Related papers: A Dimer ABC
A monomer-dimer model with a short-range attractive interaction favoring colinear dimers is considered on the lattice $\mathbb{Z}^2$. Although our choice of the chemical potentials results in more horizontal than vertical dimers, the…
These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…
Mirror symmetry has proven to be a powerful tool to study several properties of higher dimensional superconformal field theories upon compactification to three dimensions. We propose a quiver description for the mirror theories of the…
Inspired by the tropical duality in cluster algebras, we introduce c-vectors for finite-dimensional algebras via $\tau$-tilting theory. Let $A$ be a finite-dimensional algebra over a field $k$. Each c-vector of $A$ can be realized as the…
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…
The paper deals with the problem of identifying the internal dependencies and similarities among a large number of random processes. Linear models are considered to describe the relations among the time series and the energy associated to…
Lecture notes from a minicourse given at the ICTP in May 2002.
We suggest an interpretation of mirror symmetry for toric varieties via an equivalence of two conformal field theories. The first theory is the twisted sigma model of a toric variety in the infinite volume limit (the A-model). The second…
We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…
We study the module categories of a tilted algebra C and the corresponding cluster-tilted algebra B. We investigate how various properties of a C-module are affected when considered in the module category of B. We give a complete…
In this paper, we introduce the interested reader to homological mirror symmetry. After recalling a little background knowledge, we tackle the simplest cases of homological mirror symmetry: curves of genus zero and one. We close by…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
The classical dimer model is concerned with the (weighted) enumeration of perfect matchings of a graph. An $n$-dimer cover is a multiset of edges that can be realized as the disjoint union of $n$ individual matchings. For a probability…
This is an expository article on the A-side of Kontsevich's Homological Mirror Symmetry conjecture. We give first a self-contained study of $A_\infty$-categories and their homological algebra, and later restrict to Fukaya categories, with…
The most usual option to stabilize Dark Matter (DM) is a $Z_2$ symmetry. In general, though, DM may be stabilized by any $Z_N$ with $N \ge 2$. We consider the way $Z_N$ is a subgroup of the internal-symmetry group $G$ of a model; we…
Last year observations had a profound impact on our views on the amount and nature of dark matter in the universe. We give a brief review of the recent history of dark matter models beyond the pure cold dark matter universe. In view of the…
This is the second in a series of papers that develops the theory of reflection monoids, motivated by the theory of reflection groups. Reflection monoids were first introduced in arXiv:0812.2789. In this paper we study their presentations…
There suggested a modification of the Dirac electron theory, eliminating its mathematical incompleteness. The modified Dirac electron, called dual, is described by two waves, one of which is the Dirac wave and the second dynamically…
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…
In the present paper we examine the relationship between several type $A$ cluster theories and structures. We define a 2D geometric model of a cluster theory, which generalizes cluster algebras from surfaces, and encode several existing…