On occasion of the visit of students from the University of Utrecht at the City College on March 18, we present a series of five mini lectures on general topics in mathematics, which will last about 20 minutes each. These lectures are aimed at undergraduate students and everybody else interested. In particular, we invite all CCNY students to come.

The talks will take place on Friday, March 18, in lecture hall NAC 5/101. The schedule is as follows.

 Time 10.00 Joseph Bak An Intriguing Bankruptcy Problem from the Talmud 10.25 Asohan Amarasingham The Neural Code: Mathematical Challenges Coffee break 11.20 Pat Hooper Loops in Truchet tilings 11.45 David Rumschitzki How do your arteries start to clog? Mathematical modeling of early events in atherogenesis 12.10 Ethan Akin The 3X+1 Problem

Abstracts

An Intriguing Bankruptcy Problem from the Talmud (Joseph Bak)

The Talmud, which was completed almost 1500 years ago, records a set of rulings for the division of an estate in the case of bankruptcy. The Talmud itself challenges the rulings as they appear to be self-contradictory and at odds with other precedents. We will try to unravel the puzzles in the ruling, as formulated by CCNY alumnus and Nobel-prize winner Prof. Robert Aumann. Somewhat surprisingly, Prof. Aumann shows how the Talmudic ruling is in perfect consonance with some of the latest approaches in game theory.

The Neural Code: Mathematical Challenges (Asohan Amarasingham)

One of the foundational questions in neuroscience involves how neurons communicate information to one another by way of patterned electrical signals. I will provide a brief overview of the experimental state-of-the-art, and describe some of the mathematical and statistical challenges that arise in the course of analysing these measurements.

Loops in Truchet tilings (Pat Hooper)

The Truchet tiles are a pair of squares decorated by arcs. When the squares are put together to form a tiling of the plane, the arcs join to form a collection of curves in the plane. I will discuss the question: What is the probability that a curve of the tiling closes up? I will discuss some cases where the answer can be given. I will also discuss some variants of this question which haven't been answered yet.

The 3X+1 Problem (Ethan Akin)

Start with a positive, odd number. Multiply by 3, add 1 and divide away all the factors of 2 until you get back to an odd, positive number. If you keep repeating this process do you always hit 1? This simple problem is unsolved and -alas- I won't solve it. I will explain why the problem is harder than it appears.