Publications

PUBLISHED AND ACCEPTED:

with P.Biran and J.Zhang - Triangulation, Persistence, and Fukaya categories, to appear in Memoirs of the European Mathematical Society, arXiv:2304.01785, 175 pages (pdf)

with P. Biran and J.Zhang - Persistence K-theory, Quantum Topology,  (2024), DOI 10.4171/QT/222, 82 pages (pdf)

with P. Biran - A Lagrangian Pictionary,  Kyoto Math. J.  (invited contribution for a volume in honour of K. Fukaya) 61 (2021), 399-493 (pdf)

with P. Biran and E. Shelukhin - Lagrangian shadows and triangulated categories, Astérisque, 426 (2021), 128 pages (pdf).

with E. Shelukhin - Lagrangian cobordism and metric invariants,  Journal of Differential Geometry, 112 (2019) 1-45 (pdf).

with P. Biran - Lagrangian cobordism in Lefschetz fibrations, Selecta Mathematica, 23 (2017) 2635- 2704 (pdf).

with F. Charette - Categorification of Seidel's representation,  Israel Journal of Math., 211 (2016), 67-104 (pdf).

Lagrangian cobordism: Rigidity and Flexibility Aspects, Proceedings of the Inaugural Mathematical Congress of the Americas, AMS Contemporary Math.  656 (2016), 41-63 (pdf ).

with P. Biran - Lagangian Cobordism and Fukaya Categories (an earlier version had the title  ``Lagrangian Cobordism II''),  GAFA,  24 (2014) 1731–1830  (recent revision pdf).

with Paul Biran, Lagrangian Cobordism I,  J. Amer. Math. Soc., 26 (2013), no. 2, 295-340 ( pdf).  

with Paul Biran, Lagrangian topology and enumerative geometry,  Geometry & Topology, 16 (2012), 963-1052  ( pdf).

with K. A. de Rezende, M.R. da Silveira, Spectral sequences in Conley's theory, Ergod. Th. & Dynam. Sys. (2010), 30, 1009-1054 (pdf file).

with Paul Biran, Rigidity and uniruling for Lagrangian manifolds,  Geometry and Topology 13 (2009) 2881-2989 (pdf file )

with P. Biran, A Lagrangian Quantum Homology,  New Perspectives and Challenges in Symplectic Field Theory, CRM Proceedings and Lecture Notes, 49 (2009), 1--44., CRM-AMS ( pdf file).

with J.-F. Barraud - Quantization of the Serre spectral sequence, Journal of Symplectic Geometry  5 (2007), 249-280 (abstract,  pdf  file).

with J.-F. Barraud - Lagrangian intersections and the Serre spectral sequence,   Annals of Mathematics, 166 (2007), 657-722  (abstract, pdf  file).

with F. Lalonde - Cluster Homology: an overwiev of the construction and results, ERA - AMS   12 (2006), 1-12     (abstract, pdf file).

with J.-F. Barraud - Homotopical dynamics in Symplectic Topology,  in Morse theoretical Methods in Non-Linear Analysis and Symplectic Topology, Springer (2006) 109-148  (abstract,  pdf  file).

New obstructions to the thickenig of CW complexes,  Proc. AMS  132 (2004), 2769-2781         ( abstract, pdf file ).

with A. Ranicki - Rigidity and Glueing for Morse and Novikov complexes,  Journal of the European Math. Soc. 5  (2003) , 343-394  (abstract, pdf  file).

Homotopical Dynamics IV: Hopf invariants and Hamiltonian flows,    Communications on Pure and Applied Math.55 (2002) 1033-1088  (abstract ,  dvi  file ).

Homotopical Dynamics II: Hopf invariants, smoothings and the Morse complex,    Ann. Scient.   Ec. Norm. Sup. 35 (2002) 549-573 (abstract,   dvi file).

Homotopical Dynamics III: real singularities and Hamiltonian flows, Duke Mathematical Journal 109 (2001) 183--204
 (abstract , dvi   file).

Homotopical Dynamics: Suspension and Duality, Erg. Th. and Dyn. Syst.  20 - 2 (2000) 379--391 (abstract and dvi file).

Homotopical dynamics of gradient flows, Homotopy and Geometry, Banach Center Publications, 45 (1998), 41-46 ( abstract and dvi file).

Spanier-Whitehead duality and critical points,  in Homotopy Theory via Algebraic Geometry and Group Representations, AMS Contemp. Math. 220 (1998) 47-63 (abstractanddvi file).

with Y.Felix and J.M.Lemaire - Rational Category and Cone-length of Poincaré Complexes, Topology 37 (1998) 743-748  ( abstract and dvi file).

Some properties of relative L.S.-category, Fields  Inst. Commun. 19, AMS (1998) 67-72  (abstract and dvifile).

