Proceedings of the Gökova Geometry-Topology Conference 2014 Editors Selman Akbulut Department of Mathematics, Michigan State University East Lansing, MI 48824, USA Denis Auroux Department of Mathematics, University of California Berkeley, CA 94720, USA Turgut Önder Department of Mathematics, Middle East Technical University 06800 Ankara, Turkey Gökova Geometry-Topology Conferences
Proceedings of the Gökova Geometry-Topology Conference 2014 editors: Selman Akbulut, Michigan State University Denis Auroux, University of California at Berkeley Turgut Önder, Middle East Technical University, Ankara, Turkey Copyright 2014, 2015 by Gökova Geometry-Topology Conferences Published in 2015 by International Press, Somerville, Massachusetts, U.S.A. under license from Gökova Geometry-Topology Conferences. All rights reserved. Individual readers of this publication, and non-profit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgement of the source is given. Republication, systematic copying, or mass reproduction of any material in this publication is permitted only under license from Gökova Geometry-Topology Conferences. ISBN 978-1-57146-307-4 Printed in the United States of America. 19 18 17 16 15 1 2 3 4 5 6 7 8 9
21st GÖKOVA GEOMETRY-TOPOLOGY CONFERENCE May 26 May 30, 2014 Participants of the 21 st Gökova Geometry-Topology Conference
PREFACE Once again this year, at Gökova, we had many interesting talks on subjects varying from algebraic geometry, contact and symplectic topology, moduli spaces, Floer homologies, Gromov-Witten invariants to 4-manifolds. We also had a very stimulating mini-course on tropical geometry, delivered by four experts of the field (E. Brugalle, I. Itenberg, G. Mikhalkin, and K. Shaw). We thank all the participants for making this conference a very informative enjoyable event. We thank TUBITAK and NSF for funding this conference, and thank IP for printing and distributing these proceedings. We also thank Selahi Durusoy for putting these proceedings together, and we finally thank Hotel Yücelen (which is located on the scenic shores of the Gökova Bay) for supporting and hosting this conference. March 2015 The Editors
CONTENTS Brief introduction to tropical geometry...1 E. BRUGALLÉ, I. ITENBERG, G. MIKHALKIN, and K. SHAW Floer homology and Lagrangian concordance...76 B. CHANTRAINE, G. DIMITROGLOU RIZELL, P. GHIGGINI, and R. GOLOVKO The birational geometry of the moduli spaces of sheaves on P 2...114 I. COSKUN and J. HUIZENGA Nijenhuis operator in contact homology and descendant recursion in symplectic field theory...156 P. ROSSI The space of paths in complex projective space with real boundary conditions...192 N. HINGSTON and A. OANCEA Surgery and tightness in contact 3-manifolds...234 A. WAND On minimal genus problem... 250 Z. WU Isotoping 2-spheres in 4-manifolds...264 S. AKBULUT
st 21 GÖKOVA GEOMETRY-TOPOLOGY CONFERENCE May 26 May 30, 2014 List of Participants Abouzaid, Mohammed Akbulut, Selman Akyol, Ayşegül Altunöz, Tülin Argüz, N. Hülya Arıkan, Fırat Arslan, Aykut Aslan, Hatice Bazhov, Ivan Bhupal, Mohan Bircan, Karatuğ Ozan Brugallé, Erwan Cengiz, Merve Cengiz, Mustafa Chantraine, Baptiste Coşkun, İzzet Coşkunüzer, Barış Çalışkan, Elçin Çelik, Münevver Çeliker, Aslıhan Çineli, Erman Degtyarev, Alexander Demirhan, H. Arda Demir, Ümmühan Erdal, Mehmet Akif Finashin, Sergey Ghiggini, Paolo Güneş, Çisem Güntürkün, Hakan Columbia University, USA Michigan State University, USA Abdullah Gül University, Turkey University of Hamburg, Germany Fırat University, Turkey Université degenève, Switzerland École polytechnique, CMLS-UMR, France Boğaziçi University, Turkey Université de Nantes, France University of Illinois at Chicago, USA METU North Cyprus Campus, North Cyprus Boğaziçi University, Turkey Bilkent University, Turkey Boğaziçi University, Turkey Boğaziçi University, Turkey Bilkent University, Turkey Université de Nantes, France Bilkent University, Turkey Gediz University, Turkey
Ilbıra, Sabahattin Ionel, Eleny İrimağzı, Canberk Itenberg, Ilia Kalafat, Mustafa Kalinin, Nikita Karakurt, Çağrı Kartal, Yusuf Barış Keating Ailsa Kişisel, Özgür Koçak, Şahin Köse, Feride Ceren López de Medrano, Lucia Melvin, Paul Mikhalkin, Grigory Okay, Cihan Önder, Turgut Özbağcı, Burak Özkan, Recep Öztürk, Ferit Pekavcılar, Berna Petrunin, Anton Risler, Jean-Jacques Rossi, Paolo Sağlam, K. Nur Salepci, Nermin Sarı, Ramazan Sarıoğlan, Samet Seçgin, Merve Shaw, Kristin Shkolnikov, Mikhail Siebert, Bernd Sözer, Kürşat Şahin, Mehmet A. Stanford University, USA IMJ-PRG, Université Pierre et Marie Curie, France Tunceli University, Turkey Université degenève, Switzerland University of Texas at Austin, USA MIT, USA Anadolu University, Turkey Universitad Nacional Autónema de Mexico, Mexico Bryn Mawr College, USA Université degenève, Switzerland University of British Columbia, Canada Bilkent University, Turkey Boğaziçi University, Turkey Hacettepe University, Turkey Pennsylvania State University, USA IMJ-PRG, Université Pierre et Marie Curie, France IMB-Université de Bourgogne, France University of Minessota, USA Université LyonI, France Gaziosmanpaşa University, Turkey Hacettepe University, Turkey University of Toronto, Canada Université degenève, Switzerland Universität Hamburg, Germany Gebze, Turkey
Şentürk, Berrin Şimşir, Muazzez Ünal, İbrahim Ünal, İnan Ünlü, Hatice Varolgüneş, Umut Viro, Oleg Wand, Andy Wu, Zhongtao Yıldırım, Üstün Zabun, R. Arzu Zvonkine, Dimitri Bilkent University, Turkey Hitit University, Turkey METU North Cyprus Campus, North Cyprus Tunceli University, Turkey MIT, USA Stony Brook University, USA Université de Nantes, France The Chinese University of Hong Kong, Hong Kong Michigan State University, USA IMJ-PRG, Université Pierre et Marie Curie, France