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Return to NTS Fall 2015

Sep 03

Kiran Kedlaya
On the algebraicity of (generalized) power series

A remarkable theorem of Christol from 1979 gives a criterion for detecting whether a power series over a finite field of characteristic p represents an algebraic function: this happens if and only if the coefficient of the n-th power of the series variable can be extracted from the base-p expansion of n using a finite automaton. We will describe a result that extends this result in two directions: we allow an arbitrary field of characteristic p, and we allow "generalized power series" in the sense of Hahn-Mal'cev-Neumann. In particular, this gives a concrete description of an algebraic closure of a rational function field in characteristic p (and corrects a mistake in my previous attempt to give this description some 15 years ago).

Sep 10

Sean Rostami
Fixers of Stable Functionals

Coming soon...

Dec 17

Nathan Kaplan
Coming soon...

Coming soon...