Memorandon Ergo

Memorandon Ergo, October 29, 2015

Great Circle of Mysteries: Mathematics, the World, the Mind

Great Circle of Mysteries: Mathematics, the World, the Mind. November 15, 2015

Overlap Properties of Geometric Expanders

Overlap Properties of Geometric Expanders, Jacob Fox, Mikhael Gromov, Vincent Lafforgue, Assaf Naor and Janos Pach

Generalizations of the Kolmogorov-Barzdin embedding estimates

Generalizations of the Kolmogorov-Barzdin embedding estimates, Misha Gromov and Larry Guth

Metric Inequalities with Scalar Curvature

Metric Inequalities with Scalar Curvature, Misha Gromov 

A Dozen Problems, Questions and Conjectures about Positive Scalar Curvature

A Dozen Problems, Questions and Conjectures about Positive Scalar Curvature, Misha Gromov, September 19, 2017 

101 Questions, Problems and Conjectures around Scalar Curvature

101 Questions, Problems and Conjectures around Scalar Curvature. (Incomplete and United Version), October 1, 2017 uncategorizeduncategorized

Manifolds : Where do we come from ? What are we ? Where are we going ?

Manifolds : Where do we come from ? What are we ? Where are we going ? (2010), 1-68.

Singularities, expanders and topology of map. Part 2: From combinatorics to topology via algebraic isoperimetry

Singularities, expanders and topology of map. Part 2: From combinatorics to topology via algebraic isoperimetry. GAFA, Geom. func. anal.,20 (2010), 416-526.

Crystals, proteins, stability and isoperimetry

Crystals, proteins, stability and isoperimetry. (2010), 1-30.

Singularities, expanders and topology of maps. Part 1 : Homology versus volume in the spaces of cycles

Singularities, expanders and topology of maps. Part 1 : Homology versus volume in the spaces of cycles. GAFA, Geom. func. anal.,19 (2009) n 3, 743-841.

Cuts in Kähler Groups

Cuts in Kähler Groups, Thomas Delzant and Misha Gromov, Progress in Mathematics, Vol. 248, 31-55, 2005 Birkhäuser Verlag Basel/Switzerland

Courbure mésoscopique et théorie de la toute petite simplification

Courbure mésoscopique et théorie de la toute petite simplification, Thomas Delzant et Misha Gromov Journal of Topology, 1:4 pp 804-836 (2008)

A Few Recollections

A Few Recollections. (January 6, 2011)

Quotations and Ideas.

Quotations and Ideas. December 6, 2014 

In a Search for a Structure, Part 1: On Entropy

In a Search for a Structure, Part 1: On Entropy. July 6, 2012 

Ergostructures, Ergodic and the Universal Learning Problem: Chapters 1, 2

Ergostructures, Ergodic and the Universal Learning Problem: Chapters 1, 2.

Dirac and Plateau Billiards in Domains with Corners

Dirac and Plateau Billiards in Domains with Corners. April 23, 2013 

Number of Questions

Number of Questions. April 26, 2014

Math Currents in the Brain

Math Currents in the Brain. June 13, 2014 

Geometry, Topology and Spectra of Non-Linear Spaces of Maps

Geometry, Topology and Spectra of Non-Linear Spaces of Maps Wolfgang Pauli Lectures, May 25, 2009

Six Lectures on Probabiliy, Symmetry, Linearity

Six Lectures on Probabiliy, Symmetry, Linearity. October 2014, Jussieu. ( unedited)- November 6, 2014 

Geometric, Algebraic and Analytic Descendants of Nash Isometric Embedding Theorems

Geometric, Algebraic and Analytic Descendants of Nash Isometric Embedding Theorems, October 9, 2015

Mathematical slices of molecular biology

Mathematical slices of molecular biology, with Lisa Carbone. Numéro spécial La Gazette des Mathematiciens, 88:11-80, Société Mathématique de France (2001).

Functional labels and syntactic entropy on DNA strings and proteins

Functional labels and syntactic entropy on DNA strings and proteins, with Lisa Carbone, preprint IHES 2001

Pattern formation in Biology, Vision and Dynamics

Pattern formation in Biology, Vision and Dynamics, Editors with A. Carbone and P. Prusinkiewicz. Published by World Scientific Publishing Co. Pte. Ltd (2000)

On a geometrical hypothesis of Banach

On a geometrical hypothesis of Banach, Izv. Akad. Nauk SSSR 31 (1967), 1105-1114.

