Mathematical Sciences: Research in Geometrical Analysis

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Three investigators will study problems in Kaehler geometry, calibrations, spinors, and Teichmuller theory. These involve Chern currents, slicing, spin structures, harmonic maps between Teichmuller spaces, the Thurston boundary of Teichmuller space, and moduli spaces of compact Riemannian surfaces. Differential geometry is the study of the structure and shape of generalized surfaces. These investigators will concentrate their efforts on surfaces based on the complex numbers rather than the real numbers. A Teichmuller space is the reduction of one of these complex generalized surfaces to a system of lower dimensional objects which are easier to understand. These investigators will continue their studies of such spaces in an effort to apply these new theories to questions arising from particle physics.