. The…
Using a combination of techniques from conformal and complex geometry, we show the potentialization of 4-dimensional closed Einstein-Weyl structures which are half-algebraically special and admit a "half-integrable" almost-complex…
On a $3$D manifold, a Weyl geometry consists of pairs $(g, A) =$ (metric, $1$-form) modulo gauge $\widehat{g} = {\rm e}^{2\varphi} g$, $\widehat{A} = A + {\rm d}\varphi$. In 1943, Cartan showed that every solution to the Einstein-Weyl…
We prove a uniform version of the Dynamical Mordell-Lang Conjecture for \'etale maps; also, we obtain a gap result for the growth rate of heights of points in an orbit along an arbitrary endomorphism of a quasiprojective variety defined…
The asymptotic symmetry group of general relativity in asymptotically flat spacetimes can be extended from the Bondi-Metzner-Sachs (BMS) group to the generalized BMS (GMBS) group suggested by Campiglia and Laddha, which includes arbitrary…
We explore the non-singlet sector of matrix quantum mechanics dual to $c=1$ Liouville theory. The non-singlets are obtained by adding $N_{f}\times N$ bi-fundamental fields in the gauged matrix quantum mechanics model as well as a one…
In algebraic geometry, one studies the solutions to polynomial equations, or, equivalently, to linear partial differential equations with constant coefficients. These lecture notes address the more general case when the coefficients are…
We extend the finite-distance Jacobi-metric Gauss-Bonnet framework of Li \textit{et al}. [10.1103/PhysRevD.101.124058] to massive test particles carrying intrinsic spin. At pole-dipole order, the Mathisson-Papapetrou-Dixon dynamics…
The variational multiscale (VMS) formulation formally segregates the evolution of the coarse-scales from the fine-scales. VMS modeling requires the approximation of the impact of the fine scales in terms of the coarse scales. In linear…
In the L\'evy construction of Brownian motion, a Haar-derived basis of functions is used to form a finite-dimensional process $W^{N}$ and to define the Wiener process as the almost sure path-wise limit of $W^{N}$ when $N$ tends to infinity.…
The logarithmic minimal models are not rational but, in the W-extended picture, they resemble rational conformal field theories. We argue that the W-projective representations are fundamental building blocks in both the boundary and bulk…