[Turkmath:5319] İ.Ü. Matematik Bölüm Semineri

[TEMHA ERKOÇ YILMAZTÜRK]

Merhabalar,

22.12.2021 tarihinde  saat 14.00 te İzmir Yüksek Teknoloji Enstitüsünde Dr.
Öğr. Üyesi Faruk Temur  başlık ve özeti aşağıda verilen bir konuşma
yapacaktır.  Seminer Zoom programı üzerinden online yapılacaktır. Katılmak
isteyenlerin katılım bilgilerini alabilmeleri için "
huseyinuysal at istanbul.edu.tr "  adresine mail atmaları gerekmektedir.

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*Başlık: *Discrete fractional integrals via lattice point counting

*Özet: *Arkhipov and Oskolkov initiated the study of discrete fractional
integrals with their work on boundedness of certain Fourier multipliers
about thirty years ago. Since then study of these operators, carried out
mostly by E. Stein, his students and collaborators, concentrated on cases
with translation invariant or quasitranslation invariant phase polynomial,
to exploit applicability of  the Fourier transform and the Hardy-Littlewood
circle method to these cases. In 2018, in joint work with E. Sert, we
introduced methods from number theory to study discrete fractional integral
operators along binary quadratic forms. More specifically we investigate
the distribution of lattice points  on conics via classical theory of
binary quadratic forms  and apply these to discrete fractional integral
operators using some delicate decompositions. In 2021, in continuation of
this work, using further information about  distribution of lattice points
on conics obtained from sieving,   analogous results for the even more
general case of bivariate quadratic polynomials were obtained. Also in this
latter work, connections to diophantine approximation were established, and
new results on certain well-known conjectures on lattice points
concentration were obtained. In this talk we will review these
developments, together with their historical and mathematical context.
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İyi günler dilerim.

Temha

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