PURE Math Residents

2012

 
2012_Residents_Photo.html

Research Projects

All projects were directed by Dr. John Little


Co-circular Kite Central Configurations in the 4-Body Problem

Tasheena Barrett, Alicia Lozano, Liliana Manrique


Abstract          Technical Paper            Presentation


Real Root Counting for Central Configurations

Wako Bungula, Ashlee Kalauli, Samantha Warren


Abstract           Technical Paper           Presentation


The n-Vortex Problem for Co-circular Central Configurations

Jonathan Gomez, Alexander Gutierrez, Jesse Robert


Abstract           Technical Paper           Presentation


Constructing Continua of Central Configurations with a Negative Mass

Julian Hachmeister, Jasmine McGhee, and Spencer Sasarita


Abstract           Technical Paper           Presentation

Resident Advisor: Dr. John Little - College of the Holy Cross

Resident Assistant: Dr. Roberto Pelayo - University Of Hawai`i at Hilo

Graduate Assistant: Christopher O’Neill - Duke University


Residents

Tasheena Barrett - BYU Idaho

Wako Bungala - Texas Lutheran University

Jonathan Gomez - BYU Hawai`i

Alex Gutierrez - Arizona State University

Julian Hachmeister - University of Hawai`i at Hilo

Ashlee Kalauli - University of Hawai`i at Hilo

Alicia Lozano - Bryn Mawr College
Liliana Manrique - Cal Poly Pomona

Jasmine Mcghee - Loyola Marymount University

Jesse Robert - University of Hawai`i at Hilo

Spencer Sasarita - University of Arizona

Samantha Warren - University of Portland

Publications

Julian Hachmeister, John Little, Jasmine McGhee, Roberto Pelayo, and Spencer Sasarita.

    Continua of central configurations with a negative mass in the n-body problem,

    Celest. Mech. Dyn. Astr. 115 (2013), 427-438, DOI 10.1007/s10569-013-9471-1.

    This was inaugural year of the PURE Math Residents component.  The Residents topics introduced twelve advanced undergraduates to computational algebraic geometry / commutative algebra. Their research projects involved applying these theoretical tools to projects in celestial mechanics on central configurations. The Residents program was directed by Dr. John Little with assistance from Dr. Roberto Pelayo and Christopher O’Neill.

Course Descriptions

Applications of Algebraic Geometry - The first three weeks of this eight-week program were devoted to an intensive short course on aspects of computational algebraic geometry and commutative algebra, plus material on central configurations in the Newtonian n-body problem that serves as background for the research projects. One of the major questions concerning central configurations is one posed by Stephen Smale:  Given a collection of positive masses, is the number of different central configurations they can form finite, up to a notion of equivalence allowing translations, rotations, and scaling?  Because the conditions defining a central configuration are purely algebraic, this opened the way for the application of various tools from computational algebraic geometry and commutative algebra. PURE Math Residents spent the remaining weeks working on applying these tools to various projects arising from celestial mechanics.