Related papers: Strong 1-boundedness, $L^2$-Betti numbers, algebra…

This paper consists of two parts. First, motivated by classic results, we determine the subsets of a given nilpotent Lie algebra $\mathfrak{g}$ (respectively, of the Grassmannian of two-planes of $\mathfrak{g}$) whose sign of Ricci…

Graph products of monoids provide a common framework for direct and free products, and graph monoids (also known as free partially commutative monoids). If the monoids in question are groups, then any graph product is, of course, a group.…

We construct countable groups $G$ with the following new degree of W*-superrigidity: if $L(G)$ is virtually isomorphic, in the sense of admitting a bifinite bimodule, with any other group von Neumann algebra $L(\Lambda)$, then the groups…

We consider N=2 supersymmetric gauge theories perturbed by tree level superpotential terms near isolated singular points in the Coulomb moduli space. We identify the Seiberg-Witten curve at these points with polynomial equations used to…

Let $F$ be a totally real field, and $\mathbb{A}_F$ be the adele ring of $F$. Let us fix $N$ to be a positive integer. Let $\pi_1=\otimes\pi_{1,v}$ and $\pi_2=\otimes\pi_{2,v}$ be distinct cohomological cuspidal automorphic representations…

We calculate the microstates free entropy dimension of natural generators in an amalgamated free product of certain von Neumann algebras, with amalgamation over a hyperfinite subalgebra. In particular, some `exotic' Popa algebra generators…

We give an efficient randomized algorithm to construct a box representation of any graph G on n vertices in $1.5 (\Delta + 2) \ln n$ dimensions, where $\Delta$ is the maximum degree of G. We also show that $\boxi(G) \le (\Delta + 2) \ln n$…

We consider a variant of the strong multiplicity one theorem. Let $\pi_{1}$ and $\pi_{2}$ be two unitary cuspidal automorphic representations for $\mathrm{GL(2)}$ that are not twist-equivalent. We find a lower bound for the lower Dirichlet…

Let $\Fth$ be a 2 graph generated by $m$ blue edges and $n$ red edges, and $\omega$ be the distinguished faithful state associated with its graph C*-algebra $\O_\theta$. In this paper, we characterize the factorness of the von Neumann…

Let $\mathfrak{g}$ be a symmetrizable Kac-Moody Lie algebra with Cartan subalgebra $\mathfrak{h}$. We prove a unique factorization property for tensor products of parabolic Verma modules. More generally, we prove unique factorization for…

We prove that the normalizer of any diffuse amenable subalgebra of a free group factor $L(\Bbb F_r)$ generates an amenable von Neumann subalgebra. Moreover, any II$_1$ factor of the form $Q \vt L(\Bbb F_r) $, with $Q$ an arbitrary subfactor…

We prove that certain free products of factors of type ${\rm I}$ and other von Neumann algebras with respect to nontracial, almost periodic states are almost periodic free Araki-Woods factors. In particular, they have the free absorption…

We consider supersymmetric sigma models on the Kahler target spaces, with twisted mass. The Kahler spaces are assumed to have holomorphic Killing vectors. Introduction of a superpotential of a special type is known to be consistent with N=2…

It was recently proved that every planar graph is a subgraph of the strong product of a path and a graph with bounded treewidth. This paper surveys generalisations of this result for graphs on surfaces, minor-closed classes, various…

This is a continuation of our previous paper studying the structure of Cartan subalgebras of von Neumann factors of type II_1. We provide more examples of II_1 factors having either zero, one or several Cartan subalgebras. We also prove a…

Graph product is a fundamental tool with rich applications in both graph theory and theoretical computer science. It is usually studied in the form $f(G*H)$ where $G$ and $H$ are graphs, * is a graph product and $f$ is a graph property. For…

We completely classify the atomic summands in a graph product $(M,\varphi) = *_{v \in \mathcal{G}} (M_v,\varphi_v)$ of von Neumann algebras with faithful normal states. Each type I factor summand $(N,\psi)$ is a tensor product of type I…

We investigate the problem of computing tensor product multiplicities for complex semisimple Lie algebras. Even though computing these numbers is #P-hard in general, we show that if the rank of the Lie algebra is assumed fixed, then there…

Gaudin algebra is the commutative subalgebra in $U(\mathfrak{g})^{\otimes N}$ generated by higher integrals of the quantum Gaudin magnet chain attached to a semisimple Lie algebra $\mathfrak{g}$. This algebra depends on a collection of…

The paper is devoted to the investigation of finite dimensional commutative nilpotent (associative) algebras N over an arbitrary base field of characteristic zero. Due to the lack of a general structure theory for algebras of this type (as…