The mathematical work of Jean-Michel Bismut: a brief summary

From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), pp. xxv-xxxvii.

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The mathematical work of Jean-Michel Bismut: a brief summary, dans From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), pp. xxv-xxxvii. http://www.numdam.org/item/AST_2009__327__R25_0/

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[1] J.-M. Bismut, Intégrales convexes et probabilités, C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A915-A917. | MR | Zbl

[2] J.-M. Bismut, Quelques propriétés des multiapplications mesurables et des intégrales convexes, C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A983-A985. | MR | Zbl

[3] J.-M. Bismut, Conjugate convex functions in optimal stochastic control, J. Math. Anal. Appl. 44 (1973), 384-404. | DOI | MR | Zbl

[4] J.-M. Bismut, An example of interaction between information and control: the transparency of a game, IEEE Trans. Automatic Control AC-18 (1973), no. 5, 518-522. | DOI | MR | Zbl

[5] J.-M. Bismut, Intégrales convexes et probabilités, J. Math. Anal. Appl. 42 (1973), 639-673. | DOI | MR | Zbl

[6] J.-M. Bismut, An example of optimal stochastic control with constraints, SIAM J. Control 12 (1974), 401-418. | DOI | MR | Zbl

[7] J.-M. Bismut, Contrôle des processus de sauts, C. R. Acad. Sci. Paris Sér. A-B 281 (1975), no. 18, Aii, A767-A770. | MR | Zbl

[8] J.-M. Bismut, Growth and optimal intertemporal allocation of risks, J. Econom. Theory 10 (1975), no. 2, 239-257. | DOI | MR | Zbl

[9] J.-M. Bismut, Théorie du potentiel et contrôle des diffusions markoviennes, Control theory, Numerical Methods and Computer Systems Modelling (Internat. Sympos., IRIA LABORIA, Rocquencourt, 1974), Springer, Berlin, 1975, pp. 283-295. Lecture Notes in Econom. and Math. Systems, Vol. 107. | DOI | MR | Zbl

[10] J.-M. Bismut, Contrôle stochastique et arrêt optimal, C. R. Acad. Sci. Paris Sér. A-B 282 (1976), no. 3, Aii, A163-A165. | MR | Zbl

[11] J.-M. Bismut, Jeux différentiels stochastiques, C. R. Acad. Sci. Paris Sér. A-B 282 (1976), no. 6, Aii, A333-A335. | MR | Zbl

[12] J.-M. Bismut, Le problème de temps d'arrêt optimal, C. R. Acad. Sci. Paris Sér. A-B 283 (1976), no. 22, Aii, A989-A992. | MR

[13] J.-M. Bismut, Linear quadratic optimal stochastic control with random coefficients, SIAM J. Control Optimization 14 (1976), no. 3, 419-444. | DOI | MR | Zbl

[14] J.-M. Bismut, Sur un problème de Dynkin, C. R. Acad. Sci. Paris Sér. A-B 282 (1976), no. 11, Aii, A603-A604. | MR | Zbl

[15] J.-M. Bismut, Théorie Probabiliste du Contrôle des Diffusions, Mem. Amer. Math. Soc. 4 (1976), no. 167, xiii+130 pp. | MR | Zbl

[16] J.-M. Bismut and B. Skalli, Le problème général d'arrêt optimal, C. R. Acad. Sci. Paris, Sér. A-B 283 (1976), no. 6, Av, A385-A386. | MR | Zbl

[17] J.-M. Bismut, Contrôle stochastique, jeux et temps d'arrêt: applications de la théorie probabiliste du potentiel, Z. Wahrsch. Verw. Gebiete 39 (1977), no. 4, 315-338. | DOI | MR | Zbl

[18] J.-M. Bismut, Dualité convexe, temps d'arrêt optimal et contrôle stochastique, Z. Wahrsch. Verw. Gebiete 38 (1977), no. 3, 169-198. | DOI | MR | Zbl

[19] J.-M. Bismut, On optimal control of linear stochastic equations with a linear-quadratic criterion, SIAM J. Control Optimization 15 (1977), no. 1, 1-4. | DOI | MR | Zbl

