Computer Science and Mathematics
Title: Mathematics in drug design
Abstract: We show how mathematics can help in the complex process of drug discovery. We give an example of modification of a common cancer drug that reduces unwanted side effects. The mathematical model used to do this relates to the hydrophobic effect, something not yet fully understood. The hydrophobic effect modulates the dielectric behavior of water, and this has dramatic effects on how we process drugs. Future mathematical advances in this area hold the process of making drug discovery more rational, and thus more rapid and predictable, and less costly.
Please join Dr. Ridgway at a reception;following his lecture in 130 Computer Science building.
Title: Two tales about Newton's method
Abstract: We talk about Newton's method for solving nonlinear (systems of) equations, a common topic in Calculus. We describe two new areas of research that are related to Newton's method. We show that the "endgame" for Newton's method (that is, the behavior of the iterates viewed as a dynamical system) in multiple dimensions can be extremely complex, leading to tensor eigenvalue problems. We also show how Newton's method for solving nonlinear ODE's can provide a productive approach to creating parallelism in what would seem to be essentially sequential computations.
Prior to the colloauium, please join Dr. Ridgway and the Department of Mathematics for coffee in Weber 117 at 3:30 pm.
Title: Optimal algorithms using optimal meshes
Abstract: We discuss two problems involving adaptive meshes. The first relates to non-nested multigrid in two and three dimensions. We review what is known theoretically and describe some recent work related to optimal implementation. The second involves meshes in arbitrary dimensions. We show that there are meshes in which the number of nodes grows linearly in the dimension, and give some evidence via a quantum mechanics example that an h-P strategy can be effective to obtain good convergence behavior on these meshes. If time permits, we will describe some on-going work developing new formulations for nonlinear and nonlocal dielectric models for proteins.
Prior to the seminar, please join Dr. Ridgway and the Department of Mathematics for coffee in Weber 117 at 3:30am.
The lectures are supported by the Arne Magnus Lecture Fund and the Albert C. Yates Endowment in Mathematics.
Contributions to the Magnus Fund are greatly appreciated and may be made through the Department of Mathematics. Please contact Sheri Hofeling (email@example.com) at at (970)-491-7047 for specific information.
All lectures are free and open to the public.