On the number of simplexes of subdivisions of finite complexes

On the number of simplexes of subdivisions of finite complexes, Matematicheskie Zametki 3 (1968), 511-522. Russian version

On simplexes inscribed in a hypersurface

On simplexes inscribed in a hypersurface, Matematicheskie Zametki 5 (1969), 81-89. Russian version

Isometrical immersions, hyperbolic geometry and Burago’s isoperimetric inequality

Isometrical immersions, hyperbolic geometry and Burago’s isoperimetric inequality, preprint SUNY (1977).

Monotonicity of the volume of intersection of balls

Monotonicity of the volume of intersection of balls, Lect. Notes in Math. Springer-Verlag 1267 (1987), 1-4.

Estimates of Bernstein width of Sobolev spaces

Estimates of Bernstein width of Sobolev spaces, (with J. Bourgain), Geom. Anal. Functional Anal., Lecture Notes in Mathematics 1376 (1989), 176-185.

Cell division and hyperbolic geometry

Cell division and hyperbolic geometry, prépublication IHÉS 1990.

Possible trends in mathematics in coming decades

Possible trends in mathematics in coming decades, Notices AMS 45 : 7 (1998), 846-847

Interview: Mickhael Gromov 1, 213, Development of Mathematics 1950-2000

Interview: Mickhael Gromov 1, 213, Development of Mathematics 1950-2000, edited by Jean-Paul pier, Boston, MA, Birkhäuser (2000). On google books

Interview with Mikhail Gromov Martin Raussen and Christian Skau

Interview with Mikhail Gromov Martin Raussen and Christian Skau, Notices of the AMS, 391-403 (2010)

Structures, Learning and Ergosystems Chapters 1-4, 6

Structures, Learning and Ergosystems Chapters 1-4, 6. Dec. 30, 2011

The spherical isoperimetric inequality in Banach spaces

The spherical isoperimetric inequality in Banach spaces, (with V. Milman) Compositio Math. 62 (1987), 263-282

Spectral geometry of semi-algebraic sets

Spectral geometry of semi-algebraic sets, in Ann. Inst. Fourier 42 (1992), 249-274.

Isoperimetry of waists and concentration of maps

Isoperimetry of waists and concentration of maps, GAFA, Geom. funct. anal.,13 (2003), 178-215. Preprint IHES 2002.

Holomorphic maps into elliptic spaces

Holomorphic maps into elliptic spaces, J. Amer. Math. Soc. 2 (1989), 851-897.

Embeddings of Stein manifolds

Embeddings of Stein manifolds, (with Y. Eliashberg) Ann. Math. 136 (1992), 123-135.

Holomorphic L2 functions on coverings of pseudo-convex coverings

Holomorphic L2 ­ functions on coverings of pseudo-convex coverings (with G. Henkin and M. Shubin), GAFA 8 (1998), 552-585.

Endomorphisms of symbolic algebraic varieties

Endomorphisms of symbolic algebraic varieties, J. Europ. Math. Soc. (1999), 109-197.

Dynamical Morse entropy, in: Modern dynamical systems and applications

Dynamical Morses entropy, in: Modern dynamical systems and applications, with Mélanie Bertelson, (2004) 27-44. Cambridge Univ. Press, Cambridge, 2004

Cauchy-Riemann equation in Lagrange intersection theory

Cauchy-Riemann equation in Lagrange intersection theory, Proc. Conf. on Periodic Orbits of Hamiltonian Systems Il Ciocco, Italie (1986), Rabinowitz ed.

Soft and hard symplectic geometry

Soft and hard symplectic geometry, Proc. Int. Congress Math. 1986 Videotape (NTSC; 60 mn).

Convex symplectic manifolds

Convex symplectic manifolds, (with Y. Eliashberg) Proc. Symp. Pure Math. 52 (1991), Part 2, 135-162.

