Date: Wednesday, February 02, 2022
Location: 3866 East Hall (4:00 PM to 5:30 PM)
Title: Height gaps for groups of matrices and almost laws
Abstract: The famous "Tits alternative" states that a pair of matrices which generate a non-solvable group must contain a free group. Around 2008, Breuillard proved a strong version of this result by showing that a pair of (algebraic) matrices generating a non-solvable group must generate a matrix with large eigenvalues (in some valuation). We will discuss this theorem and some of its applications. We will also offer a new proof based on the existence of curious word maps known as almost laws. Joint work with Homin Lee and Lvzhou Chen.
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Speaker: Sebastian Hurtado
Institution: U Chicago
Event Organizer: spatzier
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