The motivic fundamental group
Event details
| Date | 01.10.2012 › 05.10.2012 |
| Speaker | Marc Levine |
| Location |
AAC006
|
| Category | Conferences - Seminars |
The fundamental group in topology is, as its name 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 over 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 selects an appropriate Tannakian category of motives, one arrives at one of many possible motivic fundamental groups. In the first part of this mini-course, we will look at the fundamental groups associated to various categories of mixed Tate motives and their relation to algebraic cycles, multiple polylogarithms and multiple zeta values.
The first point of view, that of a group of loops, has an algebraic analog as well, given by motivic 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 resulting A¹ fundamental group has a surprisingly interesting structure, even for varieties we usually think of as simply connected, such as projective spaces. In the second portion of the mini-course, we will give an introduction to motivic homotopy theory and both structural and computational aspects of the A¹ fundamental group.
The first point of view, that of a group of loops, has an algebraic analog as well, given by motivic 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 resulting A¹ fundamental group has a surprisingly interesting structure, even for varieties we usually think of as simply connected, such as projective spaces. In the second portion of the mini-course, we will give an introduction to motivic homotopy theory and both structural and computational aspects of the A¹ fundamental group.
Practical information
- General public
- Free
- This event is internal
Organizer
- Hélène Esnault (U. Duisburg-Essen), Andrew Kresch (U. Zürich), Bjorn Poonen (MIT), Alexei Skorobogatov (Imperial College London).
Contact
- Rana Gherzeddine