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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Connection probabilities for random-cluster model and uniform spanning treeConnection probabilities for random-cluster model and uniform spanning tree
随机 聚类模型 均匀生成树 连接概率
2023/5/16
Conformal invariance of critical lattice models in two-dimensional has been vigorously studied for decades. The first example where the conformal invariance was rigorously verified was the planar unif...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Legendrian knots and cluster algebras via augmentations
Legendarian结 簇代数 增广
2023/5/16
Legendrian knots and their exact Lagrangian fillings are central objects to study in low dimensional contact and symplectic topology. In recent developments, cluster algebras have proven to be powerfu...
International Workshop on Cluster Algebras and Related Topics
International Workshop Cluster Algebras and Related Topics
2017/2/15
The purposes of this conference are to discuss the structures and classifications of the cluster algebras of geometric type, the recent advances of several main conjectures of cluster theory, the conn...
Applications of Geometric Cluster Algorithms.
Directed random walk on an oriented percolation cluster
Random walk, dynamical random environment, oriented percolation, supercritical cluster, central limit theorem in random environment
2012/4/16
We consider directed random walk on the infinite percolation cluster generated by supercritical oriented percolation, or equivalently the space-time embedding of the `ancestral lineage' of an individu...
The local $h$-vector of the cluster subdivision of a simplex
Local h-vector barycentric subdivision cluster complex cluster subdivision
2012/4/18
The cluster complex $\Delta (\Phi)$ is an abstract simplicial complex, introduced by Fomin and Zelevinsky for a finite root system $\Phi$. The positive part of $\Delta (\Phi)$ naturally defines a simp...
Skein algebras and cluster algebras of marked surfaces
Skein algebras cluster algebras marked surfaces Quantum Algebra Geometric Topology
2012/4/17
This paper defines several algebras associated to an oriented surface S with a finite set of marked points on the boundary. The first is the skein algebra Sk_q(S), which is spanned by links in the sur...
VATdt: Visual Assessment of Cluster Tendency Using Diagonal Tracing
Clustering Dissimilarity Measures Data Visualization Clustering Tendency
2013/1/30
The visual assessment of tendency (VAT) technique, for visually finding the number of meaningful clusters in data, developed by J. C. Bezdek, R. J. Hathaway and J. M. Huband, is very useful, but there...
清华大学博士后张杰: On the cluster category of a marked surface&On the cluster algebra of a marked surface
清华大学 博士后张杰 cluster category marked surface&On cluster algebra
2012/1/5
This is a joint work with Thomas Brustle. We study the cluster category C(S,M) of a marked surface (S,M). We explicitly describe the indecomposable objects in C(S,M) as homotopy classes of curves in (...
Abstract: We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type - a cluster integrable system. The phase space of the classical system ...
Large deviations for cluster size distributions in a continuous classical many-body system
Classical particle system canonical ensemble equilibrium statistical mechanics dilute system large deviations
2011/9/14
Abstract: An interesting problem in statistical physics is the condensation of classical particles in droplets or clusters when the pair-interaction is given by a stable Lennard-Jones-type potential. ...
Poisson Ideals in Cluster Algebras and the Spectra of Quantized Coordinate Rings
Poisson Ideals Cluster Algebras the Spectra of Quantized Coordinate Rings Quantum Algebra
2011/9/6
Abstract: We describe the Poisson ideals and attached symplectic geometry of a cluster algebra with compatible Poisson structure. We apply these results to determine the spectrum of a quantum cluster ...
A geometric interpretation of the triangulated structure of m-cluster categories
m-cluster categories triangulated structure Auslander-Reiten triangles orbit categories Auslander Reiten quivers
2011/8/25
Abstract: The aim of this note is to answer several open problems arising from the geometric description of the $m$-cluster categories of type $A_n$ and their realization in terms of the $m$-th power ...
Integral cluster categories of acyclic quivers have recently been used in the representation-theoretic approach to quantum cluster algebras. We show that over a principal ideal domain, such categories...
The purpose of this chapter is to give an introduction to the theory of cluster categories and cluster-tilted algebras, with some background on the theory of cluster algebras, which motivated these to...