[Turkmath:7364] Cebir-Geometri Günleri, 24-25-26 Aralık 2010, TÜBİTAK - FEZA GÜRSEY ENSTİTÜSÜ

13 Ara 2010 Pzt 12:28:27 EET

  Cebir-Geometri Günleri

      24-25-26 Aralık 2010

      TÜBİTAK - FEZA GÜRSEY ENSTİTÜSÜ

/Konuşmaların Dili:/ Cebir-Geometri Günlerinde konuşmaların dili, 
olabildiğince /Türkçe/ olacak. Bazı konuşmaların tümü ya da bazı 
kısımları İngilizce olması olasıdır.

*Konuşmacılar:*

    * Mahir Bilen Can, Tulane Üniversitesi
    * Kıvanç Ersoy, Mimar Sinan Güzel Sanatlar Üniversitesi ve Salerno
      Üniversitesi
    * Sevgi Harman, İTÜ
    * Refik Keskin, Sakarya Üniversitesi
    * Celal Cem Sarıoğlu, DEÜ, GSÜ, FGE
    * Ayberk Zeytin, ODTÜ

*24 Aralık 2010, Cuma*
/Lisans Öğrencileri Günü/

    * *Ayberk Zeytin:* Did Galois know that women belong to outer space?

      We will try to make a completely elementary introduction to Galois
      action on algebraic curves defined over number fields. We will
      state open problem as we proceed. The talk is aimed towards
      undergraduate students, thus only basic knowledge of complex
      analysis and algebra will be assumed.

    * *Mahir Bilen Can:*

    * *Kıvanç Ersoy:* Cebirsel gruplar ve Lie tipi basit gruplar

      In this talk we will give some basic notions of the theory of
      algebraic groups. An algebraic group is an algebraic variety,
      which is also a group where the group operations are also variety
      morphisms. We will give basic definitions related to the subject,
      briefly mention about the conjugacy classes of semisimple and
      unipotent elements. We will explain the relations between
      algebraic groups and simple groups of Lie type. We will present
      some important results on the subject, mainly related to the
      classification of finite simple groups.

*25 Aralık 2010, Cumartesi*

    * *Kıvanç Ersoy:* Çözülebilir olmayan, sonsuz Camina grupları

      Let G be a group. An element aG is called an anticentral element
      if aG=aG. A non-perfect group is called a Camina group if every
      element xGGis anticentral. Finite groups containing an anticentral
      element are solvable by a result of F. Ladisch \cite{ladisch}. In
      this work, we will prove some results on infinite locally finite
      Camina groups and we will give a method to construct infinite
      non-solvable Camina groups. Indeed, we will prove that for each
      connected algebraic group, there are countably many non-isomorphic
      infinite non-locally solvable Camina groups.

      This is an ongoing study under the supervision of Prof. Mercede
      Maj and Prof. Patrizia Longobardi of University of Salerno. This
      study is supported by TÜBİTAK BİDEB 2219 International Post
      Doctoral Research Fellowship. The speaker thanks TÜBİTAK for the
      support.

    * *Mahir Bilen Can:* Unipotent invariant (complete) quadrics

      The variety of complete quadrics, which is used by Schubert in his
      famous computation of the number of space quadrics tangent to 9
      quadrics in general position, is a particular compactification of
      the space of non-singular quadric hypersurfaces in n dimensional
      complex projective space.

      In this talk, towards a theory of Springer fibers for complete
      quadrics, I will describe our recent work on the unipotent
      invariant complete quadrics. These results involve interesting
      combinatorics, and in particular, give a new q-analog of Fibonacci
      numbers as the Poincare polynomial of a unipotent fixed subvariety
      of quadrics.

      This is joint work with Michael Joyce.

    * *Refik Keskin:* Fibonacci and Lucas congruences and their
      applications

      In this paper we obtain some new identities containing Fibonacci
      and Lucas numbers. These identities allow us to give some
      congruences concerning Fibonacci and Lucas numbers such as;
      L2mn+k−1m+1nLkmod Lm, F2mn+k−1m+1nFkmod Lm, L2mn+k−1mnLkmod Fmand
      F2mn+k−1mnFkmod Fm. By the achieved identities, divisibility
      properties of Fibonacci and Lucas numbers are given. Then it is
      proved that there is no Lucas number Lnsuch that Ln=L2ktLmx2for m1
      and k1. Moreover it is proved that Ln=LmLris impossible if m and
      rare positive integers greater than 1. Moreover, a conjecture
      related to the subject is given.