[20] J.-M. Bismut, Probability theory methods in zero-sum stochastic games, SIAM J. Control Optimization 15 (1977), no. 4, 539-545. | DOI | MR | Zbl

[21] J.-M. Bismut, Sur un problème de Dynkin, Z. Wahrsch. Verw. Gebiete 39 (1977), no. 1, 31-53. | DOI | MR | Zbl

[22] J.-M. Bismut, Temps d'arrêt optimal et quasi-temps d'arrêt, C. R. Acad. Sci. Paris Sér. A-B 284 (1977), no. 23, A1519-A1521. | MR | Zbl

[23] J.-M. Bismut, Temps d'arrêt optimal et retournement du temps, C. R. Acad. Sci. Paris Sér. A-B 285 (1977), no. 2, A71-A72. | MR | Zbl

[24] J.-M. Bismut and B. Skalli, Temps d'arrêt optimal, théorie générale des processus et processus de Markov, Z. Wahrsch. Verw. Gebiete 39 (1977), no. 4, 301-313. | DOI | MR | Zbl

[25] J.-M. Bismut, Applications de la théorie du potentiel à des problèmes de contrôle, Séminaire de Théorie du Potentiel, No. 3 (Paris, 1976/1977), Lecture Notes in Math., vol. 681, Springer, Berlin, 1978, pp. 7-17. | DOI | MR | Zbl

[26] J.-M. Bismut, An approximation method in optimal stochastic control, SIAM J. Control Optimization 16 (1978), no. 1, 122-130. | DOI | MR | Zbl

[27] J.-M. Bismut, Control of jump processes and applications, Bull. Soc. Math. Prance 106 (1978), no. 1, 25-60. | EuDML | Numdam | MR | Zbl

[28] J.-M. Bismut, Contrôle des systèmes linéaires quadratiques: applications de l'intégrale stochastique, Séminaire de Probabilités, XII (Univ. Strasbourg, Strasbourg, 1976/1977), Lecture Notes in Math., vol. 649, Springer, Berlin, 1978, pp. 180-264. | DOI | EuDML | Numdam | MR | Zbl

[29] J.-M. Bismut, Duality methods in the control of densities, SIAM J. Control Optim. 16 (1978), no. 5, 771-777. | DOI | MR | Zbl

[30] J.-M. Bismut, An introductory approach to duality in optimal stochastic control, SIAM Rev. 20 (1978), no. 1, 62-78. | DOI | MR | Zbl

[31] J.-M. Bismut, Régularité et continuité des processus, Z. Wahrsch. Verw. Gebiete 44 (1978), no. 3, 261-268. | DOI | MR | Zbl

[32] J.-M. Bismut, Contrôle de processus alternants et applications, Z. Wahrsch. Verw. Gebiete 47 (1979), no. 3, 241-288. | DOI | MR | Zbl

[33] J.-M. Bismut, An introduction to duality in random mechanics, Stochastic Control Theory and Stochastic Differential Systems (Proc. Workshop, Deutsch. Forschungsgemeinsch., Univ. Bonn, Bad Honnef, 1979), Lecture Notes in Control and Information Sci., vol. 16, Springer, Berlin, 1979, pp. 42-60. | DOI | MR | Zbl

[34] J.-M. Bismut, Potential theory in optimal stopping and alternating processes, Stochastic Control Theory and Stochastic Differential Systems (Proc. Workshop, Deutsch. Forschungsgemeinsch., Univ. Bonn, Bad Honnef, 1979), Lecture Notes in Control and Information Sci., vol. 16, Springer, Berlin, 1979, pp. 285-293. | DOI | MR | Zbl

[35] J.-M. Bismut, Problèmes à frontière libre et arbres de mesures, Séminaire de Probabilités, XIII (Univ. Strasbourg, Strasbourg, 1977/78), Lecture Notes in Math., vol. 721, Springer, Berlin, 1979, pp. 495-520. | DOI | EuDML | Numdam | MR | Zbl

[36] J.-M. Bismut, Temps d'arrêt optimal, quasi-temps d'arrêt et retournement du temps, Ann. Probab. 7 (1979), no. 6, 933-964. | DOI | MR | Zbl

