Mathematical Sciences Research Institute

Home » Workshop » Schedules » A Galois theory of exponential periods

A Galois theory of exponential periods

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

March 28, 2017 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Javier Fresán (ETH Zürich)
Location: MSRI: Simons Auditorium
  • Galois theory

  • Galois orbits

  • Periods

  • transcendental numbers

  • de Rham complex

  • flat connections

  • algebraic geometry

  • algebraic varieties

  • comparison isomorphism

  • Gamma function

  • irregular singularities

  • Euler-Mascheroni constant

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



Exponential periods form a class of complex numbers containing the special values of the gamma and the Bessel functions, the Euler constant and other interesting numbers which are not expected to be periods in the usual sense. However, they appear as coefficients of the comparison isomorphism between two cohomology theories associated to varieties with a regular function: the de Rham cohomology of a connection with irregular singularities and the so-called “rapid decay” cohomology. I will explain how this point of view allows one to construct a Tannakian category of exponential motives and to produce Galois groups which conjecturally govern all algebraic relations among these numbers. The focus will be on examples and open questions rather than on the more abstracts aspects of the theory. This is a joint work with Peter Jossen.

28370?type=thumb Fresan.Notes 6.18 MB application/pdf Download
Video/Audio Files


H.264 Video 7-Fresan.mp4 628 MB video/mp4 rtsp://videos.msri.org/data/000/028/107/original/7-Fresan.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.