Jennifer Daniel

STAIRSTEP: An interdisciplinary program fo retention and outreach in STEM

Lamar Universitys Students Advancing through Involvement in Research Student Talent Expansion Program (STAIRSTEP) is designed to increase the number of United States students receiving undergraduate degrees in science, technology, engineering and mathematics (STEM). The programs goals are to attract students to STEM, retain them through to graduation, and help them transition to careers or advanced study in STEM. The STAIRSTEP program targets talented “at risk” students who face social and economic barriers that can make it difficult for them to complete degrees in STEM. This includes women and minorities who are underrepresented in STEM, low income and first generation students. It uses recognized strategies from the literature for increasing participation in STEM and implements them in an innovative way. The program has been very successful in its first two years. This paper describes the programs strategies, activities and results achieved during this time. Benefits and challenges of the interdisciplinary approach are discussed, and key elements essential to the programs success are identified.

Work in progress - STAIRSTEP - a program for expanding the student pipeline

This paper introduces Lamar Universitys Students Advancing through Involvement in Research Student Talent Expansion Program (STAIRSTEP), which is designed to increase the number of U. S. citizens receiving undergraduate degrees in science disciplines including computing, mathematics, physics, chemistry, geology and earth science. STAIRSTEP uses the experience gathered from two successful programs in computer science for student retention and recruiting of women and underrepresented minorities at Lamar University. STAIRSTEP expands these efforts by including several science disciplines and addressing a broader population of talented ‘at risk’ students. STAIRSTEP adopts recognized strategies from the literature for increasing participation in Science, Technology, Engineering and Mathematics (STEM). It is innovative in the way it puts this research into practice. This paper describes the STAIRSTEP approach, its expected results, evaluation plan, and current status.

Algorithms for Computations in Local Symmetric Spaces

In the last two decades much of the algebraic/combinatorial structure of Lie groups, Lie algebras, and their representations has been implemented in several excellent computer algebra packages, including LiE, GAP4, Chevie, Magma, and Maple. The structure of reductive symmetric spaces or more generally symmetric k-varieties is very similar to that of the underlying Lie group, with a few additional complications. A computer algebra package enabling one to do computations related to these symmetric spaces would be an important tool for researchers in many areas of mathematics, including representation theory, Harish Chandra modules, singularity theory, differential and algebraic geometry, mathematical physics, character sheaves, Lie theory, etc. In this article we lay the groundwork for computing the fine structure of symmetric spaces over the real numbers and other base fields, give a complete set of algorithms for computing the fine structure of symmetric varieties and use this to compute nice bases for the local symmetric varieties.

Computing the fine structure of real reductive symmetric spaces

Much of the structure of Lie groups has been implemented in several computer algebra packages, including LiE, GAP4, Chevie, Magma and Maple. The structure of reductive symmetric spaces is very similar to that of the underlying Lie group and a computer algebra package for computations related to symmetric spaces would be an important tool for researchers in many areas of mathematics. Until recently only very few algorithms existed for computations in symmetric spaces due to the fact that their structure is much more complicated than that of the underlying group. In recent work, Daniel and Helminck [Daniel, J.R., Helminck, A.G., 2004. Algorithms for computations in local symmetric spaces. Comm. Algebra (in press)] gave a complete set of algorithms for computing the fine structure of Riemannian symmetric spaces. In this paper we make the first step in extending these results to general real reductive symmetric spaces and give a number of algorithms for computing some of their fine structure. This case is a lot more complicated since it involves the intricate relations of five root systems and their Weyl groups instead of just two as in the Riemannian case. We show first that this fine structure can be obtained from the setting of a complex reductive Lie group with a pair of commuting involutions. Then we proceed to give a number of algorithms for computing the fine structure of the latter.