Examples of o-minimality in algebraic geometry

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 )

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Stanford algebraic geometry seminar

Series comments: This seminar requires both advance registration, and a password. Register at stanford.zoom.us/meeting/register/tJEvcOuprz8vHtbL2_TTgZzr-_UhGvnr1EGv Password: 362880

If you have registered once, you are always registered for the seminar, and can join any future talk using the link you receive by email. If you lose the link, feel free to reregister. This might work too: stanford.zoom.us/j/95272114542

More seminar information (including slides and videos, when available): agstanford.com

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