## Seminar:

Spring 2010, Thursdays, Milner 216, 4:00-4:50 PM
__ Date:__ ** February 18 **

**" Mini-Talk "**

* Prof. Maurice Rojas

* Prof. Andrea Bonito

* Prof. Maurice Rojas

* Prof. Andrea Bonito

__Abstract__ * M. Rojas*:** "When Number Theory and Numerical Analysis Intersect" Abstract**: How does one prove the existence of an object without actually revealing the object? How does specify an irrational real number by giving only finitely many digits? These basic quasi-philosophical questions are answered by many modern algorithms.

In this talk, we'll see how iterative algorithms for solving equations are closely related to certain results from Diophantine approximation. We will deal entirely with concrete examples involving real and p-adic roots of polynomials, so we assume no background in numerical analysis or number theory. You may also learn what a p-adic number is.

*A. Bonito*:

**"FROM MODELLING TO NUMERICAL SIMULATIONS: 3 SHORT STORIES"**

Abstract: Finite Element Methods are extremely powerful tools known to produce impressive numerical simulations of physical processes. Their success hinges on the fundamental mathematical understanding of the methods.

Abstract

The journey from mathematical modelling to actual numerical simulation is briefly illustrated through three projects (viscoelastic flows, lab-on-chip devices and biomembranes). A special emphasis is made on the basic principles and mathematical tools employed