Speakers and Workshop Descriptions
Keynote Speaker: Dr. Julia Walk
Workshop title: The Mathematics of Travel and Route Planning
Have you ever planned a road trip based on lowest cost or shortest distance? Have you tried to plan a vacation so that you can make it to all of your must-see attractions within a certain number of days? This workshop will explore how mathematicians and computer scientists have approached these types of questions, and you will try out one of the methods that has been developed to answer them. We will also discuss applications of these questions in areas such as biology and business.
Workshop title: What is the smallest region inside which we can rotate a needle?
A needle of length 1 is resting on the table. We want to rotate it 180 degrees, without lifting it from the table. As it rotates, it sweeps a region on the table. How small can we make this region, while still being able to rotate the needle inside of it? This is a problem with a surprising solution and many applications!
Workshop title: The mathematics behind constructing a globe
Ann’s Globes and Sara’s Atlases have always been in competition. The feud goes many years back, but there’s no time for that now. A new company,“Globes are Us” have just moved into town and they have a computer program that prints globes and atlases in pairs. This means that customers get a globe and atlas which match spherical coordinates with the flat coordinates on the map. The people at Globes can’t do this themselves so the computer has to double print each pair of coordinates on the map and sphere. That’s just a mess. As employees of these local businesses, we can’t let this new company take over. If we can learn how to make this conversion ourselves, we won’t need to double print and can take back the globe & atlas business!
Workshop title: How to draw an n-dimensional cube
What is the difference between an interval, a square, and a cube? An interval is a part of a straight line, a square is a part of a plane, a cube is a part of our space. What is common about an interval, a square, and a cube? It turns out that there is a deep analogy among the geometric processes of drawing them. Even more importantly, this analogy, about which I will tell in my workshop, can be taken much further, and it is logically possible to consider a four-dimensional cube, and a five-dimensional cube, and a six-dimensional cube, and eventually an n-dimensional cube for any natural n. After introducing algebraically the n-dimensional cube, I will concentrate in this workshop on how to draw a layout of an n-dimensional cube, i.e., how to represent this object geometrically.