9457821 WEITSMAN Jonathan TITLE: Mathematical Sciences : NSF Young Investigator Technical Narrative: This research, supported by a National Science Foundation Young Investigator award, will be concerned with results and conjectures arising in mathematical physics and the geometry of moduli spaces associated to Riemann surfaces. It is intended to pursue specific applications of several techniques arising in integrable nonlinear differential equations, three dimensional topological structures and the cohomology ring of the moduli space of curves. The research is potentially of an interdisciplinary nature with anticipated applications to mathematical physics. The National Science Foundation Young investigator award recognizes outstanding young faculty. This award recognizes the recipient's strong potential for continued professional growth as a research mathematician and for significant development as a teacher and academic leader. ***