Gamma values: regular and irregular


Javier Fresan
2016-12-16  13:30 - 14:30
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)

The values of the gamma function at rational numbers remain quite mysterious, one of the reasons being that, conjecturally, they are not periods in the usual sense of algebraic geometry. However, the arithmetic theory of regular singular connections allows one to show that suitable products of them are periods of Hodge structures with complex multiplication, as predicted by Gross and Deligne. To deal with single gamma values, one needs to consider irregular singular connections instead. In the first half of the talk, I will survey on my results about the Gross-Deligne conjecture. Then I will move to a recent joint work with P. Jossen where we construct a Tannakian category of exponential motives in which single gamma values become periods. This will shed some light on the classical transcendence conjectures for these numbers.