[37] J.-M. Bismut, Un problème de contrôle stochastique avec observation partielle, Z. Wahrsch. Verw. Gebiete 49 (1979), no. 1, 63-95. | DOI | MR | Zbl

[38] J.-M. Bismut, Diffusions hamiltoniennes, optimalité stochastique et équations de Hamilton-Jacobi, C. R. Acad. Sci. Paris Sér. A-B 290 (1980), no. 14, A669-A672. | MR | Zbl

[39] J.-M. Bismut, Duality methods in the control of semimartingales, Analysis and Optimisation of Stochastic Systems (Proc. Internat. Conf., Univ. Oxford, Oxford, 1978), Academic Press, London, 1980, pp. 49-72. | MR | Zbl

[40] J.-M. Bismut, Flots stochastiques et formule de Itö-Stratonovitch généralisée, C. R. Acad. Sci. Paris Sér. A-B 290 (1980), no. 10, A483-A486. | MR | Zbl

[41] J.-M. Bismut, Formulation géométrique du calcul de Itö, relèvement de connexions et calcul des variations, C. R. Acad. Sci. Paris Sér. A-B 290 (1980), no. 9, A427-A429. | MR | Zbl

[42] J.-M. Bismut, Intégrales stochastiques non monotones et calcul différentiel stochastique, C. R. Acad. Sci. Paris Sér. A-B 290 (1980), no. 13, A625-A628. | MR | Zbl

[43] J.-M. Bismut, Calcul des variations sur les processus de sauts, C. R. Acad. Sci. Paris Sér. I Math. 293 (1981), no. 11, 565-568. | MR | Zbl

[44] J.-M. Bismut, Convex inequalities in stochastic control, J. Funct. Anal. 42 (1981), no. 2, 226-270. | DOI | MR | Zbl

[45] J.-M. Bismut, A generalized formula of Itō and some other properties of stochastic flows, Z. Wahrsch. Verw. Gebiete 55 (1981), no. 3, 331-350. | DOI | MR | Zbl

[46] J.-M. Bismut, Martingales, the Malliavin calculus and Hörmander's theorem, Stochastic Integrals (Proc. Sympos., Univ. Durham, Durham, 1980), Lecture Notes in Math., vol. 851, Springer, Berlin, 1981, pp. 85-109. | DOI | MR | Zbl

[47] J.-M. Bismut, Martingales, the Malliavin calculus and hypoellipticity under general Hörmander's conditions, Z. Wahrsch. Verw. Gebiete 56 (1981), no. 4, 469-505. | DOI | MR | Zbl

[48] J.-M. Bismut, Mécanique Aléatoire, Lecture Notes in Math., vol. 866, Springer-Verlag, Berlin, 1981, xvi+563 pp. With an English summary. | MR | Zbl

[49] J.-M. Bismut and D. Michel, Diffusions conditionnelles. I. Hypoellipticité partielle, J. Funct. Anal. 44 (1981), no. 2, 174-211. | DOI | MR | Zbl

[50] J.-M. Bismut and D. Michel, Structure des diffusions conditionnelles et calcul des variations, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 15, 731-734. | MR | Zbl

[51] J.-M. Bismut, An introduction to the stochastic calculus of variations, Stochastic differential systems (Bad Honnef, 1982), Lecture Notes in Control and Inform. Sci. vol. 43, Springer, Berlin, 1982, pp. 33-72. | DOI | MR | Zbl

[52] J.-M. Bismut, Mécanique aléatoire, Tenth Saint Flour Probability Summer School-1980 (Saint Flour, 1980), Lecture Notes in Math., vol. 929, Springer, Berlin, 1982, pp. 1-100. | MR | Zbl

[53] J.-M. Bismut, Partially observed diffusions and their control, SIAM J. Control Optim. 20 (1982), no. 2, 302-309. | DOI | MR | Zbl

[54] J.-M. Bismut and D. Michel, Diffusions conditionnelles. II. Générateur conditionnel. Application au filtrage, J. Funct. Anal. 45 (1982), no. 2, 274-292. | MR | Zbl

[55] J.-M. Bismut, Calcul des variations stochastique et processus de sauts, Z. Wahrsch. Verw. Gebiete 63 (1983), no. 2, 147-235. | DOI | MR | Zbl

