Related papers: Multiple chordal SLE(0) and classical Calogero-Mos…
We discuss the possible set of operators from various boundary conformal field theories to build meaningful correlators that lead via a Loewner type procedure to generalisations of SLE($\kappa,\rho$). We also highlight the necessity of…
This paper proves a commutative algebraic extension of a generalized Skolem-Mahler-Lech theorem due to the first author. Let $A$ be a finitely generated commutative $K$-algebra over a field of characteristic $0$, and let $\sigma$ be a…
SLE(kappa,rho) is a generalisation of Schramm-Loewner evolution which describes planar curves which are statistically self-similar but not conformally invariant in the strict sense. We show that, in the context of boundary conformal field…
Calogero-Moser models can be generalised for all of the finite reflection groups. These include models based on non-crystallographic root systems, that is the root systems of the finite reflection groups, H_3, H_4, and the dihedral group…
Discrete dynamical systems defined on the state space {0,1,...,p-1}^n have been used in multiple applications, most recently for the modeling of gene and protein networks. In this paper we study to what extent well-known theorems by Smale…
We analyze properties of the Sp(2M) conformally invariant field equations in the recently proposed generalized $\half M(M+1)$-dimensional space-time $\M_M$ with matrix coordinates. It is shown that classical solutions of these field…
We propose a general scheme to construct multiple Lagrangians for completely integrable non-linear evolution equations that admit multi- Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a…
The Calogero model with external harmonic oscillator potential is discussed from sL(2,R) algebra point of view. Explicit formulae for functions with exponential time behaviour are given; in particular, the integrals of motion are…
Suppose that $\eta$ is a Schramm-Loewner evolution (SLE$_\kappa$) in a smoothly bounded simply connected domain $D \subset {\mathbb C}$ and that $\phi$ is a conformal map from ${\mathbb D}$ to a connected component of $D \setminus…
The Shcramm-Loewner evolution (SLE) is a correlated exploration process, in which for the chordal set up, the tip of the trace evolves in a self-avoiding manner towards the infinity. The resulting curves are named SLE$_{\kappa}$,…
The goal of this expository article is to explain how a fundamental functional on the space of Jordan curves arising from SLE - Loewner energy - is connected to a seemingly far apart subject: the K\"ahler geometry of universal Teichm\"uller…
We consider a class of Hamiltonian systems in 3 degrees of freedom, with a particular type of quadratic integral and which includes the rational Calogero-Moser system as a particular case. For the general class, we introduce separation…
The main result of this paper is an explicit description of the stratification of the phase space of Calogero--Moser--Sutherland (CMS) integrable systems corresponding to Lie groups $SU(n)$. The phase space decomposes into symplectic strata…
Scharmm-Loewner evolution (SLE) and conformal field theory (CFT) are popular and widely used instruments to study critical behavior of two-dimensional models, but they use different objects. While SLE has natural connection with lattice…
A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…
The equations of motion of multiple M0{brane (multiple M-wave or mM0) system in an arbitrary D = 11 supergravity superspace, which generalize the Matrix model equations for the case of inter- action with a generic 11D supergravity…
We use Monte Carlo simulations and tensor network methods to study a classical monomer-dimer model on the square lattice with a hole (monomer) fugacity $z$, an aligning dimer-dimer interaction $u$ that favors columnar order, and an…
Let $\mathbb{A}_n^m$ be an arbitrary $n$-dimensional commutative associative algebra over the field of complex numbers with $m$ idempotents. Let $e_1=1,e_2,\ldots,e_k$ with $2\leq k\leq 2n$ be elements of $\mathbb{A}_n^m$ which are linearly…
We speculate on the relationship between the solvable monodromy extension (SME) property and log canonical models. A motivating example is the moduli space of smooth curves which, by earlier work, is known to have this SME property. In this…
We consider the whole-plane Shramm-Loewner evolution. Using exact solutions of fundamental equations for moments of derivative of conformal mappings we determine its average integral means beta-spectrum.