Lagrangian Intersection theory : Finite dimensional approach

Lagrangian Intersection theory : Finite dimensional approach, (with Y. Eliashberg) Amer. Math. Soc. Transl. (2) 186 (1998), 27-118

Lagrangian intersections and the stable Morse theory

Lagrangian intersections and the stable Morse theory. (with Y. Eliashberg) Boll. Unione Mat. Ital., VII. Ser., B 11 Suppl. (1997), 289-326.

On the entropy of holomorphic maps

On the entropy of holomorphic maps, preprint SUNY (1977).

On the ergodicity of frame flows

On the ergodicity of frame flows, (with M. Brin) Inventiones Math. 60 (1980), 1-8

Rigid transformations groups

Rigid transformations groups, in Géométrie différentielle (Paris 1986) (D. Bernard, Y. Choquet-Bruhat ed.) Travaux en Cours, 33, Hermann, Paris (1988), 65-139.

Paul Levy’s isoperimetric inequality

Paul Levy’s isoperimetric inequality, preprint IHÉS (1979), reprinted in [105].

A topological application of the isoperimetric inequality

A topological application of the isoperimetric inequality, (with V. Milman) J. Amer.Math. 105 (1983), 843-854.

Isoperimetric inequalities in Riemannian manifolds

Isoperimetric inequalities in Riemannian manifolds Lect. Notes in Math. Springer-Verlag 1200 (1986), 114-130.

The Riemann-Roch theorem for elliptic operators and solvability of elliptic equations with additional conditions on compact subsets

The Riemann-Roch theorem for elliptic operators and solvability of elliptic equations with additional conditions on compact subsets, (with M. Shubin) Inventiones Math. 117 (1994), 165-180

The Riemann-Roch theorem for elliptic operators

The Riemann-Roch theorem for elliptic operators (with M. Shubin) I. M. Gelfand Seminar. Part 1: Papers of the Gelfand seminar in funct. anal. Moscow Univ., Russia, September 1993. Gelfand, S. ed. et al., translated from Adv. Sov. Math. 16 (1993), 211-241 Amer. Math. Soc., Providence.

Erratum to: ”Von Neumann spectra near zero”

Erratum to: ”Von Neumann spectra near zero” (with M. Shubin) Geom. Anal. Funct. Anal. 5 (1995), 729.

L2 holomorphic functions on pseudo-convex coverings

L2 holomorphic functions on pseudo-convex coverings. in Operator theory for complex and hypercomplex analysis. (with G. Henkin, M. Shubin) Ramirez de Arellano ed. Proc. conf., Mexico City, Mexico, December 12–17, 1994 Amer. Math. Soc. Contemp. Math. 212 (1998), 81-94

Hyperbolic manifolds, groups and actions

Hyperbolic manifolds, groups and actions, Ann. Math. Studies 97 (1981), 183-215, Princeton University Press, Princeton.

Groups of polynomial growth and expanding maps

Groups of polynomial growth and expanding maps, Publ. Math. IHÉS 53 (1981), 53-73

Infinite groups as geometric objects

Infinite groups as geometric objects, Proc. Int. Congress Math. Warsaw 1983 1 (1984), 385-392

Hyperbolic groups, Essays in Group Theory

Hyperbolic groups, Essays in Group Theory, S. Gersten ed., MSRI Publications 8 (1987), 75-265 Springer.

Random walk in random groups

Random walk in random groups, preprint IHES (2001). GAFA, Geom. funct. anal., Vol. 13 (2003) 73 146 1016-443X/03/010073-74

CAT(kappa)-space: construction and concentration

CAT(kappa)-space: construction and concentration (to Victor Abramovich Zalgaller), preprint IHES, January 2001.

Small cancellation, unfolded hyperbolicity, and transversal measures

Small cancellation, unfolded hyperbolicity, and transversal measures, to appear in a volume dedicated to André Haefliger

Pinching constants for hyperbolic manifolds

Pinching constants for hyperbolic manifolds, (with W.P.Thurston) Inventiones Math. 89 (1987), 1-12.

Non-arithmetic groups in Lobatchevski spaces

Non-arithmetic groups in Lobatchevski spaces, (with I. Piatetski-shapiro) Publ. Math. IHÉS 66 (1988), 93-103.

