# Examples of o-minimality in algebraic geometry

### Hunter Spink (Stanford)

02-Sep-2022, 19:00-20:00 (5 months ago)

Abstract: In this introductory talk, we will define o-minimality (a way of augmenting algebraic geometry with functions like $e^x$, $\sin$, $\cos$, etc.), and show:

(1) The number of solutions to a system of polynomials equations is bounded by a function of the sizes of the supports of the equations, independent of the sizes of the exponents.

(2) For an irreducible polynomial $f(x,y)$ not of the form $ax^iy^j+bx^ky^l$ there are only finitely many solutions to $f(x,y)=0$ with $x$, $y$ roots of unity.

algebraic geometry

Audience: researchers in the topic

( slides | video )