**FGC-HRI-IPM** Joint Number Theory Seminar

**When:**Wednesdays

**Where:**Zoom

**Meeting ID:**85613860958

**Passcode:**513992

**Seminar mailing list:**google group

## Upcoming Talks

** Speaker: ** Alia Hamieh

** Title:** *TBA *

** Abstract:** TBA

**Date:** April 5, 2023

**Time:** 17:30-19:00 Tehran local time

** Speaker: ** Asgar Jamneshan

** Title:** *TBA *

** Abstract:** TBA

**Date:** April 19, 2023

**Time:** 17:30-19:00 Tehran local time

** Speaker: ** Rahul Gupta

** Title:** *TBA *

** Abstract:** TBA

**Date:** May 3, 2023

**Time:** 17:30-19:00 Tehran local time

** Speaker: ** Cristiana Bertolin

** Title:** *Periods of 1-motives and their polynomials relations *

** Abstract:** The integration of differential forms furnishes an isomorphism between
the De Rham and the Hodge realizations of a 1-motive M. The coefficients of the matrix
representing this isomorphism are the so-called "periods" of M. In the semi-elliptic
case (i.e. the underlying extension of the 1-motive is an extension of an elliptic
curve by the multiplicative group), we compute explicitly these periods.
If the 1-motive M is defined over an algebraically closed field,
Grothendieck's conjecture asserts that the transcendence degree of
the field generated by the periods is equal to the dimension of the motivic
Galois group of M. If we denote by I the ideal generated by the polynomial
relations between the periods, we have that "the numbers of periods of M minus
the rank of the ideal I is equal to the dimension of the motivic Galois group of M",
that is a decrease in the dimension of the motivic Galois group is equivalent to
an increase of the rank of the ideal I. We list the geometrical phenomena which
imply the decrease in the dimension of the motivic Galois group and in each case
we compute the polynomials which generate the corresponding ideal I.

**Date:** May 17, 2023

**Time:** 17:30-19:00 Tehran local time

** Speaker: ** Carlo Pagano

** Title:** *TBA *

** Abstract:** TBA

**Date:** May 31, 2023

**Time:** 17:30-19:00 Tehran local time