[Turkmath:5638] MSGSU Mathematics Seminars (25 May 2022, 15:00)

[İpek Tuvay]

Dear all,

You can see the information for this week's seminar in our department
below.
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*Time: *Wednesday, 25 May 2022, 15:00

*Speaker:* Neslihan Girgin (MSGSÜ)

*Title: *A Number Theoretical Approach to the Polynomials over Finite Fields

*Abstract:* Let q be a prime power and Fq be the finite field with q
elements. The explicit constructions of irreducible polynomials over Fq is
one of the main problems in the arithmetic of finite fields which has many
applications in several areas such as coding theory, cryptography, etc. In
general, some recursive methods are preferred to do these constructions
using rational transformations. In particular, we are interested in methods
that are obtained by using quadratic transformations. For doing this, we
will first classify and normalize the rational transformations of degree 2
using the behaviour of the ramified places in the corresponding rational
function field extensions over the finite field Fq. Then we will
investigate the constructions using Galois theory and some basic
observations in group theory. This approach provides to understand the
iterative constructions better and gives various generalisations of them.
It also helps to determine the requirements put on the initial polynomials
easier.

*Link: *
https://teams.microsoft.com/l/meetup-join/19%3a1eaca84648fa440e94bc4d7382675247%40thread.tacv2/1653225334681?context=%7b%22Tid%22%3a%22ddd5afa6-82d7-4e0e-b457-3000f5a23749%22%2c%22Oid%22%3a%22b11f2b28-e233-4b68-b781-77d2029695cb%22%7d
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*For future talks please visit: *
https://researchseminars.org/seminar/MSGSUMath

Best,

İpek Tuvay
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