Mathematical Sciences Research Institute

Home » Workshop » Schedules » Galois theory for motivic cyclotomic multiple zeta values

Galois theory for motivic cyclotomic multiple zeta values

Hot Topics: Galois Theory of Periods and Applications March 27, 2017 - March 31, 2017

March 30, 2017 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Claire Glanois (Max-Planck-Institut für Mathematik)
Location: MSRI: Simons Auditorium
  • Galois theory

  • Galois orbits

  • Periods

  • multiple zeta values

  • roots of unity

  • shuffle product

  • iterated integrals

  • motivic integration

  • weight spaces of modular forms

  • cohomology comparison isomorphisms

  • Lefschetz motive

  • cyclotomic fields

  • Hopf algebras

  • motivic periods

  • motivic fundamental group

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



Cyclotomic multiple zeta values (CMZV), are an interesting first bunch of examples of periods and a fruitful recent approach is to look at their motivic version (MCMZV), which are motivic periods of the fundamental groupoid of ℙ1 ∖ {0, μN, ∞}. Notably, MCMZV have a Hopf comodule structure, dual of the action of the motivic Galois group on these specific motivic periods; the explicit combinatorial formula of the coaction (Goncharov, Brown) enables, via the period map (isomorphism under Grothendieck’s period conjecture), to deduce results on CMZV. We will here highlight how to apply some Galois descents ideas to the study of these motivic periods and look at how periods of the fundamental groupoid of ℙ1 ∖ {0, μN', ∞} are embedded into periods of π1(ℙ1 ∖ {0, μN, ∞}), when N′ | N, via a few examples

28376?type=thumb Glanois.Notes 600 KB application/pdf Download
Video/Audio Files


H.264 Video 14-Glanois.mp4 660 MB video/mp4 rtsp://videos.msri.org/data/000/028/127/original/14-Glanois.mp4 Download
Troubles with video?

Please report video problems to itsupport@msri.org.

See more of our Streaming videos on our main VMath Videos page.