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 GOKOVA¨ GEOMETRY-TOPOLOGY CONFERENCE May 26 – May 30, 2014

Participants of the 21st G¨okova Geometry-Topology Conference

PREFACE

Once again this year, at G¨okova, 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 Y¨ucelen (which is located on the scenic shores of the G¨okova Bay) for supporting and hosting this conference.

March 2015 The Editors

CONTENTS

Brief introduction to tropical geometry ...... 1 E. BRUGALLE,´ 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 P2 ...... 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

21st GOKOVA¨ GEOMETRY-TOPOLOGY CONFERENCE May 26 – May 30, 2014

List of Participants

Abouzaid, Mohammed Columbia University, USA Akbulut, Selman Michigan State University, USA Akyol, Ay¸seg¨ul Abdullah G¨ul University, Turkey Altun¨oz, Tulin¨ Middle East Technical University, Turkey Arg¨uz, N. H¨ulya University of Hamburg, Germany Arıkan, Fırat Middle East Technical University, Turkey Arslan, Aykut Ko¸cUniversity,Turkey Aslan, Hatice Fırat University, Turkey Bazhov, Ivan Universit´edeGen`eve, Switzerland Bhupal, Mohan Middle East Technical University, Turkey Bircan, Karatu˘g Ozan Ko¸cUniversity,Turkey Brugall´e, Erwan Ecole´ polytechnique, CMLS-UMR, France Cengiz, Merve Ko¸cUniversity,Turkey Cengiz, Mustafa Bo˘gazi¸ci University, Turkey Chantraine, Baptiste Universit´e de Nantes, France Co¸skun, Izzet˙ University of Illinois at Chicago, USA Co¸skun¨uzer, Barı¸s Ko¸cUniversity,Turkey C¸alı¸skan, El¸cin Middle East Technical University, Turkey C¸ elik, M¨unevver MET U North Cyprus Campus, North Cyprus C¸ eliker, Aslıhan Ko¸cUniversity,Turkey C¸ ineli, Erman Bo˘gazi¸ci University, Turkey Degtyarev, Alexander Bilkent University, Turkey Demirhan, H. Arda Bo˘gazi¸ci University, Turkey Demir, U¨mmuhan¨ Bo˘gazi¸ci University, Turkey Erdal, Mehmet Akif Bilkent University, Turkey Finashin, Sergey Middle East Technical University, Turkey Ghiggini, Paolo Universit´e de Nantes, France G¨une¸s, C¸isem Bilkent University, Turkey G¨unt¨urk¨un, Hakan Gediz University, Turkey Ilbıra, Sabahattin Middle East Technical University, Turkey Ionel, Eleny Stanford University, USA Iri˙ ma˘gzı, Canberk Ko¸cUniversity,Turkey Itenberg, Ilia IMJ-PRG, Universit´e Pierre et Marie Curie, France Kalafat, Mustafa Tunceli University, Turkey Kalinin, Nikita Universit´edeGen`eve, Switzerland Karakurt, C¸a˘grı University of Texas at Austin, USA Kartal, Yusuf Barı¸s Middle East Technical University, Turkey Keating Ailsa MIT,USA Ki¸sisel, Ozg¨¨ ur Middle East Technical University, Turkey Ko¸cak, S¸ahin Anadolu University, Turkey K¨ose, Feride Ceren Middle East Technical University, Turkey L´opez de Medrano, Lucia Universitad Nacional Aut´onema de Mexico, Mexico Melvin, Paul Bryn Mawr College, USA Mikhalkin, Grigory Universit´edeGen`eve, Switzerland Okay, Cihan University of British Columbia, Canada Onder,¨ Turgut Middle East Technical University, Turkey Ozba˘¨ gcı, Burak Ko¸cUniversity,Turkey Ozkan,¨ Recep Bilkent University, Turkey Ozt¨¨ urk, Ferit Bo˘gazi¸ci University, Turkey Pekavcılar, Berna Hacettepe University, Turkey Petrunin, Anton Pennsylvania State University, USA Risler, Jean-Jacques IMJ-PRG, Universit´e Pierre et Marie Curie, France Rossi, Paolo IMB-Universit´e de Bourgogne, France Sa˘glam, K. Nur University of Minessota, USA Salepci, Nermin Universit´eLyonI,France Sarı, Ramazan Gaziosmanpa¸sa University, Turkey Sarıo˘glan, Samet Hacettepe University, Turkey Se¸cgin, Merve Middle East Technical University, Turkey Shaw, Kristin University of Toronto, Canada Shkolnikov, Mikhail Universit´edeGen`eve, Switzerland Siebert, Bernd Universit¨at Hamburg, Germany S¨ozer, K¨ur¸sat Middle East Technical University, Turkey S¸ahin, Mehmet A. Gebze, Turkey S¸ent¨urk, Berrin Bilkent University, Turkey S¸im¸sir, Muazzez Hitit University, Turkey Unal,¨ Ibrahi˙ m METU North Cyprus Campus, North Cyprus Unal,¨ Inan˙ Tunceli University, Turkey Unl¨¨ u, Hatice Middle East Technical University, Turkey Varolg¨une¸s, Umut MIT,USA Viro, Oleg Stony Brook University, USA Wand, Andy Universit´e de Nantes, France Wu, Zhongtao The Chinese University of Hong Kong, Hong Kong Yıldırım, Ust¨¨ un Michigan State University, USA Zabun, R. Arzu Middle East Technical University, Turkey Zvonkine, Dimitri IMJ-PRG, Universit´e Pierre et Marie Curie, France