Is there a smallest algebraic integer?

Job Candidate Talk
Thursday, January 27, 2022 - 11:00am for 1 hour (actually 50 minutes)
Vesselin Dimitrov – University of Toronto
Anton Leykin

The Schinzel-Zassenhaus conjecture describes the narrowest collar width around the unit circle that contains a full set of conjugate algebraic integers of a given degree, at least one of which lies off the unit circle. I will explain what this conjecture precisely says and how it is proved. The method involved in this solution turns out to yield some other new results whose ideas I will describe, including to the closest interlacing of Frobenius eigenvalues for abelian varieties over finite fields, the closest separation of Salem numbers in a fixed interval, and the distribution of the short Kobayashi geodesics in the Siegel modular variety.