Student AIM Seminar

This will be a planning meeting for the Fall semester. We will discuss:

• Topics for the semester -- cool mathematics that you have heard about and want to learn more about (so bring some ideas);
• Starting a student SIAM chapter here in Michigan;
• Reserving slots for giving a talk.

Please don't hesitate to join us if you are interested in seeing how mathematics gets applied to the real world. All are welcome.

I will talk about the MAGMA Computer Algebra System, including how to access and run it, and some basic MAGMA syntax. I will then investigate how the problem of finding nowhere-zero k-flows in graphs, which is related to planar graph coloring. I shall follow paper 15 in "Discovering Mathematics with MAGMA." This talk should be relevant to anyone interested computational discrete mathematics.

In this talk, we will introduce some of the basic ideas involved in mathematical finance. We will begin with a brief discussion of financial markets and derivative securities, and the rest of our talk will focus on methods to price these securities. In particular, we will mention the fundamental theorem of asset pricing, the binomial model, and then we will derive and solve the celebrated Black-Scholes PDE for a simple European call option on an asset paying no dividends.

This talk is meant to be an opening to dialogue on how mathematicians can involve themselves in the science of climate change. If there is enough interest, the talk could go any number of directions, but here is the plan.

One of the most pressing issues our society faces is the impact we have on our planet. Accurate predictions of the future climate are vital for policy makers and social scientists. Difficult decisions regarding resource allocation, disaster management, and urban planning must be made keeping in mind what a future earth will be like. Massive computational models have been developed at several centers throughout the world to simulate the earth's climate. These General Circulation Models (GCM) are then used to forecast the conditions of the earth's climate in the future.

These GCM's are not perfect however, and there are a plethora of mathematical issues one can raise with each individual model. After briefly describing several mathematical problems in climate change, I will point out a few particular issues that are of interest to myself in fluid dynamics.

I will introduce some of the common problems in image processing and give a brief overview of some of the common approaches to solving these problems. Then I will specialize to the problem of image segmentation and a variant of the piecewise-constant Mumford-Shah (PCMS) model. I'll link this problem to the problem of finding a minimum capacity cut (MC) in a flow network. The max-flow min-cut problem allows us to reduce the (MC) problem to find a maximum flow (MF) on the same network, which can often be solved in polynomial time. I'll conclude by demonstrating a simple MATLAB implementation to solve (PCMS) via (MF). No prior experience with either image processing models or graphs is presumed.