Title:Ā On the discrete Hilbert transform Abstract: Ā The discrete Hilbert transform, acting on the space of (doubly infinite) sequences, was introduced by David Hilbert at the beginning of the 20th century. It is the discrete analogue of the continuous Hilbert transform acting on functions on the real line (conjugate function in the periodic case).
Title: An overview of numerical algorithms for the Poisson-Boltzmann equation in biomolecular electrostatics Abstract: The Poisson-Boltzmann Equation (PBE) is a widely used implicit solvent model for the electrostatic analysis of solvated biomolecules. The numerical solution of the PBE is known to be challenging, due to the consideration of discontinuous coefficients, complex geometry of protein structures,
Title:Ā Calderon-Zygmund theory for nonlinear partial differential equations and applications Abstract:Ā In this talk, we will discuss several recent developments on regularity theory estimates in Sobolev spaces for solutions ofĀ several classes of elliptic and parabolic nonlinear PDEs. Some classes of consideredĀ equations may be singular andĀ degenerate.Ā Important ideas and techniques will be highlighted. Connections and applications of the results
Topic:Ā 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,Ā total positivity, quiver representations, string theory, statistical
Title:Ā Predict the Ligand-Receptor Binding/Unbinding Kinetics with the Variational Implicit-Solvent Model and the String Method Abstract: Ā 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