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.

Asymptotically holomorphic families of symplectic submanifolds.
Geom. Funct. Anal. 7 (1997), 971995.
(Publisher web site)

Symplectic 4manifolds as branched coverings of
CP2.
Inventiones Math. 139 (2000), 551602.
(Publisher web site)

Branched coverings of
CP2
and invariants of symplectic 4manifolds.
(with L. Katzarkov)
Inventiones Math. 142 (2000), 631673.
(Publisher web site)

Symplectic maps to projective spaces and symplectic invariants.
Proceedings of the 7th Gökova GeometryTopology Conference (2000).
Turkish J. Math. 25 (2001), 142.
(arXiv: math.GT/0007130)
(Publisher web site)

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, 130.
(arXiv: math.SG/0010052)

Symplectic hypersurfaces in the complement of an isotropic submanifold.
(with D. Gayet and J.P. Mohsen)
Math. Ann. 321 (2001), 739754.
(Publisher web site)

A remark about Donaldson's construction of symplectic submanifolds.
J. Symplectic Geom. 1 (2002), 647658.
(arXiv: math.DG/0204286)
(Publisher web site)

Fiber sums of genus 2 Lefschetz fibrations.
Proceedings of the 9th Gökova GeometryTopology Conference (2002).
Turkish J. Math. 27 (2003), 110.
(arXiv: math.GT/0204285)
(Publisher web site)

Luttinger surgery along Lagrangian tori and nonisotopy for singular
symplectic plane curves.
(with S. K. Donaldson and L. Katzarkov)
Math. Ann. 326 (2003), 185203.
(arXiv: math.GT/0206005)
(Publisher web site)

Fundamental groups of complements of plane curves and symplectic
invariants.
(with S. K. Donaldson, L. Katzarkov, M. Yotov)
Topology 43 (2004), 12851318.
(arXiv: math.GT/0203183)
(Publisher web site)

Regular homotopy of Hurwitz curves.
(with V. S. Kulikov and V. V. Shevchishin)
Izv. Math. 68 (2004), 521542.
(arXiv: math.SG/0401172)
(Publisher web site)

A stable classification of Lefschetz fibrations.
Geom. Topol. 9 (2005), 203217.
(arXiv: math.GT/0412120)
(Publisher web site)

Singular Lefschetz pencils.
(with S. K. Donaldson and L. Katzarkov)
Geom. Topol. 9 (2005), 10431114.
(arXiv: math.DG/0410332)
(Publisher web site)

Some open questions about symplectic 4manifolds, singular plane
curves, and braid group factorizations.
Proc. 4th European Congress of Mathematics (Stockholm,
2004), A. Laptev Ed., European Math. Soc., 2005, 2340.
(arXiv: math.GT/0410119)
(Publisher web site)

Lagrangian submanifolds and Lefschetz pencils.
(with V. Muñoz and F. Presas)
J. Symplectic Geom. 3 (2005), 171219.
(arXiv: math.SG/0407126)
(Publisher web site)

Symplectic 4manifolds, singular plane curves, and isotopy problems.
Floer Homology, Gauge Theory,
and Low Dimensional Topology (Budapest, 2004), Amer. Math. Soc.,
Clay Math. Proceedings 5 (2006), 263276.
(arXiv: math.GT/0411233)

Mapping class group factorizations and symplectic 4manifolds: some
open problems.
Problems on Mapping Class Groups and Related Topics, B. Farb Ed.,
Amer. Math. Soc., Proc. Symp. Pure Math., 74 (2006), 123132.

Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent
sheaves.
(with L. Katzarkov and D. Orlov)
Inventiones Math. 166 (2006), 537582.
(arXiv: math.AG/0506166)
(Publisher web site)

The canonical pencils on Horikawa surfaces.
Geom. Topol. 10 (2006), 21732217.
(arXiv: math.GT/0605692)
(Publisher web site)

Mirror symmetry and Tduality in the complement of an anticanonical divisor
J. Gökova Geom. Topol. 1 (2007), 5191.
(arXiv: 0706.3207)
(Publisher web site)

Lefschetz pencils, branched covers and symplectic invariants.
(with I. Smith)
Symplectic 4manifolds and algebraic surfaces (Cetraro, 2003),
Springer, Lect. Notes in Math. 1938, Springer, 2008, 153.
(arXiv: math.SG/0401021)
(Publisher web site)

A degree doubling formula for braid monodromies and Lefschetz
pencils.
(with L. Katzarkov)
Pure Appl. Math. Q. 4 (2008), 237318.
(arXiv: math.SG/0605001)
(Publisher web site)

Mirror symmetry for weighted projective planes and their noncommutative
deformations.
(with L. Katzarkov and D. Orlov)
Ann. Math. 167 (2008), 867943.
(arXiv: math.AG/0404281)
(Publisher web site)

Special Lagrangian fibrations, mirror symmetry and CalabiYau double
covers.
Géométrie différentielle, physique
mathématique, mathématiques et société (I),
O. Hijazi Ed., Soc. Math. Fr., Astérisque 321 (2008),
99128.
(arXiv: 0803.2734)

Special Lagrangian fibrations, wallcrossing, and mirror symmetry.
Surveys in Differential Geometry, Vol. 13, Intl. Press, 2009, 147.
(arXiv: 0902.1595)

La conjecture de Weinstein en dimension 3 (d'après C. H. Taubes).
Séminaire Bourbaki, vol. 2008/09, exposé n^{o}
1002, Astérisque 332 (2010), 135159.

