The international component of the GK-12 program at CSUN allowed GK-12 Fellow Cynthia Shepherd to do a research paper on composite membrances along with graduate students Aldo Lopes and Russell Howes. This project was under the advisement of Professor Renato Pedrosa at UNICAMP (Universidade de Campinas), Brazil. It was part of the IRES (International Research Experience for Students) Program. The research was funded by NSF and the GK-12 grant as well as the Federal Brazilian Agency CNPq.
The study of vibrating membranes is an aspect of mathematical physics that is primarily concerned with the geometries of the membrane corresponding to its frequencies. Their paper concentrated on determining the shape of membranes with minimal eigenvalues; in particular the first eigenvalue, or fundamental frequency, of such membranes.
As part of the same program GK-12 Fellow Sara Frietze worked with graduate students Robert Gerrity and Tiago Picon. Their work, The inviscid limit of incompressible fluid flow in an annulus, supervised by Brazilian researchers Helena Lopes and Max Souza, concerned fluid flow in an annulus within the low-viscosity limit. This was an open problem in fluid mechanics. The analysis of velocity solutions and vorticity production in the inviscid limit led to a solution at the end of the four-week program. Doctors Lopes and Souza will use the work completed in the summer by the graduate students to publish a paper in a journal of mathematics.
This experience for GK-12 Fellows provided a unique opportunity to do mathematical research for the first time and to write a paper with the promise of publication. The Fellows gained invaluable experience in communicating mathematics and developing their potential as future research mathematicians.
Gk-12 teacher Tania Lopez accompanied partner Fellows Cynthia and Sara to Brazil. While interacting with Brazilian graduate students, she attended three professional development programs for teachers at the Brazilian University. She describes her experience as well as her views on the Brazilian Math Standards for high school education in the her article Math and Math Education in Brazil.
Still in the international component of the GK-12 program Fellow Tigran Mkrtchyan participated in a workshop on differential geometry in Campinas, Brazil in December 2006. Since he is working on an open problem in differential (Riemannian) geometry, this workshop has had a great impact on him as a future mathematician. He was introduced to professors from different countries, including world-renown differential geometers who do research in differential geometry. He attended their presentations, talked to them individually about their research experience. Some of the topics were closely related to his thesis so the help was practical. The workshop let Tigran get a real sense of doing research and inspired him to go on and get a Ph.D. in mathematics.