      *Keywords:* Fibonacci numbers; Lucas numbers; Cogruences.

      *References:*

          o D. M. Burton, /Elementary Number Theory/, McGraw -Hill Comp.
            Inc., 1998.
          o J. H. E. Cohn, /On Square Fibonacci Numbers/, J. Lond. Math.
            Soc., 39 (1964), 537-540.
          o J. H. E. Cohn, /Square Fibonacci Numbers, etc./, Fibonacci
            Quarterly, 2 (1964), 109-113.
          o M. Farrokhi D. G., /Some Remarks On The Equation/ Fn=kFm/In
            Fibonacci Numbers/, Journal of Integer Sequences, 10 (2007),
            1-9.
          o R. Keskin and B. Demirturk, /Some New Fibonacci and Lucas
            Identities by Matrix Methods,/International Journal of
            Mathematical Education in Science and Technology. (accepted
            for publication)
          o T. Koshy, /Fibonacci and Lucas numbers with applications/ ,
            John Wiley and Sons, Proc., New York-Toronto, 2001.
          o I. Niven, H. S. Zuckerman, and H. L. Montgomery, /An
            Introduction to the Theory of Numbers/, John Wiley & Sons,
            Inc., Canada, 1991.
          o N. Robbins, /Fibonacci numbers of the form/ px2/, where/ p
            /is prime/, Fibonacci Quarterly, 21 (1983), 266-271.
          o N. Robbins, /Fibonacci numbers of the form/ cx2/, where/
            1c1000, Fibonacci Quarterly 28 (1990), 306-315.
          o N. Robbins, /Lucas numbers of the form/ px2/, where/ p/is
            prime/, Inter. J. Math. Math. Sci. 14 (1991), 697-703.
          o S. Vajda, /Fibonacci and Lucas numbers and the golden
            section/, Ellis Horwood Limited Publ., England, 1989.
          o C. Zhou, /A general conclusion on Lucas numbers of the form/
            px2/where/ p/is prime/, Fibonacci Quarterly 37 (1999), 39-45.

    * *Ayberk Zeytin:* Combinatorics and Cohomology

      For the sake of understanding the absolute Galois group many
      sophisticated methods are/have been used. Among them combinatorial
      ones have proven themselves to be useful. In this talk, we will
      begin with combinatorial objects, triangulations/quadrangulations,
      and then realise them as classes in some cohomology group, which
      we will try to describe explicitly.

*26 Aralık 2010, Pazar*

    * *Sevgi Harman:* Radically perfect prime ideals in commutative rings

    * *Celal Cem Sarıoğlu:* Orbifold Riemann yüzeyleri ve jeodezik
      fonksiyonlar

*Konaklama:*
Cebir-Geometri Günlerine katılacak katılımcılardan isteyenler (İstanbul 
içi ya da dışı) TÜBİTAK - Feza Gürsey Enstitüsü'nde ücretsiz olarak 
konuk edilecektir. Düzenlemenin en sağlıklı şekilde yapılması için 
İstanbul içinden ya da dışından gelecek tüm katılımcıların başvuru 
formunu doldurması gereklidir.

*Konaklama tarihleri:* 23 - 26 Aralık 2010

*Kontenjan: 30 kişi*

*Program, Istanbul Matematik Gündemindedir:*
http://www.google.com/calendar/embed?src=jdf754c331751cbt6q9vc281es%40group.calendar.google.com&ctz=Europe/Istanbul 
<http://www.google.com/calendar/embed?src=jdf754c331751cbt6q9vc281es%40group.calendar.google.com&ctz=Europe/Istanbul> 

*Başvuru için:* http://www.gursey.gov.tr/apps/app-frm-gen.php?id=algeo1012

*Son başvuru tarihi:* 21 Aralık 2010

*Programda konuşma vermek için lütfen iletişime geçiniz. *

*Düzenleyiciler:*
Celal Cem Sarıoğlu, DEÜ
Kürşat Aker, FGE

*Web sayfası:* http://www.gursey.gov.tr/new/algeo1012/

*İletişim:* aker at gursey.gov.tr <mailto:aker at gursey.gov.tr>

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Cebir-Geometri Günleri

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