# Dusa McDuff

Professor Emerita of Mathematics

Email: dusa@math.columbia.edu

Now at Barnard College, Columbia University

### Recent preprints and papers

Some $6$ dimensional Hamiltonian $S^1$-manifolds, (July 08), revision of July 09 available in pdf . To be published by Journal of Topology.

(with Susan Tolman) Polytopes with mass linear functions, part I, July 08, available in pdf .

Symplectic embeddings of 4-dimensional ellipsoids, version of Nov08,, published in Journal of Topology (2009) vol 2,1-22; available in pdf .

Monodromy in Hamiltonian Floer theory, revised version Jan 2010, published in Commentarii Math. Helveticae, available in pdf .

Hamiltonian S^1 manifolds are uniruled, June 07 rev. May 08, published in Duke Math Journal, available in pdf .

The Symplectomorphism group of a Blow up, Sep 06, with small revisions July 07 available in pdf . To appear in special conference issue of Geometriae Dedicata, original publication will soon be available at www.springerlink.com.

Groupoids, Branched manifolds and Multisections, Sep 05 with final minor revisions in Dec 06, available in pdf with figures. Published in Journal of Symplectic Geometry vol 4, (2007) 259--315.

(with S. Tolman) Topological Properties of Hamiltonian circle actions, SG/0404338 revised version (Aug 05) available in pdf. Published in Internat. Math. Research Papers (2006)

Enlarging the Hamiltonian group, SG/0503268 available in pdf. Published in Journal of Symplectic Topology, vol 3 (2005), 481-530.

(with S. Tolman) On nearly semifree circle actions, SG/0503467 available in pdf.

### Recent survey articles

Symplectic Embeddings and Continued fractions: a survey, Notes for the Takagi lectures, Sapporo, Japan, June 2009, available in pdf ,

What is symplectic geometry?, March 2009, an elementary survey article available in pdf .

Loops in the Hamiltonian group: a survey, written for the AMS Summer conference in Snowbird, Utah, July 2007, available in pdf .

Floer theory and low dimensional topology, written for the AMS Current Events Session, Winter meeting Jan 2005. available in pdf . Pubished in Bulletin of AMS, 2006.

A survey of topological properties of groups of symplectomorphisms, SG/0404340, in {\it Topology, Geometry and Quantum Field Theory}, Proceedings of 2002 Symposium in honor of G.B. Segal, ed U.L. Tillmann, Cambridge Univ. Press (2004). available in pdf

Symplectomorphism groups and quantum cohomology, written on the occasion of I.M. Gel'fand's 90th birthday, June 2004. available in pdf . (last revised Sept 2006; published in "The Unity of Mathematics": in honor of the 90th birthday of I.M. Gelfand}, Birkhauser, Boston (2005)).

Lectures on groups of symplectomorphisms, SG/0201032 notes from courses given in Paris July 2001 and Srni Jan 2003 available in pdf . Published in {\it Rendiconti di Circolo di Mat, Palermo} (2004).

A Glimpse into Symplectic Geometry, in {\it Mathematics: Frontiers and Perspectives 2000}, AMS, Providence available in pdf

### Survey articles from the nineties

Symplectic structures -- a new approach to geometry. This is a very general introductory article published in the Notices of the AMS 1998.

Lectures on Symplectic Topology; a gentle introduction to J-holomorphic curves, written in 1994 and published in the IAS/Park City proceedings.

J-curves and the classification of rational and ruled symplectic 4-manifolds;, a more or less self-contained exposition, written with F. Lalonde in 1995.

Symplectic Topology and Capacities; a general talk given in Princeton 1997.

### Autobiographical Sketch

This sketch was written in 1991. Here is a current vita.

### Books

Here is the revised 1995 text of the book "J-holomorphic curves and Quantum Homology" (AMS Lecture Notes, 1994) that I wrote with Salamon. This book is the first version of "J-holomorphic curves and Symplectic Topology" (AMS 2004). It contains a few mistakes and many omissions which are detailed in this Commentary of October 2007.

(with D. Salamon) Erratum to "J-holomorphic curves and Symplectic Topology" (AMS 2004), last edited 21 April 2008, available in pdf

(with D. Salamon) Erratum to "Introduction to Symplectic Topology" (OUP 1998) available in pdf

### Selected recent papers

(with J. Kedra) Homotopy properties of Hamiltonian group actions, SG/0404539, published in "Geom. Topol.", 9 (2005), 121-162; revised version available in pdf.

(with F. Lalonde) Symplectic structures on Fiber Bundles, SG/0010275, {\it Topology} {\bf 42} (2003), 309--347. available in pdf This version has erratum added in Dec 04.

Geometric Variants of the Hofer norm, {\it Journal of Symplectic Geometry}, {\bf 1} (2002), 197--252. available in pdf. This version has minor revisions from Aug 06.

(with J. Slimowitz) Hofer--Zehnder capacity and length minimizing Hamiltonian paths, SG/0101085, {\it Geom. Topol.} {\bf 5} (2001), 799--830. available in pdf

Symplectomorphism groups and almost complex structures, SG/0010274, Enseignement Math {\bf 38} (2001), 1--30. available in pdf with minor corrections.

Quantum homology of fibrations over $S^2$, {\it Internat. Journ. Math} {\bf 11} (2000), 665--721 available in pdf

From symplectic deformation to isotopy, May 1996, in {\it Topics in Symplectic $4$-manifolds}, ed R Stern, International Press (1998), available in pdf

The Virtual Moduli Cycle, Amer. Math. Soc Transl. (2) vol 196,(1999) available in pdf

(with F. Lalonde and L. Polterovich) On the Flux conjectures, in CRM Proceedings, vol 15 (1998), Amer. Math. Soc., available in pdf .

(with F. Lalonde) Positive Paths in the Linear Symplectic Group, in {\it Arnold--Gelfand mathemtical Seminars: Geometry and Singularity theory} Birkhauser, (1997) 361-388. pdf