Denis Auroux - Papers

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Articles

These articles are available in PDF format. The version posted here may differ from the final published version.

1. Asymptotically holomorphic families of symplectic submanifolds.
   Geom. Funct. Anal. 7 (1997), 971-995.   (Publisher web site)
2. Symplectic 4-manifolds as branched coverings of CP2.
   Inventiones Math. 139 (2000), 551-602.   (Publisher web site)
3. Branched coverings of CP2 and invariants of symplectic 4-manifolds.
   (with L. Katzarkov)
   Inventiones Math. 142 (2000), 631-673.   (Publisher web site)
4. Symplectic maps to projective spaces and symplectic invariants.
   Proceedings of the 7th Gökova Geometry-Topology Conference (2000).
   Turkish J. Math. 25 (2001), 1-42.   (arXiv: math.GT/0007130)   (Publisher web site)
5. Estimated transversality in symplectic geometry and projective maps.
   In "Symplectic Geometry and Mirror Symmetry", Proceedings of the 4th KIAS International Conference, Seoul (2000), World Scientific, Singapore, 2001, 1-30.   (arXiv: math.SG/0010052)
6. Symplectic hypersurfaces in the complement of an isotropic submanifold.
   (with D. Gayet and J.-P. Mohsen)
   Math. Ann. 321 (2001), 739-754.   (Publisher web site)
7. A remark about Donaldson's construction of symplectic submanifolds.
   J. Symplectic Geom. 1 (2002), 647-658.   (arXiv: math.DG/0204286)   (Publisher web site)
8. Fiber sums of genus 2 Lefschetz fibrations.
   Proceedings of the 9th Gökova Geometry-Topology Conference (2002).
   Turkish J. Math. 27 (2003), 1-10.   (arXiv: math.GT/0204285)   (Publisher web site)
9. Luttinger surgery along Lagrangian tori and non-isotopy for singular symplectic plane curves.
   (with S. K. Donaldson and L. Katzarkov)
   Math. Ann. 326 (2003), 185-203.   (arXiv: math.GT/0206005)   (Publisher web site)
10. Fundamental groups of complements of plane curves and symplectic invariants.
    (with S. K. Donaldson, L. Katzarkov, M. Yotov)
    Topology 43 (2004), 1285-1318.   (arXiv: math.GT/0203183)   (Publisher web site)
11. Regular homotopy of Hurwitz curves.
    (with V. S. Kulikov and V. V. Shevchishin)
    Izv. Math. 68 (2004), 521-542.   (arXiv: math.SG/0401172)   (Publisher web site)
12. A stable classification of Lefschetz fibrations.
    Geom. Topol. 9 (2005), 203-217.   (arXiv: math.GT/0412120)   (Publisher web site)
13. Singular Lefschetz pencils.
    (with S. K. Donaldson and L. Katzarkov)
    Geom. Topol. 9 (2005), 1043-1114.   (arXiv: math.DG/0410332)   (Publisher web site)
14. Some open questions about symplectic 4-manifolds, singular plane curves, and braid group factorizations.
    Proc. 4th European Congress of Mathematics (Stockholm, 2004), A. Laptev Ed., European Math. Soc., 2005, 23-40.   (arXiv: math.GT/0410119)   (Publisher web site)
15. Lagrangian submanifolds and Lefschetz pencils.
    (with V. Muñoz and F. Presas)
    J. Symplectic Geom. 3 (2005), 171-219.   (arXiv: math.SG/0407126)   (Publisher web site)
16. Symplectic 4-manifolds, singular plane curves, and isotopy problems.
    Floer Homology, Gauge Theory, and Low Dimensional Topology (Budapest, 2004), Amer. Math. Soc., Clay Math. Proceedings 5 (2006), 263-276.   (arXiv: math.GT/0411233)
17. Mapping class group factorizations and symplectic 4-manifolds: some open problems.
    Problems on Mapping Class Groups and Related Topics, B. Farb Ed., Amer. Math. Soc., Proc. Symp. Pure Math., 74 (2006), 123-132.
18. Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves.
    (with L. Katzarkov and D. Orlov)
    Inventiones Math. 166 (2006), 537-582.   (arXiv: math.AG/0506166)   (Publisher web site)
19. The canonical pencils on Horikawa surfaces.
    Geom. Topol. 10 (2006), 2173-2217.   (arXiv: math.GT/0605692)   (Publisher web site)
20. Mirror symmetry and T-duality in the complement of an anticanonical divisor
    J. Gökova Geom. Topol. 1 (2007), 51-91.   (arXiv: 0706.3207)   (Publisher web site)
21. Lefschetz pencils, branched covers and symplectic invariants.
    (with I. Smith)
    Symplectic 4-manifolds and algebraic surfaces (Cetraro, 2003), Springer, Lect. Notes in Math. 1938, Springer, 2008, 1-53.   (arXiv: math.SG/0401021)   (Publisher web site)
22. A degree doubling formula for braid monodromies and Lefschetz pencils.
    (with L. Katzarkov)
    Pure Appl. Math. Q. 4 (2008), 237-318.   (arXiv: math.SG/0605001)   (Publisher web site)
23. Mirror symmetry for weighted projective planes and their noncommutative deformations.
    (with L. Katzarkov and D. Orlov)
    Ann. Math. 167 (2008), 867-943.   (arXiv: math.AG/0404281)   (Publisher web site)
24. Special Lagrangian fibrations, mirror symmetry and Calabi-Yau double covers.
    Géométrie différentielle, physique mathématique, mathématiques et société (I), O. Hijazi Ed., Soc. Math. Fr., Astérisque 321 (2008), 99-128.   (arXiv: 0803.2734)
25. Special Lagrangian fibrations, wall-crossing, and mirror symmetry.
    Surveys in Differential Geometry, Vol. 13, H.D. Cao and S.T. Yau Eds., Intl. Press, 2009, 1-47.   (arXiv: 0902.1595)
26. La conjecture de Weinstein en dimension 3 (d'après C. H. Taubes).
    Séminaire Bourbaki, vol. 2008/09, exposé n^o 1002, Astérisque 332 (2010), 135-159.  
27. Fukaya categories of symmetric products and bordered Heegaard-Floer homology.
    J. Gökova Geom. Topol. 4 (2010), 1-54.   (arXiv: 1001.4323)   (Publisher web site)
28. Fukaya categories and bordered Heegaard-Floer homology.
    Proc. International Congress of Mathematicians (Hyderabad, 2010), Vol. II, Hindustan Book Agency, 2010, 917-941.   (arXiv: 1003.2962)
29. On Khovanov-Seidel quiver algebras and bordered Floer homology.
    (with E. Grigsby and S. Wehrli)
    Selecta Math., in press   (arXiv: 1107.2841)