[56] J.-M. Bismut, Calcul des variations stochastiques et grandes déviations, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 23, 1009-1012. | MR | Zbl

[57] J.-M. Bismut, Le théorème d'Atiyah-Singer pour les opérateurs elliptiques classiques: une approche probabiliste, C. R. Acad. Sci. Paris Sér. I Math. 297 (1983), no. 8, 481-484. | MR | Zbl

[58] J.-M. Bismut and M. Yor, An inequality for processes which satisfy Kolmogorov's continuity criterion. Application to continuous martingales, J. Funct. Anal. 51 (1983), no. 2, 166-173. | DOI | MR | Zbl

[59] J.-M. Bismut, Addendum: "Control of alternating processes and applications" [Z. Wahrsch. Verw. Gebiete 47 (1979), no. 3, 241-288;], | DOI | MR | Zbl

J.-M. Bismut, Addendum: "Control of alternating processes and applications" Z. Wahrsch. Verw. Gebiete 66 (1984), no. 3, 485. | DOI | MR | Zbl

[60] J.-M. Bismut, The Atiyah-Singer theorems: a probabilistic approach. I. The index theorem, J. Funct. Anal. 57 (1984), no. 1, 56-99. | DOI | MR | Zbl

[61] J.-M. Bismut, The Atiyah-Singer theorems: a probabilistic approach. II. The Lefschetz fixed point formulas, J. Funct. Anal. 57 (1984), no. 3, 329-348. | DOI | MR | Zbl

[62] J.-M. Bismut, The calculus of boundary processes, Ann. Sci. Ecole Norm. Sup. (4) 17 (1984), no. 4, 507-622. | DOI | EuDML | Numdam | MR | Zbl

[63] J.-M. Bismut, Jump processes and boundary processes, Stochastic Analysis (Katata/Kyoto, 1982), North-Holland Math. Library vol. 32, North-Holland, Amsterdam, 1984, pp. 53-104. | MR | Zbl

[64] J.-M. Bismut, Large Deviations and the Malliavin Calculus, Progress in Mathematics, vol 45, Birkhäuser Boston Inc., Boston, MA, 1984, viii+216 pp. | MR | Zbl

[65] J.-M. Bismut, On the set of zeros of certain semimartingales, Proc. London Math. Soc. (3) 49 (1984), no. 1, 73-86. | DOI | MR | Zbl

[66] J.-M. Bismut, Formules de Lefschetz délocalisées, Bony-Sjôstrand-Meyer seminar, 1984-1985, École Polytech., Palaiseau, 1985, Exp. No. 7, 13 pp. | Numdam | MR | Zbl

[67] J.-M. Bismut, Index theorem and equivariant cohomology on the loop space, Comm. Math. Phys. 98 (1985), no. 2, 213-237. | DOI | MR | Zbl

[68] J.-M. Bismut, Inégalités de Morse dégénérées et complexe de Witten, C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 1, 23-25. | MR | Zbl

[69] J.-M. Bismut, The infinitesimal Lefschetz formulas: a heat equation proof, J. Funct. Anal. 62 (1985), no. 3, 435-457. | DOI | MR | Zbl

[70] J.-M. Bismut, Last exit decompositions and regularity at the boundary of transition probabilities, Z. Wahrsch. Verw. Gebiete 69 (1985), no. 1, 65-98. | DOI | MR | Zbl

[71] J.-M. Bismut, Le théorème de l'indice des familles: une démonstration par l'équation de la chaleur, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), no. 20, 691-693. | MR | Zbl

[72] J.-M. Bismut, Transformations différentiables du mouvement brownien, Astérisque (1985), no. 131, 61-87, Colloquium in Honor of Laurent Schwartz, Vol. 1 (Palaiseau, 1983). | Numdam | MR | Zbl

[73] J.-M. Bismut and D. S. Freed, Fibré déterminant et invariant êta, C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 14, 707-710. | MR | Zbl

[74] J.-M. Bismut, The Atiyah-Singer index theorem for families of Dirac operators: two heat equation proofs, Invent. Math. 83 (1986), no. 1, 91-151. | DOI | EuDML | MR | Zbl

