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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...
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...
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 ...
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...
We apply the new theory of cluster algebras of Fomin and Zelevinsky to study some combinatorial problems arising in Lie theory. This is joint work with Geiss and Schr¨oer (§3, 4, 5, 6), and with Herna...
This paper investigates the Poisson geometry associate to a cluster algebra over the complex numbers, and its relationship to compatible torus actions.

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