# Mentor

## Dr. Oscar Vega

Dr. Oscar Vega's research is on Finite Geometries, which is a mix of axiomatic geometry, combinatorics and abstract algebra.

He has mentored two REU groups. One in 2010 at The University of Iowa, and another in 2012 at Fresno State. In these REUs he worked with 9 students, and their work resulted in three publications; two of them about to be published and the other still under review. His mentees have also presented their work at the JMM, where a couple of them won outstanding poster presentation awards.

Dr. Vega has supervised six other Fresno State students, and one University High School student, in undergraduate research. Their work has also ended up in articles and presentations at various conferences.

The projects students have worked on involve topics ranging from Number Theory, to a mix of Graph Theory with Finite Geometries, to playing games on graphs.

Below are some of the accomplishments of his students so far:

- K. Mellinger
**, Ryan Vaughn**, and O. Vega**.***Graphs Embedded into Finite Projective Planes*. Submitted to The Australasian Journal of Combinatorics. **E. Aceves, D. Heywood, A. Klahr**, and O. Vega.*Cycles in Projective Spaces*. To appear in Journal of Geometry.**I. Birnbaum, R. McDonald, M. Kuneli, K. Urabe**, and O. Vega.*The well-covered dimension of products of graphs*. To appear in Discussiones Mathematicae Graph Theory.**J. Peabody, J. White**, and O. Vega.*Cycles, wheels, and gears in finite planes*. To appear in Contributions to Discrete Mathematics.**D. Holden**.*Results on the 3x+1 and 3x+d conjectures*. Fibonacci quarterly. Vol 49 (2). 2011. 131-133**Ashley Klahr**- Talk at the JMM in San Diego, January 2013. She also gave a talk at USD Undergraduate Research Conference. April 2013.**Ryan Vaughn**- Poster at the JMM in San Diego, January 2013 (Outstanding Poster Award).- Poster at the JMM in San Diego, January 2013 (Outstanding Poster Award).**Jamie Peabody and Jordan White**- Poster at the JMM in San Diego, January 2013. He also gave a talk at PCUMC in March 2013.**Benjamin Wright****Elaina Aceves and David Heywood**- Poster at the JMM in San Diego, January 2013. They also gave a talk at PCUMC in March 2013.- Talk at at JMM in Washington DC, January 2012. They also gave a talk at PCUMC in Pomona CA. March 2012.**Jamie Peabody and Karen Willis****Robyn McDonald and Megan Kuneli**- Talk at at JMM in Washington DC, January 2012. They also gave a talk at PCUMC in Pomona CA. March 2012.**Isaac Birnbaum**- Poster at the JMM in San Francisco, January 2010.