[75] J.-M. Bismut, Localization formulas, superconnections, and the index theorem for families, Comm. Math. Phys. 103 (1986), no. 1, 127-166. | DOI | MR | Zbl

[76] J.-M. Bismut, Probability and geometry, Probability and Analysis (Varenna, 1985), Lecture Notes in Math., vol. 1206, Springer, Berlin, 1986, pp. 1-60. | DOI | MR | Zbl

[77] J.-M. Bismut, The Witten complex and the degenerate Morse inequalities, J. Differential Geom. 23 (1986), no. 3, 207-240. | DOI | MR | Zbl

[78] J.-M. Bismut and D. S. Freed, The analysis of elliptic families. I. Metrics and connections on determinant bundles, Comm. Math. Phys. 106 (1986), no. 1, 159-176. | MR | Zbl

[79] J.-M. Bismut and D. S. Freed, The analysis of elliptic families. II. Dirac operators, eta invariants, and the holonomy theorem, Comm. Math. Phys. 107 (1986), no. 1, 103-163. | DOI | MR | Zbl

[80] J.-M. Bismut, Demailly's asymptotic Morse inequalities: a heat equation proof, J. Funct. Anal. 72 (1987), no. 2, 263-278. | DOI | MR | Zbl

[81] J.-M. Bismut, Filtering equation, equivariant cohomology and the Chern character, VIIIth International Congress on Mathematical Physics (Marseille, 1986), World Sci. Publishing, Singapore, 1987, pp. 17-56. | MR

[82] J.-M. Bismut, Index theorem and the heat equation, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) (Providence, RI), Amer. Math. Soc., 1987, pp. 491-504. | MR | Zbl

[83] J.-M. Bismut and J. Cheeger, Invariants êta et indice des familles pour des variétés à bord, C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), no. 4, 127-130. | MR | Zbl

[84] J.-M. Bismut, H. Gillet, and C. Soulé, Torsion analytique et fibres déterminants holomorphes, C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), no. 3, 81-84. | MR | Zbl

[85] J.-M. Bismut, Formules de Lichnerowicz et théorème de l'indice, Géométrie différentielle (Paris, 1986), Travaux en Cours, vol. 33, Hermann, Paris, 1988, pp. 11-31. | MR | Zbl

[86] J.-M. Bismut, Formules de localisation et formules de Paul Lévy, Astérisque (1988), no. 157-158, 37-58, Colloque Paul Lévy sur les Processus Stochastiques (Palaiseau, 1987). | Numdam | MR | Zbl

[87] J.-M. Bismut, Localisation du caractère de Chern en géométrie complexe et superconnexions, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), no. 10, 523-526. | MR | Zbl

[88] J.-M. Bismut, Transgressed Chern forms for Dirac operators, J. Funct. Anal. 77 (1988), no. 1, 32-50. | DOI | MR | Zbl

[89] J.-M. Bismut and J.-B. Bost, Fibrés déterminants, métriques de Quillen et dégénérescence des courbes, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), no. 7, 317-320. | MR | Zbl

[90] J.-M. Bismut, H. Gillet, and C. Soulé, Analytic torsion and holomorphic determinant bundles. I. Bott-Chem forms and analytic torsion, Comm. Math. Phys. 115 (1988), no. 1, 49-78. | DOI | MR | Zbl

[91] J.-M. Bismut, H. Gillet, and C. Soulé, Analytic torsion and holomorphic determinant bundles. II. Direct images and Bott-Chern forms, Comm. Math. Phys. 115 (1988), no. 1, 79-126. | DOI | MR | Zbl

[92] J.-M. Bismut, H. Gillet, and C. Soulé, Analytic torsion and holomorphic determinant bundles. III. Quillen metrics on holomorphic determinants, Comm. Math. Phys. 115 (1988), no. 2, 301-351. | DOI | MR | Zbl

[93] J.-M. Bismut, H. Gillet, and C. Soulé, Classes caractéristiques secondaires et immersions en géométrie complexe, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), no. 11, 565-567. | MR | Zbl

[94] J.-M. Bismut and E. Vasserot, Comportement asymptotique de la torsion analytique associée aux puissances d'un fibré en droites positif, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), no. 14, 779-781. | MR | Zbl