Hyperbolic 4-manifolds and conformally flat 3-manifolds

Hyperbolic 4-manifolds and conformally flat 3-manifolds, (with H.B. Lawson Jr., W.P. Thurston) Publ. Math. IHÉS 68 (1988), 27-45.

Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one

Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one, (with R. Schoen), Publ. Math. IHES 76 (1992), 165-246

Spin and scalar curvature in the presence of a fundamental group

Spin and scalar curvature in the presence of a fundamental group, (with H. B. Lawson Jr.) Ann. of Math. 111 (1980), 209-230.

The classification of simply connected manifolds of positive scalar curvature

The classification of simply connected manifolds of positive scalar curvature, (with H. B. Lawson Jr.) Ann. of Math. 111 (1980), 423-434.

Pseudo-holomorphic curves in symplectic manifolds

Pseudo-holomorphic curves in symplectic manifolds, Inventiones Math. 82 (1985), 307-347

Dimension, non-linear spectra and width

Dimension, non-linear spectra and width, Lect. Notes in Math. Springer-Verlag 1317 (1988), 132-185.

Conjecture de Novikov et fibrés presque plats

Conjecture de Novikov et fibrés presque plats, (with A. Connes and H. Moscovici), C.R. Acad. Sci. Paris 310 (1990), 273- 277

Foliated plateau problem, part I, part II

Foliated plateau problem, part I, part II, Geom. Anal. Functional Anal. 1(1991), 14-79 ; idem 1 (1991), 253-320.

Metric Invariants of Kähler manifolds

Metric Invariants of Kähler manifolds, Proc. Workshop on J. Differential Geom. and Topology, Alghero, Italy 20-26 June, 1992 Caddeo, Tricerri ed. World Sci. (1993), 90-117.

Geometric reflections on the Novikov conjecture

Geometric reflections on the Novikov conjecture, Lecture notes taken by J. Rosenberg, Oberwolfach (1993) à paraître dans Proc. Conference on the Novikov Conjecture

Asymptotic invariants of infinite groups. Geometric group theory. Volume 2

Asymptotic invariants of infinite groups. Geometric group theory. Volume 2 Proc. Symp. Sussex Univ., Brighton, July 14-19, 1991 Lond. Math. Soc. Lecture Notes 182 Niblo and Roller ed., Cambridge Univ. Press, Cambridge (1993), 1-295.

Group cohomology with Lipschitz control and higher signatures

Group cohomology with Lipschitz control and higher signatures (with A. Connes, H. Moscovici) Geom. Anal. Funct. Anal. 3 (1993), 1-78.

Positive curvature, macroscopic dimension, spectral gaps and higher signatures. in Functional analysis on the eve of the 21st century

Positive curvature, macroscopic dimension, spectral gaps and higher signatures. in Functional analysis on the eve of the 21st century, Gindikin, Simon (ed.) et al Volume II. In honor of the eightieth birthday of I. M. Gelfand. Proc. conf. Rutgers Univ., New Brunswick, NJ, USA, October 24-27, 1993. Prog. Math. 132 (1996), 1-213, Birkhäuser, Basel

Quantitative homotopy theory

Quantitative homotopy theory, Rossi, Hugo (ed.), Prospects in mathematics. Invited talk on the occasion of the 250th anniversary of Princeton University. Papers from the conference, Princeton, NJ, USA, March 17-21, 1996. Providence, NJ, USA, American Mathematical Society, 45-49 (1999).

Finite propagation speed, kernel estimates, and the geometry of complete Riemannian manifolds

Finite propagation speed, kernel estimates, and the geometry of complete Riemannian manifolds, (with J. Cheeger, M. Taylor) J. Differential Geom. 17 (1982), 15-53.

Positive scalar curvature and the Dirac operator on complete Riemannian manifolds

Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, (with H. B. Lawson Jr.) Publ. Math. IHÉS 58 (1983), 295-408.

Von Neumann spectra near zero

Von Neumann spectra near zero, (with M. Shubin) Geom. Anal. Functional Anal. 1 (1991), 375-404.

Near cohomology of Hilbert complexes

Near cohomology of Hilbert complexes, (with M. Shubin) preprint ETH 1991.