Difference between revisions of "NTS ABSTRACT"

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== Sep 03 ==
  
 
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''SPEAKER'''
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Kiran Kedlaya'''
 
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| bgcolor="#BCD2EE"  align="center" | ''On the algebraicity of (generalized) power series''
 
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ABSTRACT
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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
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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
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an arbitrary field of characteristic p, and we allow "generalized power series" in the sense of Hahn-Mal'cev-Neumann. In particular, this gives
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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).
 
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== Sep 10 ==
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sean Rostami'''
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| bgcolor="#BCD2EE"  align="center" | Fixers of Stable Functionals
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Coming soon...
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Revision as of 21:21, 24 August 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...