[95] J.-M. Bismut, Complexe de Koszul, oscillateur harmonique et classe de Todd, C. R. Acad. Sci. Paris Sér. I Math. 309 (1989), no. 2, 111-114. | MR | Zbl

[96] J.-M. Bismut, Le théorème d'indice local pour des variétés non kählériennes, C. R. Acad. Sci. Paris Sér. I Math. 308 (1989), no. 5, 139-142. | MR | Zbl

[97] J.-M. Bismut, A local index theorem for non-Kahler manifolds, Math. Ann. 284 (1989), no. 4, 681-699. | DOI | EuDML | MR | Zbl

[98] J.-M. Bismut and J. Cheeger, $η$ -invariants and their adiabatic limits, J. Amer. Math. Soc. 2 (1989), no. 1, 33-70. | MR | Zbl

[99] J.-M. Bismut and G. Lebeau, Immersions complexes et métriques de Quillen, C. R. Acad. Sci. Paris Sér. I Math. 309 (1989), no. 7, 487-491. | MR | Zbl

[100] J.-M. Bismut and E. Vasserot, The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle, Comm. Math. Phys. 125 (1989), no. 2, 355-367. | DOI | MR | Zbl

[101] J.-M. Bismut, Equivariant Bott-Chern currents and the Ray-Singer analytic torsion, Math. Ann. 287 (1990), no. 3, 495-507. | DOI | EuDML | MR | Zbl

[102] J.-M. Bismut, Eta invariants and complex immersions, Bull. Soc. Math. France 118 (1990), no. 2, 211-227. | DOI | EuDML | Numdam | MR | Zbl

[103] J.-M. Bismut, Koszul complexes, harmonic oscillators, and the Todd class, J. Amer. Math. Soc. 3 (1990), no. 1, 159-256. With an appendix by the author and C. Soulé. | DOI | MR | Zbl

[104] J.-M. Bismut, Métriques de Quillen et plongements complexes, Séminaire sur les Equations aux Dérivées Partielles, 1989-1990, École Polytech., Palaiseau, 1990, Exp. No. XX, 21 pp. | EuDML | Numdam | MR | Zbl

[105] J.-M. Bismut, Superconnection currents and complex immersions, Invent. Math. 99 (1990), no. 1, 59-113. | DOI | EuDML | MR | Zbl

[106] J.-M. Bismut and J.-B. Bost, Fibrés déterminants, métriques de Quillen et dégénérescence des courbes, Acta Math. 165 (1990), no. 1-2, 1-103. | DOI | MR | Zbl

[107] J.-M. Bismut and J. Cheeger, Families index for manifolds with boundary, superconnections, and cones. I. Families of manifolds with boundary and Dirac operators, J. Funct. Anal. 89 (1990), no. 2, 313-363. | DOI | MR | Zbl

[108] J.-M. Bismut and J. Cheeger, Families index for manifolds with boundary, superconnections and cones. II. The Chern character, J. Funct. Anal. 90 (1990), no. 2, 306-354. | DOI | MR | Zbl

[109] J.-M. Bismut, H. Gillet, and C. Soulé, Bott-Chern currents and complex immersions, Duke Math. J. 60 (1990), no. 1, 255-284. | DOI | MR | Zbl

[110] J.-M. Bismut, H. Gillet, and C. Soulé, Complex immersions and Arakelov geometry, The Grothendieck Festschrift, Vol. I, Progress in Mathematics, vol. 86, Birkhauser Boston, Boston, MA, 1990, pp. 249-331. | MR | Zbl

[111] J.-M. Bismut and E. Vasserot, The asymptotics of the Ray-Singer analytic torsion of the symmetric powers of a positive vector bundle, Ann. Inst. Fourier (Grenoble) 40 (1990), no. 4, 835-848. | DOI | EuDML | Numdam | MR | Zbl

[112] J.-M. Bismut, Superconnexions, indice local des familles, déterminant de la cohomologie et métriques de Quillen, Mém. Soc. Math. France (N.S.) (1991), no. 46, 27-72, | DOI | EuDML | Numdam | MR | Zbl

J.-M. Bismut, Superconnexions, indice local des familles, déterminant de la cohomologie et métriques de Quillen, Analyse Globale et Physique Mathématique (Lyon, 1989). | Numdam | MR | Zbl

