Milner 216

Thursdays, 1:00-2:00 PM

Texas A&M University

**Thursday, September 23
Milner 216, 1:00 PM**

**Title:** *On effective Witt decomposition and Cartan-Dieudonné
theorem*

**Abstract:** A classical theorem of Witt states that a bilinear
space can be decomposed into an orthogonal sum of hyperbolic planes,
singular, and anisotropic components. I will discuss the existence of
such a decomposition of bounded height for a symmetric bilinear space
over a number field, where all bounds on height are explicit. I will
also talk about an effective version of Cartan-Dieudonné theorem on
representation of an isometry of a regular symmetrice bilinear space
as a product of reflections. Finally, if time permits, I will show a
special version of Siegel's Lemma for a bilinear space, which provides
a small-height orthogonal decomposition into one-dimensional
subspaces.