Date: Mar. 16, 2017

Title: Innovation Using Mathematical Modelling and Simulation

Abstract: Over the centuries, human beings have innovated by making use of mathematics to solve problems in multiple areas of everyday life. Mathematics has varied perspectives ranging from the development of complex intellectual theories, to the modeling of phenomena that occur in our environment.

By deriving mathematical models, computer simulators are developed to capture images of complex structures. The cardiovascular system, the respiratory system, the transportation of crude through pipes, recovery of crude, among other problems, are all fractal systems. The new mathematical methodologies are the means to consider the phenomena from another perspective closer to reality, and looking for new technologies to study the stability/instability of the systems.

In 1988, at the American Mathematical Society Assembly, it was said: “Recent developments in the mathematical sciences suggest that there will be a significant potential increase in fundamental advances in life sciences, which will depend in large part on mathematical models and computing.” And this is what we have been seeing through the last years.

This lecture will explain what a modeling process is. The objective is to simulate computationally the flow behavior of two concentric immiscible fluids, which travel inside a cylindrical tube with circular cross-sections, typical in the transportation of crude through pipes. Also, insoluble surfactants are present at the interface between the two fluids. The goal is to present how to go from the setting of the real life problem to the final simulation. This simulation must be designed so that an average user of computers, or related devices, can experiment and learn from the behavior of the phenomena considered in the original problem, without the need to be a mathematician.

Date: Mar. 23, 2017

Title: Coming Clean about the Poincare Conjecture and Stolen Bikes

Abstract: A few years ago, Professor Poirier gave a public lecture titled “The Poincare Conjecture: Or How I Learned to Stop Worrying and Lock My Bike,” which contained a little white lie. Luckily, the audience let her get away with the lie, but she’s been feeling guilty about it ever since! In this Math Club talk, she’ll introduce the Poincare Conjecture, which was first posed in 1904 and which stumped mathematicians for the next 100 years. She’ll also tell you how it can help you lock up your own bike. And she’ll finally come clean about the lie.

Date: May 11, 2017

Title: Turing: From Computers to Machines

Abstract: What is computation? What is an algorithm? In 1936, a 24-year old Cambridge mathematics student named Alan Turing published a paper titled “On Computable Numbers, with an Application to the Entscheidungsproblem” which addressed these questions.

In his paper, Turing defined certain “logical computing machines”—what we now call Turing machines.  Turing machines are not physical machines, but rather a mathematical definition of algorithmic computation, based on Turing’s careful analysis of what a human “computer” does in carrying out a computation. In the ensuing decades, Turing machines became the standard model for understanding computation, formed the theoretical foundation for the first physical computers (including through Turing’s own work after World War II), and have become central to discussions in mathematical logic, theoretical computer science, philosophy of mind, cognitive science, and artificial intelligence.

In this talk, we will discuss the basic concepts of Turing’s work on computability, by examining the definition of Turing machines and working with some examples. We will also sketch Turing’s remarkable construction of a universal Turing machine: a single machine which can simulate any other machine, i.e., which can carry out any algorithm, and his proof that some questions are algorithmically undecidable, i.e., cannot be answered by any algorithm.