FRIAS Colloquium - Giancarlo Urzua

"Some geometry from continued fractions" 

Algebraic geometry was born with the interpretation of geometric figures through solutions of polynomial equations and vice versa. This more or less started with Descartes and Fermat 400 years ago, passing through an algebraic (Noether, Zariski, Weil, etc) revolution, and an abstract algebraic (Grothendieck and others) revolution. Algebraic geometry typically offers bridges between different areas in Mathematics. I will talk about a simple bridge that is very much involved in my recent work on the birational geometry of Markov numbers. The main characters are the Hirzebruch-Jung continued fractions. I will explain what they are, and some geometry behind them.