[Turkmath:5780] number theory seminars

[Özlem Ejder]

Dear all,

FGC-HRI-IPM is a joint online seminar that is held twice a month on Mondays
at 4pm Istanbul time between Feza Gürsey Institute (Istanbul)-IPM
(Tahran)-HRI (Allahabad).

Mohammad Sadek (Sabanci University) is our speaker in the first FGC-HRI-IPM
Number Theory Seminar this Fall. Join us on *October 24, Monday at 4pm. *
The zoom link will be shared later this week. You can find the abstract and
title below.

*Title*: How often do polynomials hit squares?

*Abstract*:
Given a polynomial with rational coefficients, one may investigate the
possible values that may be attained by these polynomials over the set of
rational numbers. For centuries, number theorists have been giving due
attention to square rational values assumed by rational polynomials. It
turns out that seeking an answer to this question connects number theory
and geometry. Answering this question for a polynomial in one variable will
lead us to study the arithmetic of certain algebraic curves. We will spend
some time explaining the geometry beneath the question when the degree of
the polynomial is at least 3. For polynomials in more than one variable,
the geometric structure is remote. In the latter case, we will present some
of the old and recent developments in the theory shedding some light on
some classical Diophantine questions.

---------
Sevgiler,
Özlem
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