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SUMMARY:Rational Point Count Distributions for Varieties over Finite Field
 s via Coding Theory
DTSTART:20141022T151500
DTEND:20141022T161500
DTSTAMP:20260407T102717Z
UID:3aedbc10a30b7de2f0ce9a5576dac8869b8ad5c7721959517ee3f5b3
CATEGORIES:Conferences - Seminars
DESCRIPTION:Nathan Kaplan\nWe will discuss an approach of Elkies to counti
 ng points in families of varieties over a fixed finite field.  A vector s
 pace of polynomials gives a linear subspace of (F_q)^N\, a linear code\, b
 y the evaluation map.  Studying properties of this code and its associate
 d dual code gives information about the distribution of rational point cou
 nts for the family of varieties defined by these polynomials.  We will de
 scribe how this approach works for families of genus one curves and del Pe
 zzo surfaces.  We will explain how Fourier coefficients of modular forms 
 appear in these enumerative questions and will discuss further problems re
 lated to rational points on intersections of varieties.  No previous fami
 liarity with coding theory will be assumed.
LOCATION:Room MA 30 http://plan.epfl.ch/?lang=fr&room=MA30
STATUS:CONFIRMED
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