##### Department of Mathematics,

University of California San Diego

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### Final Defense

## John D. Foley

## Comparing Kac-Moody groups over the complex numbers and fields of positive characteristic via homotopy theory

##### Abstract:

Kac-Moody groups generalize Lie groups but are typically infinite dimensional. This defense will quickly introduce discrete and topological Kac-Moody groups and outline a direct comparison between complex topological Kac-Moody groups and discrete Kac-Moody groups over the algebraic closure of the field with p elements. This result uses newly constructed homotopy decompositions for the "unipotent" factors of parabolic subgroups of a discrete Kac-Moody group in terms of unipotent algebraic groups. Additional applications will be given and the topics of infinite Coxeter groups, BN-pairs, and root group data systems will be visited.

### June 4, 2012

### 11:00 AM

### AP&M 6402

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