You can click on individual abstracts in the schedule or jump to the full set of student paper abstracts.

Student Papers Session I:  .
 

	Double Bubble Conjectures Andrew Cotton, Harvard University and Williams College
	The Isoperimetric Problem on the Cylinder David Freeman, Harvard University and Williams College
	The Isoperimetric Problem on Singular Surfaces John Spivack, Williams College

Student Papers Session II:
 

	Diophantine Olympics--What Does It Mean to Be a World Champion? Amanda Folsom, The University of Chicago
	Diophantine Olympics--Can Perfect Squares Score a Perfect 10? Alexander Pekker, Stanford University
	Diophantine Olympics--How Do the Primes Factor in the Competition? Julia Snyder, Williams College
	Diophantine Olympics--Is It Possible for a Bad Team to Earn a Gold Medal? Rungporn Roengpitya, Williams College

Student Papers Session III:
 

	Mall Time! Irma M.E.T. Servatius, Massachusetts Academy of Mathematics and Science
	Introduction to Geometric Dissection Nancy Peratto, Keene State College

Session I:

Double Bubble Conjectures
Andrew Cotton, Harvard University and Williams College

The Double Bubble Conjecture in R³  has recently been proved.  In this talk we will discuss the Double Bubble Conjecture in the sphere, S³, and in hyperbolic space, H³, and the Triple Bubble in R² , which remain open.

In this talk we will discuss a conjectured solution to the least-perimeter way to enclose prescribed area on the surface of a cylindrical can.

In this talk we will discuss the possibly bad behavior of a perimeter-minimizing enclosure of given area along singular portions of a surface, such as the rim of a cylindrical can.

Diophantine Olympics--What Does It Mean to Be a World Champion?
Amanda Folsom, The University of Chicago

Given an irrational number, we can ask how well it can be approximated by rational numbers.  How can we find the closest rational having a denominator not exceeding 100?  We'll call the denominators coming from the sequence of best rational approximations the "world champions".  In this talk we will describe  some of their amazing properties. No Olympic or number theoretic background is required.

Diophantine Olympics--Can Perfect Squares Score a Perfect 10?
Alexander Pekker, Stanford University

What can be said about the arithmetical structure of the denominators of the best rational approximations to an irrational number?  Is it possible to construct an irrational number such that its "world champion" sequence of denominators are all perfect squares?  What about cubes?  Here we will explore these questions.  No athletic background is required.

Diophantine Olympics--How Do the Primes Factor in the Competition?
Julia Snyder, Williams College

What kind of numbers can the denominators of the best rational approximations to an irrational number equal?  Is it possible to construct an irrational number such that its "world champion" sequence of denominators are all prime numbers?  Here we will consider this question and the related issues and provide an answer.  No athletic background is required.

Diophantine Olympics--Is It Possible for a Bad Team to Earn a Gold Medal?
Rungporn Roengpitya, Williams College

An irrational number is called "badly approximable" if it has no rationals near by that have "small" denominators.  Here we will discover the rich and mysterious structure of badly approximable numbers.  We will then ask about the arithmetical structure of the denominators of the best rational approximations to a badly approximable number.  Open questions will be posed.  Some athletic ability may be useful.

Mall Time!
Irma M.E.T. Servatius, Massachusetts Academy of Mathematics and Science

Assuming a uniform maximum speed, all points that can be reached within an hour from a given point (the mall) lie on a circle.  If the uniformity is destroyed by, for example, a single road on which one can travel faster, the circle is deformed.  We investigate the new shape obtained depending on the distance of the road to the mall, and generalize the problem.

Introduction to Geometric Dissection
Nancy Peratto, Keene State College

Geometric dissection is a process through which a figure, usually a regular polygon, is cut into pieces and reformed into another figure.  We will explore a particular geometric dissection technique, called the step technique.  It has been used to illustrate the proof of the Pythagorean Theorem and in recreational puzzles.

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