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Student Opportunities in Accelerated Research

SOAR Program

 

The SOAR program is an opportunity for students of Grove City College to participate in a short term focused research project. The program first began in the summer of 2008. Each summer since, we have had three students work on a research project for four weeks during the summer. The SOAR program has been generously funded by the college's Swezey Fund for Scientific Research and Instrumentation. The Mathematics Department plans to continue the SOAR Program as long as the funding is available.

SOAR 2008

Students:  Michael Ginter, Susannah Johnson, and James McNamara

                   Advisor: Dr. Michael A. Jackson 

 

Project Title: The Strong Symmetric Genus of Small Generalized Symmetric Groups

 

Abstract:  The generalized symmetric groups, G(n,m), are defined to be the wreath product of the symmetric group on n objects with the cyclic group of order m. The strong symmetric genus of a finite group G is the smallest genus of a closed orientable topological surface on which G acts faithfully as a group of orientation preserving symmetries. This research project found the strong symmetric genus of the groups G(n,m) for n equal to 3, 4 or 5.

 

The students had the opportunity to present their work in several different forums:

  • They were the inaugural talk in the Hopeman Student Research Seminar Series at Grove City College. An article in the Collegian about this talk can be found on the front page of the October 10, 2008 issue.

  • The students also presented their work at the Joint Mathematics Meetings in Washington, D.C. in January 2009. Here is the schedule (they were the last talk on Monday in this session).

  • They represented Grove City College at the Undergraduate Research at the Capitol - Pennsylvania. Their poster can be seen below.

  • Their poster was also a part of the first Student Research Showcase during Parent's Weekend 209 at Grove City College. The poster can be found here in pdf - format

  • SOAR 2009 - Harrisburg
    from left: Michael Ginter, Susannah Johnson, and James McNamara

 

 

SOAR 2009

Students:  Michelle Bowser, Trevor Partridge, and Kirsten Rodgers

                   Advisor: Dr. Michael A. Jackson 

 

Project Title: The Strong Symmetric Genus of Small D-type Generalized Symmetric Groups

 

Abstract:  For each positive integers m and n, the generalized symmetric group G(n,m) is defined to be the group generated by all n x n permutation matrices and all n x n diagonal matrices with entries in the mth roots of unity. The D-type generalized symmetric group D(n,m) is the normal subgroup of G(n,m) generated by all n x n permutation matrices and all n x n diagonal matrices with entries in the mth roots of unity that have determinant 1. The strong symmetric genus of a finite group G is the smallest genus of a closed orientable topological surface on which G acts faithfully as a group of orientation preserving symmetries. We obtain the strong symmetric genus of each group D(n,m) where n = 3, 4, or 5.

 

The students also spent some time during their project finding the Strong Symmetric Genus of the groups we referred to as AD(n,m)  for n equal to 3, 4 or 5. AD(n,m) is the normal subgroup of D(n,m) generated by all n x n permutation matrices that have determinant 1, and all n x n diagonal matrices with entries in the mth roots of unity that have determinant 1.

 

The students will have the opportunity to present their work in several different forums:

  • They presented a poster in the Student Research Showcase during Homecoming 2009. Here is their poster in pdf format.

  • The students travelled to the Joint Mathematics Meetings in San Francisco in January 2010. While there they presented a talk on their work as well as participate in the Undergraduate Poster Session.

  • They will also talk in the Hopeman Student Research Seminar Series at Grove City College on March 23, 2010.  

From Left: Trevor Partridge, Kirsten Rodgers, and Michelle Bowser

 

Last Updated: 03/15/2010

2006, Grove City College Department of Mathematics

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