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Collquium: Jinbo Ren, University of Virginia, Transcendental number theory in algebraic geometry

Event Type: 
Jinbo Ren, University of Virginia
Event Date: 
Thursday, November 29, 2018 -
3:30pm to 4:30pm
SMLC 356
General PublicFaculty/StaffStudentsAlumni/Friends
Alex Buium

Event Description: 

Abstract: The classical Lindemann-Weierstrass theorem asserts that if

n algebraic numbers are linearly independent over$ \mathbb{Q}$, then

their exponentials are algebraically independent over $\mathbb{Q}$.

This theorem generalizes the fact that $e$ is a transcendental number.


More generally, the (very difficult) Schanuel's conjecture predicts

that if n complex numbers $a_1, a_2,...,a_n$ are linearly independent

over $\mathbb{Q}$, then the field $\mathbb{Q}(a_1,...,a_n,

e^{a_1},...,e^{a_n})$ has transcendence degree at least $n$ over

$\mathbb{Q}$. This assertion is very strong, for example, the

transcendence of $\pi$ is one of its simple consequences.


In my colloquium talk, I will explain how to formulate the analogues

of these classical conjectures in the context of algebraic tori,

abelian varieties and Shimura varieties. I will also discuss their

applications in Diophantine geometry.

Event Contact

Contact Name: Dimiter Vassilev

Contact Email: