9805819 Colley This work is funded through the Professional Opportunities for Women in Research and Education (POWRE) program as a Research/Educational Enhancement project. The PI will use her POWRE award to undertake a three-part project: (i) to use and extend techniques from quantum cohomology in order to develop a "higher order" contact cohomology that will enable the computation of new characteristic numbers (involving incidence, tangency, and higher-order tangency) for algebraic plane curves and possibly for curves lying in other varieties; (ii) to connect ideas from commutative algebra with those of modern intersection theory in order to understand the algebra and geometry of blowup schemes along arbitrary centers(i.e., not necessarily nonsingular or reduced); (iii) to develop a course for undergraduates in computational algebra and algebraic geometry. Topic (i) represents joint work with Gary Kennedy of the Ohio State University and Lars Ernstrom of the Royal Institute of Technology, Stockholm. The idea is to develop an associative family of products, parameterized by the Chow ring of suitable variety, that deforms the cohomology cup product. Topic (ii) is joint work with Gary Kennedy that would unite some local algebraic work with global geometry. Topic (iii) will enhance the PI's teaching expertise and enable undergraduates opportunities for individual exploration and research. This POWRE project is supported by the MPS Office of Multidisciplinary Activities (OMA).
