Topic: Introduction to cluster algebras Abstract: The theory of cluster algebras is one of the most mathematically well-studied areas in mathematical physics. Since its discovery in 2001, it has been shown that cluster algebras are related to diverse areas of mathematics such as algebraic geometry, commutative algebra, knot theory, total positivity, quiver representations, string theory, statistical
Title:Â Predict the Ligand-Receptor Binding/Unbinding Kinetics with the Variational Implicit-Solvent Model and the String Method Abstract: Â The ligand-receptor binding/unbinding is a complex biophysical process in which water plays a critical role. To understand the fundamental mechanisms of such a process, we have developed a new and efficient approach that combines our level-set variational implicit-solvent model
Title: A lower-order image denoising model for staircase reduction Abstract: In this talk, we will discuss a total-variation based lower-order image denoising model that is able to reduce the well-known staircasing phenomenon possessed by the Rudin-Osher-Fatemi model. To minimize the proposed variational model, we employ augmented Lagrangian method (ALM). Convergence analysis is established for the
Title:Â On some Bergman type spaces of functions of nonstandard growth and related questions. Abstracts: We study various Banach spaces of holomorphic functions on the unit disc and half plane. As a main question we investigate the boundedness of the corresponding holomorphic projection. We exploit the idea of V.P.Zaharyuta, V.I.Yudovich (1962) where the boundedness of