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Long Booklet INVITED TALKS Yves Aubry ....................................................................................................................... 1 Jennifer Balakrishnan ........................................................................................................ 1 Eva Bayer-Fluckiger ........................................................................................................ 1 Arzu Boysal ...................................................................................................................... 2 William D. Gillam ........................................................................................................... 2 Francesco de Giovanni ..................................................................................................... 2 Jonathan Jedwab .............................................................................................................. 3 Ali Ulaş Özgür Kişisel ..................................................................................................... 3 Michel Lavrauw ............................................................................................................... 4 Patrizia Longobardi .......................................................................................................... 5 Mercede Maj .................................................................................................................... 6 Gerriet Martens ................................................................................................................ 7 Christian Mauduit ............................................................................................................. 7 Ian Morrison ..................................................................................................................... 8 Christophe Ritzenthaler ................................................................................................... 8 Arne Winterhof ................................................................................................................ 8 WORKSHOP TALKS Hadjer Adimi ................................................................................................................ 10 Yıldırım Akbal ….......................................................................................................... 10 Melis Tekin Akçin ........................................................................................................ 11 Yusuf Alagöz ................................................................................................................ 12 Emine Albaş .................................................................................................................. 13 Nurdagül Anbar …........................................................................................................ 14 Ahmet Arıkan ............................................................................................................... 15 Aynur Arıkan ................................................................................................................ 15 Pınar Aydoğdu .............................................................................................................. 16 Mounia Bouchelaghem ................................................................................................. 17 Cafer Çalışkan .............................................................................................................. 18 Murat Cenk ................................................................................................................... 18 Khadra Dekkar .............................................................................................................. 19 Ismail Demir ................................................................................................................. 19 Fatih Demirkale ............................................................................................................ 20 Emre Kolotoğlu ............................................................................................................ 20 Altan Erdoğan ............................................................................................................... 21 Songül Esin ................................................................................................................... 21 Meriem Hamitouche ..................................................................................................... 22 Can Hatipğolu ............................................................................................................... 22 Annamaria Iezzi ............................................................................................................ 22 Leyla Işık ...................................................................................................................... 27 Ayten Koç ..................................................................................................................... 27 Nazar Şahin Öğüşlü ...................................................................................................... 28 Özkay Özkan ............................................................................................................... 28 Sibel Özkan .................................................................................................................. 29 Buket Özkaya ................................................................................................................ 30 Arzu Özkoç ................................................................................................................... 31 Özgür Deniz Polat ......................................................................................................... 32 Başak Ay Saylam .......................................................................................................... 32 Azra Souad .................................................................................................................... 33 Nil Şahin ....................................................................................................................... 33 Ming Ming Tan …......................................................................................................... 33 Müge Taşkın ................................................................................................................. 34 Vladimir Tolstykh ......................................................................................................... 35 Hatice Topçu ................................................................................................................. 36 Seher Tutdere ................................................................................................................ 37 İpek Tuvay …................................................................................................................ 37 Osmanbey Uzunkol ...................................................................................................... 38 Emine Şule Yazıcı ........................................................................................................ 38 POSTERS Sedat Akleylek, Zülfikar Saygı ..................................................................................... 39 Bilal Demir …............................................................................................................... 39 Uğur Odabaşı ................................................................................................................ 40 Ahmet Sınak, Murat Cenk ............................................................................................ 41 Zübeyir Türkoğlu ……….............................................................................................. 42 Invited Talks Algebraic geometry and Abelian varieties over finite fields Yves Aubry The first part of the talk will be devoted to an historical overview on the devel- opment of algebraic geometry. Starting from the exploration age with Descartes, we will explore the golden age of projective geometry with Segre, the birational geometry with Riemann, development and chaos with Kronecker, new structures with Hilbert and to finish by sheaves and schemes with Grothendieck. The second part of the talk will be concerned with abelian varieties over finite fields. After the description of the action of the Frobenius endomorphism on the Tate module, we will derive new bounds on the number of rational points. Universit´ede Toulon and Aix-Marseille Universit´e email: [email protected] Coleman integration and integral points on hyperelliptic curves Jennifer S. Balakrishnan We discuss explicit computations of p-adic line integrals (Coleman integrals) on hyperelliptic curves and some applications. In particular, we relate a formula for the component at p of the p-adic height pairing to a sum of iterated Coleman integrals. We use this to give a Chabauty-like method for computing p-adic approximations to integral points on such curves when the Mordell-Weil rank of the Jacobian equals the genus. This is joint work with Amnon Besser and Steffen M¨uller. University of Oxford email: [email protected] web: http://people.maths.ox.ac.uk/balakrishnan/ Euclidean Number Fields and Euclidean Minima Eva Bayer-Fluckiger If a and b are two integers, with b 6= 0, then there exist two integers q and r such that a = bq + r, and that jrj < jbj. This so-called Euclidean division property plays a fondamental role in the arithmetic of the usual integers.
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