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Harmonic 1-Cycles in Reflection Tilings

Student-Run Applied & Math Seminar

Speaker: Kathleen O'Reilly, UC Davis
Location: 2112 MSB
Start time: Wed, Nov 18 2009, 12:00AM

L2-homology groups are analytical objects one associates to noncompact topological spaces in order to better understand their asymptotic structure. It is known that any L2-homology class has a unique harmonic representative, but these are notoriously hard to find or construct. In this talk I will introduce ordinary and L2-homology, then explain the method I used to describe a harmonic representative of a given cycle in a specific hyperbolic reflection tiling. This project was the basis for my senior thesis at Santa Clara University last year with Professor Rick Scott.