[113] J.-M. Bismut and J. Cheeger, Transgression de la classe d'Euler de $s l (2 n, 𝐙)$ -fibrés vectoriels, limites adiabatiques d'invariants êta, et valeurs spéciales de fonctions L, C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 5, 399-404. | MR | Zbl

[114] J.-M. Bismut and J. Cheeger, Remarks on the index theorem for families of Dirac operators on manifolds with boundary, Differential Geometry, Pitman Monogr. Surveys Pure Appl. Math., vol. 52, Longman Sci. Tech., Harlow, 1991, pp. 59-83. | MR | Zbl

[115] J.-M. Bismut and G. Lebeau, Complex immersions and Quillen metrics, Inst. Hautes Études Sci. Publ. Math. (1991), no. 74, ii+298 pp. | EuDML | Numdam | MR | Zbl

[116] J.-M. Bismut and W. Zhang, Métriques de Reidemeister et métriques de Ray-Singer sur le déterminant de la cohomologie d'un fibré plat: une extension d'un résultat de Cheeger et Müller, C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 11, 775-782. | MR | Zbl

[117] A. Berthomieu and J.-M. Bismut, Formes de torsion analytique et métriques de Quillen, C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), no. 10, 1071-1077. | MR | Zbl

[118] J.-M. Bismut, Bott-Chern currents, excess normal bundles and the Chern character, Geom. Funct. Anal. 2 (1992), no. 3, 285-340. | DOI | EuDML | MR

[119] J.-M. Bismut, Complex equivariant intersection, excess normal bundles and Bott-Chern currents, Comm. Math. Phys. 148 (1992), no. 1, 1-55. | DOI | MR | Zbl

[120] J.-M. Bismut, On certain infinite-dimensional aspects of Arakelov intersection theory, Comm. Math. Phys. 148 (1992), no. 2, 217-248. | DOI | MR | Zbl

[121] J.-M. Bismut and J. Cheeger, Transgressed Euler classes of $s l (2 n, 𝐙)$ vector bundles, adiabatic limits of eta invariants and special values of $L$ -functions, Ann. Sci. École Norm. Sup. (4) 25 (1992), no. 4, 335-391. | DOI | EuDML | Numdam | MR | Zbl

[122] J.-M. Bismut and K. Köhler, Higher analytic torsion forms for direct images and anomaly formulas, J. Algebraic Geom. 1 (1992), no. 4, 647-684. | MR | Zbl

[123] J.-M. Bismut and W. Zhang, An Extension of a Theorem by Cheeger and Müller, Astérisque (1992), no. 205, 235 pp, With an appendix by François Laudenbach. | Numdam | MR | Zbl

[124] J.-M. Bismut, From Quillen metrics to Reidemeister metrics: some aspects of the Ray-Singer analytic torsion, Topological Methods in Modern Mathematics (Stony Brook, NY, 1991), Publish or Perish, Houston, TX, 1993, pp. 273-324. | MR | Zbl

[125] J.-M. Bismut, Métriques de Quillen équivariantes et plongements complexes, C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), no. 8, 827-832. | MR | Zbl

[126] J.-M. Bismut, Torsion analytique équivariante d'une suite exacte courte de fibrés holomorphes, C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), no. 6, 579-584. | MR | Zbl

[127] J.-M. Bismut and J. Lott, Fibrés plats, images directes et formes de torsion analytique, C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), no. 5, 477-482. | MR | Zbl

[128] J.-M. Bismut and W. Zhang, Real embeddings and eta invariants, Math. Ann. 295 (1993), no. 4, 661-684. | DOI | EuDML | MR | Zbl

[129] A. Berthomieu and J.-M. Bismut, Quillen metrics and higher analytic torsion forms, J. Reine Angew. Math. 457 (1994), 85-184. | EuDML | MR | Zbl

[130] J.-M. Bismut, Equivariant short exact sequences of vector bundles and their analytic torsion forms, Compositio Math. 93 (1994), no. 3, 291-354. | EuDML | Numdam | MR | Zbl

[131] J.-M. Bismut, Métriques de Quillen et dégénérescence de variétés kählériennes, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), no. 12, 1287-1291. | MR | Zbl