Fukaya categories of symmetric products and bordered HeegaardFloer
homology.
J. Gökova Geom. Topol. 4 (2010), 154.
(arXiv: 1001.4323)
(Publisher web site)

Fukaya categories and bordered HeegaardFloer homology.
Proc. International Congress of Mathematicians
(Hyderabad, 2010), Vol. II, Hindustan Book Agency, 2010, 917941.
(arXiv: 1003.2962)

Homological mirror symmetry for punctured spheres.
(with M. Abouzaid, A. Efimov, L. Katzarkov and D. Orlov)
J. Amer. Math. Soc. 26 (2013), 10511083.
(arXiv: 1103.4322)
(Publisher web site)

On KhovanovSeidel quiver algebras and bordered Floer homology.
(with E. Grigsby and S. Wehrli)
Selecta Math. 20 (2014), 155.
(arXiv: 1107.2841)
(Publisher web site)

A beginner's introduction to Fukaya categories.
Contact and Symplectic Topology, F. Bourgeois et al. Eds.,
Bolyai Soc. Math. Stud. 26, Springer, 2014, 85136.
(arXiv: 1301.7056)

Factorizations in SL(2,Z) and simple examples of inequivalent Stein
fillings.
J. Symplectic Geom. 13 (2015), 261277.
(arXiv: 1311.0847)
(Publisher web site)

Sutured Khovanov homology, Hochschild homology, and the
OzsváthSzabó spectral sequence.
(with E. Grigsby and S. Wehrli)
Trans. Amer. Math. Soc. 367 (2015), 71037131.
(arXiv: 1303.1986)
(Publisher web site)

Infinitely many monotone Lagrangian tori in R^{6}.
Inventiones Math. 201 (2015), 909924.
(arXiv: 1407.3725)
(Publisher web site)

Lagrangian fibrations on blowups of toric varieties and mirror symmetry
for hypersurfaces.
(with M. Abouzaid and L. Katzarkov)
Publ. Math. IHES 123 (2016), 199282.
(arXiv: 1205.0053)
(Publisher web site)

Speculations on homological mirror symmetry for hypersurfaces in
(C*)^{n}.
Surveys in Differential Geometry, Vol. 22, Intl. Press, 2018, 147.
(arXiv: 1705.06667)

Fukaya categories of surfaces, spherical objects, and mapping class groups.
(with I. Smith)
Forum Math. Sigma 9 (2021), e26, 150.
(arXiv: 2006.09689)
(Publisher web site)

Homological mirror symmetry for hypersurfaces in (C*)^{n}.
(with M. Abouzaid)
Geometry & Topology 28 (2024), 28252914.
(arXiv: 2111.06543)
(Publisher web site)

Lagrangian Floer theory for trivalent graphs and homological mirror symmetry for curves.
(with A. Efimov and L. Katzarkov)
Selecta Math. 30 (2024), art. no. 95, 58 pp.
(arXiv: 2107.01981)
(Publisher web site)
Preprints
Dissertations
Lecture notes and slides

Holomorphic discs of negative Maslov index and extended deformations in
mirror symmetry.
Slides of a talk given in the IMSA/Miami conference on Homological
Mirror Symmetry, January 2024.

Structural aspects of Fukaya categories of LG models.
Slides of a talk given in the IMSA/Miami conference "HMS and rationality" (online), January 2021.

Mirrors of curves and their Fukaya categories.
Slides of a talk given in the Montreal/IAS/Paris/Tel Aviv Symplectic Seminar (online), May 2020.

Mirrors of curves
and their Fukaya categories:
part 1,
part 2,
part 3
Notes of talks given at the Conference on Homological Mirror Symmetry,
University of Miami, January 2020.

Coisotropic branes and homological mirror symmetry tor tori.
Slides of a talk given at the Annual Meeting of the Simons Collaboration on HMS (New York, November 2019).

An invitation to homological mirror symmetry.
Slides of a talk given at the Inaugural Conference of IMSA (University of Miami, September 2019).

Two new constructions of monotone Lagrangian tori.
Slides of a talk given at the 9th CAST Workshop (Lyon, January 2015).

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
3manifolds with boundary.
Slides of my AMS invited address at the Joint Mathematics Meetings (New
Orleans, January 2011)

Fukaya categories and bordered HeegaardFloer 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, BuressurYvette, 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 4manifolds, 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 4manifolds.
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 ICMSEDGE 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 4manifolds.
Slides of a talk given at the Omega '99 conference (Lisbon, June 1999)

Invariants de SeibergWitten 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.