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PRODID:-//Memento EPFL//
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SUMMARY:The motivic fundamental group
DTSTART;VALUE=DATE:20121001
DTSTAMP:20260503T014144Z
UID:d1bf6c1f62511db101194d4440d5ba3abe62349095cf39e2a9ed32b1
CATEGORIES:Conferences - Seminars
DESCRIPTION:Marc Levine\nThe fundamental group in topology is\, as its nam
 e suggests\, a fundamental algebraic invariant of a (pointed) topological 
 space\; it can be viewed as the group of homotopy classes of pointed loops
 \, or as the group of automorphisms of the fiber of the universal cover ov
 er the base-point. Via the formalism of Tannakian categories\, the second 
 point of view may be applied in a wide variety of situations\; if one sele
 cts an appropriate Tannakian category of motives\, one arrives at one of m
 any possible motivic fundamental groups. In the first part of this mini-co
 urse\, we will look at the fundamental groups associated to various catego
 ries of mixed Tate motives and their relation to algebraic cycles\, multip
 le polylogarithms and multiple zeta values.\n\nThe first point of view\, t
 hat of a group of loops\, has an algebraic analog as well\, given by motiv
 ic homotopy theory. Here the notion of a path or a homotopy class is made 
 algebraic by replacing the unit interval with the affine line. The resulti
 ng A¹ fundamental group has a surprisingly interesting structure\, even f
 or varieties we usually think of as simply connected\, such as projective 
 spaces. In the second portion of the mini-course\, we will give an introdu
 ction to motivic homotopy theory and both structural and computational asp
 ects of the A¹ fundamental group.
LOCATION:AAC006
STATUS:CONFIRMED
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