Joseph Klerlein:  What if Pascal visited a race track and met with the Easter Bunny?
               
Abstract: We consider two different problems, one from a horse race track and one for the Easter Bunny. Surprisingly we can find a "Pascal triangle like" solution for both.
 
 
Jeffery Lawson: Finding relative equilibria on the rigid body: An application of geometric mechanics

Abstract: Saari's Conjecture states that an N-body system (N massive point particles attracted to each other by Newtonian gravity) has a constant moment of inertia if and only if the system is in relative equilibrium, that is, if the only solutions of the differential equations are uniform rotations of the entire system.  Marsden's Conjecture generalizes the statement of Saari's Conjecture general dynamical systems with symmetry. In recent literature there have appeared N-body arrangements with non-Newtonian gravity that contradict Marsden's Conjecture.
 
In this talk I'll reveal a novel counterexample to Marsden's Conjecture where the  dynamical system under consideration is nothing more than a free rigid body in three dimensions.  (``Free'' means zero potential energy.)

Examining this counterexample leads us to a unique method of identifying relative equilibria in the case where the dynamical system is any free Lie group (the most natural generalization of a rigid body) and allows us to repair Marsden's Conjecture in this context. This result illustrates the utility of geometrical approaches to solve problems in dynamical systems with symmetry.

Bill Kreahling: Branch Elminiation via Multi-Variable Condition Merging

Abstract: Conditional branches are expensive. Branches require a significant percentage of execution cycles since they occur frequently and cause pipeline  when mispredicted. In addition, branches result in forks in the control  which can prevent other code-improving transformations from being applied. In this paper we describe profile-based techniques for replacing the execution of a set of two or more branches with a single branch on a conventional scalar processor. First, we gather profile information to detect the frequently executed paths in a program. Second, we detect sets of conditions in frequently executed paths that can be merged into a single condition. Third, we estimate the benefit of merging each set of conditions. Finally, we restructure the control  to merge the sets that are deemed beneficial. The results show that eliminating branches by merging conditions can significantly reduce the number of conditional branches performed in non-numerical applications.

Sarah J. Greenwald:  Mathematical Morsels from The Simpsons and Futurama

Abstract: Did you know that The Simpsons and Futurama contain hundreds of instances of mathematics ranging from arithmetic and number theory to geometry and calculus?  Join us as we present some of our favorite mathematical moments and explore the related mathematical content, accuracy, and pedagogical value along with the mathematical backgrounds of the writers.  Special emphasis will be placed on references related to this years Mathematics Awareness Month on the Mathematics of the Cosmos. For more information, check out simpsonsmath.com