Cone-decompositions and degenerate critical points, Proceedings of the London Math. Soc  77 (1998) 437-461 ( abstract and dvifile).

Lusternik-Schnirelmann categorical sections,Ann.Scient.Ec.Norm.Sup. 28 (1995) 689-704 (abstract and dvi file).

Strong L.S.-category equals cone-length, Topology 34 (1995) 377-381(abstract and dvi file).

There is Just One Rational Cone-length, Transactions of the A.M.S. 4 (1994) 835-848 (abstractanddvi file).

Cone-length and Lusternik-Schnirelmann category, Topology 33 (1994) 95-111 (abstract and  dvi file).

The Genus and the Fundamental Group of High Dimensional Manifolds , Stud.Cerc.Mat. 4(1989) (pdf)

Unele proprietati de separare ale hipersuprafetelor, Stud.Cerc.Mat. 4(1988). (pdf)

Weak Discontinuities and Discrete Approximations, An.Univ.Buch. 3(1988) (pdf)

Proprietati comune functiilor inchise si celor cu proprietatea lui Darboux, Stud.Cerc.Mat. 1(1987). (pdf)

BOOKS:

with G. Lupton, J.Oprea, D.Tanre - Lusternik Schnirelmann Category, AMS Surveys and Monographs Series, 2003

EDITOR:

with  G. Lupton, J.Oprea, D.Tanre (editors) - Lusternik-Schnirelmann Category and Related Topics, Proceedings of the 2001 AMS-IMS-SIAM joint summer Research Conference, Contemporary Math. 316, 2002.

with  P. Biran and F. Lalonde (editors) - Morse Tehoretical Methods in Non-Linear Analysis and Symplectic Topology,  Springer 2006.

PREPRINTS:

with G. Ambrosioni and P. Biran - Approximability for Lagrangian submanifolds, preprint 2026,  https://arxiv.org/abs/2601.12506v1 , 155 pages (pdf)

with F. Lalonde - Cluster Homology, preprint 2005 (abstract,  pdf).

OTHER

Videos and slides - Lagrangian topology for the impatient - Graduate course, (Fall of 2020) + two micro-conferences.

Videos and slides - Topologie (groupe fondamental, surfaces, revetements - cours de bac, 2022).

Slides - Complexity of Lagrangian submanifolds - PIMS Distinguished Lecture, Regina (April 2025)

Slides  - Persistence K-theory - CIRM C0-symplectic topology conference (July 2023).

Slides  - Metrics on spaces of Lagrangian submanifolds - LP60: Symplectic and dynamics in honour of Leonid Polterovich's 60st birthday (June 2023).

Video interview as incoming CRM director (June 2021).

Slides - Persistence and triangulation - IHP (June 2021).

Slides  - Fragmentation pseudo-metrics - First Symplectic Zoominar (27 march, 2020)

Report - Geometrizing the Fukaya Category via Lagrangian Cobordism and Immersions -  RIP program (together with Paul Biran) at Oberwolfach, May 2017.

Video - Cost of splitting Lagrangians - of a talk at the IAS/Princeton University symplectic seminar, September 2016

Slides of a talk on Immersed Cobordism, MIT, May 2016.

Slides - Lagrangian Cobordism and Fukaya Categories - PIMS Symposium on Geometry and Topology, June 2015.

Videos  of a couple of talks at the Simons Center for Mathematics and Physics, Moduli Spaces
workshop  in May-June 2014  (video 1, video 2).

Slides  - Aspects of Lagrangian Topology - Mathematical Congress of the Americas'', August 2013 (video - and an
interview at the same conference).

Slides  - Lagrangian cobordism - ``D(ietmar Salamon's) - Days'' (ETH), June 2013.

Abstract - Towards categorification of Lagrangian Topology -  Oberwolfach, July 2012.

Audio: Lagrangian cobordism (talk at the Fields Institute, Geometry and Physics Conference, April 2011).

Video: Enumerative invariants and Lagrangian cobordism (talk at MSRI, March 2010).

Abstract - Lagrangian submanifolds: their fundamental group and Lagrangian cobordism - Oberwolfach, July 2010.

Slides - Wide and Narrow Lagrangian Submanifolds -  MSRI workshop, August 2009.

Slides - Lagrangian submanifolds, from physics to number theory -  plenary talk at the AMS-Worcester sectional meeting, April 2009.

Abstract -  Rigidity of Lagrangian submanifolds -  Oberwolfach, September 2008 (photo of the conference).

Slides - Lagrangian Quantum Structures II: Geometric and Numerical Rigidity -  ETH, September 2007

Abstract - Towards quantization of the Morse complex -  Oberwolfach, July 2006.

Slides - Measuring Lagrangians - Lectures in Leiden, April 2006.

Slides - High dimensional Floer and Morse moduli spaces and clusters - Lectures at the Seminaire de Math. Sup., 2004.