Graduate Student Seminar: Jiayi Shen - University of Notre Dame

Speaker: Jiayi Shen
University of Notre Dame

Will give a Graduate Student Seminar entitled:
Liftableness of torsion elements in $\text{GL}_n(\mathbb{Z})$

Abstract: Consider the representation $\text{Out}(F_n)\rightarrow\text{GL}_n(\mathbb{Z})$. We would like to answer the question whether all torsion elements in $\text{GL}_n(\mathbb{Z})$ can be lifted to torsion elements in $\text{Out}(F_n)$. We use a geometric approach towards torsion elements in $\text{Out}(F_n)$ and use algebraic number theory to study torsion elements in $\text{GL}_n(\mathbb{Z})$. For a matrix with prime order $p$ where $p\leq 19$, it is always liftable. For $n\geq 22$, there always exists an order $23$ matrix that can not be lifted to $\text{Out}(F_n)$.

Date: 05-03-2024
Time: 11:00 am
Location: 258 Hurley Bldg

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