Preprints

• Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces
  (with M. Abouzaid and L. Katzarkov)
  (arXiv: 1205.0053)
• Homological mirror symmetry for punctured spheres.
  (with M. Abouzaid, A. Efimov, L. Katzarkov and D. Orlov)
  (arXiv: 1103.4322)

Dissertations

• Techniques approximativement holomorphes et invariants de monodromie en topologie symplectique. (introduction in French)
  Approximately holomorphic techniques and monodromy invariants in symplectic topology.
  Habilitation thesis, Université Paris Sud, June 2003   (download the introduction only)
• Théorèmes de structure des variétés symplectiques compactes via des techniques presque complexes. (introduction in French)
  Structure theorems for compact symplectic manifolds via almost-complex techniques.
  PhD thesis, Ecole Polytechnique, January 1999 (advisors: J.P. Bourguignon and M. Gromov).
• Invariants de Seiberg-Witten et variétés symplectiques. (in French)
  Seiberg-Witten invariants and symplectic manifolds.
  Diplôme d'Etudes Approfondies, Université Paris Sud, July 1995 (advisor: J.P. Bourguignon).

Lecture notes and slides

• Mirror symmetry for open manifolds.
  Notes of a talk given at the Simons Center (Stony Brook, May 2011); discusses SYZ mirror symmetry for smoothings/resolutions of A_n surface singularities (and related spaces).
• The symplectic geometry of symmetric products and invariants of 3-manifolds with boundary.
  Slides of my AMS invited address at the Joint Mathematics Meetings (New Orleans, January 2011)
• Fukaya categories and bordered Heegaard-Floer homology.
  Slides of my talk at the ICM 2010 (Hyderabad, India, August 2010)
• Some tropical aspects of mirror symmetry: part 1, part 2, part 3
  Notes of talks given at the Introductory Workshop on Tropical Geometry, MSRI, August 2009
• Special Lagrangian fibrations and mirror symmetry: part 1, part 2, part 3
  Notes and slides of talks given at the Workshop on Homological Mirror Symmetry, Miami, January 2009
• Mirror symmetry in the complement of an anticanonical divisor.
  Slides of a talk given at the conference for Jean Pierre Bourguignon's 60th birthday (IHES, Bures-sur-Yvette, August 2007)
• Lefschetz pencils and the symplectic topology of complex surfaces.
  Slides of a talk given at the GESTA 2006 Workshop on Symplectic and Contact Topology (Madrid, August 2006)
• Homological mirror symmetry for blowups of CP2.
  Slides of a talk given at the Summer Institute in Algebraic Geometry (Seattle, July 2005)
• Mapping class group factorizations and fiber sums of Lefschetz fibrations.
  Slides of a talk given at the Cornell Topology Festival (May 2005) and the Workshop on Topology, Banff (August 2005)
• Symplectic 4-manifolds, plane curves, and isotopy problems.
  Slides of a talk given at the Clay Summer School in Budapest and at the 4th ECM in Stockholm (June 2004)
• Homological mirror symmetry for Fano surfaces.
  Slides of a colloquium talk given at Michigan State University (October 2003) and Princeton University (December 2003)
• Monodromy invariants in symplectic topology.
  Notes of lectures given at IPAM, UCLA, in March 2003   (arXiv: math.SG/0304113)
• Singular plane curves and symplectic 4-manifolds.
  Slides of a talk given at the Geometry Festival (New York, April 2002) and at the Differential Geometry satellite conference of ICM 2002 (Tianjin, August 2002)
• Techniques approximativement holomorphes et invariants de variétés symplectiques. (in French; English translation)
  Notes of invited lectures (Cours Peccot) given at Collège de France, Paris in January 2002; the English translation became a set of notes for lectures given at the ICMS-EDGE Summer School, Edinburgh, July 2002
• Estimated transversality in symplectic geometry and projective maps.
  Slides of a talk given at the KIAS Conference on Symplectic Geometry and Mirror Symmetry (Seoul, August 2000)
• Branched coverings of CP2 and invariants of symplectic 4-manifolds.
  Slides of a talk given at the Omega '99 conference (Lisbon, June 1999)
• Invariants de Seiberg-Witten en géométrie symplectique. (in French)
  Notes of lectures given in Avignon in March 1999

For a general audience

• Slides and notes of a talk (aimed at the general public) I gave on sphere packings and applications (in French) at Centre Georges Pompidou, Paris in September 2000.
• An expanded version, in English, of the same talk, given as part of the IAP Lecture Series at MIT in January 2004.