[132] J.-M. Bismut, Plongements complexes équivariants et métriques de Quillen, Les grands systèmes des sciences et de la technologie, RMA Res. Notes Appl. Math., vol. 28, Masson, Paris, 1994, pp. 95-105. | MR

[133] J.-M. Bismut and W. Zhang, Milnor and Ray-Singer metrics on the equivariant determinant of a flat vector bundle, Geom. Funct. Anal. 4 (1994), no. 2, 136-212. | DOI | EuDML | MR | Zbl

[134] J.-M. Bismut, Equivariant immersions and Quillen metrics, J. Differential Geom. 41 (1995), no. 1, 53-157. | DOI | MR | Zbl

[135] J.-M. Bismut, Familles d'immersions et formes de torsion analytique en degré supérieur, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), no. 8, 969-974. | MR | Zbl

[136] J.-M. Bismut and J. Lott, Flat vector bundles, direct images and higher real analytic torsion, J. Amer. Math. Soc. 8 (1995), no. 2, 291-363. | DOI | MR | Zbl

[137] J.-M. Bismut, Holomorphic Families of Immersions and Higher analytic Torsion Forms, Astérisque (1997), no. 244, viii+275 pp. | Numdam | MR | Zbl

[138] J.-M. Bismut, Quillen metrics and singular fibres in arbitrary relative dimension, J. Algebraic Geom. 6 (1997), no. 1, 19-149. | MR | Zbl

[139] J.-M. Bismut and F. Labourie, Formules de Verlinde pour les groupes simplement connexes et géométrie symplectique, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), no. 9, 1009-1014. | DOI | MR | Zbl

[140] J.-M. Bismut and J. Lott, Torus bundles and the group cohomology of $G L (N, 𝐙)$ , J. Differential Geom. 47 (1997), no. 2, 196-236. | DOI | MR | Zbl

[141] J.-M. Bismut, Local index theory and higher analytic torsion, Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998), no. Extra Vol. I, 1998, pp. 143-162. | EuDML | MR | Zbl

[142] J.-M. Bismut, Local index theory, eta invariants and holomorphic torsion: a survey, Surveys in Differential Geometry, Vol. III (Cambridge, MA, 1996), Int. Press, Boston, MA, 1998, pp. 1-76. | MR | Zbl

[143] J.-M. Bismut and S. Goette, Torsions analytiques équivariantes holomorphes, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999), no. 3, 203-210. | DOI | MR | Zbl

[144] J.-M. Bismut and F. Labourie, Symplectic geometry and the Verlinde formulas, Surveys in Differential Geometry: Differential Geometry Inspired by String Theory, Surv. Differ. Geom., vol. 5, Int. Press, Boston, MA, 1999, pp. 97-311. | DOI | MR | Zbl

[145] J.-M. Bismut and S. Goette, Formes de torsion analytique en théorie de de Rham et fonctions de Morse, C. R. Acad. Sci. Paris Sér. I Math. 330 (2000), no. 6, 479-484. | DOI | MR | Zbl

[146] J.-M. Bismut and S. Goette, Holomorphic equivariant analytic torsions, Geom. Funct. Anal. 10 (2000), no. 6, 1289-1422. | DOI | MR | Zbl

[147] J.-M. Bismut and S. Goette, Rigidité des formes de torsion analytique en théorie de de Rham, C. R. Acad. Sci. Paris Sér. I Math. 330 (2000), no. 6, 471-477. | DOI | MR | Zbl

[148] J.-M. Bismut and S. Goette, Families Torsion and Morse Functions, Astérisque (2001), no. 275, x+293 pp. | Numdam | MR | Zbl

[149] J.-M. Bismut and S. Goette, Torsions analytiques équivariantes en théorie de de Rham, C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), no. 1, 33-39. | DOI | MR | Zbl

[150] J.-M. Bismut, Les formes de torsion holomorphes du complexe de de Rham, C. R. Math. Acad. Sci. Paris 335 (2002), no. 3, 243-247. | DOI | MR | Zbl

[151] J.-M. Bismut and X. Ma, Familles d'immersions holomorphes et formes de torsion analytique équivariantes, C. R. