Related papers: Proof of Serban's conjecture
We derive the asymptotic expansion of the partition function of a Coulomb gas system in the determinantal case on compact Riemann surfaces of any genus g. Our main tool is the bosonization formula relating the analytic torsion and geometric…
Koszul modules and their associated resonance schemes are objects appearing in a variety of contexts in algebraic geometry, topology, and combinatorics. We present a proof of an effective version of the Chen ranks conjecture describing the…
We establish a simple algebraic relationship between the energy eigenstates of the rational Calogero-Sutherland model with harmonic oscillator and Coulomb-like potentials. We show that there is an underlying SU(1,1) algebra in both of these…
The single-particle Green's function of an interacting Fermi system with dominant forward scattering is calculated by decoupling the interaction by means of a Hubbard-Stratonowich transformation involving a bosonic auxiliary field…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
The exact normalization of a multicomponent generalization of the ground state wavefunction of the Calogero-Sutherland model is conjectured. This result is obtained from a conjectured generalization of Selberg's $N$-dimensional extension of…
Closure relations satisfied by the radial Dirac-Coulomb Sturmians are proved analytically. The Sturmian expansion of the Dirac-Coulomb Green function is transformed to the form containing only series with summations running over…
We propose a refined version of the Beilinson-Bloch conjecture for the motive associated with a modular form of even weight. This conjecture relates the dimension of the image of the relevant p-adic Abel-Jacobi map to certain combinations…
The general theory of a massless fermion coupled to a massive vector meson in two dimensions is formulated and solved to obtain the complete set of Green's functions. Both vector and axial vector couplings are included. In addition to the…
We obtain the hole propagator of the Sutherland model with SU(2) internal symmetry for coupling parameter $\beta=1$, which is the simplest nontrivial case. One created hole with spin down breaks into two quasiholes with spin down and one…
We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].
In this paper we present a combinatorial proof of Selberg's integral formula. We start by giving a bijective proof of a Theorem about the number of topological orders of a certain related directed graph. Selberg's Integral Formula then…
We consider the symmetric binary perceptron model, a simple model of neural networks that has gathered significant attention in the statistical physics, information theory and probability theory communities, with recent connections made to…
The Hubbard model, a cornerstone in the field of condensed matter physics, serves as a fundamental framework for investigating the behavior of strongly correlated electron systems. This paper presents a novel perspective on the model,…
Recently, Hao Huang proved the Sensitivity Conjecture, an important result about complexity measures of Boolean functions. We will discuss how this simple and elegant proof turns out to be closely related to physics concepts of the…
Spin generalization of the relativistic Calogero-Sutherland model is constructed by using the affine Hecke algebra and shown to possess the quantum affine symmetry $\uqglt$. The spin-less model is exactly diagonalized by means of the…
According to the method of path integral quantization for the canonical constrained system in Faddeev-Senjanovic scheme, we quantize the supersymmetrical electrodynamic system in general situation, and obtain the generating functional of…
Based on computeralgebra experiments we formulate a refined version of Green's conjecture and a conjecture of Schicho-Schreyer-Weimann which conjecturally also holds in positive characteristic. The experiments are done by using our…
This is the text of my lecture (in french) at the Bourbaki Seminar (november 2003) on the proof by Claire Voisin of the Green conjecture for a generic curve. This conjecture predicts the structure of the minimal resolution of the ideal of a…
We discuss a generalization of the conventional bosonization procedure to the case of current-current interactions which get their natural representation in terms of current instead of fermion number density operators. A consistent…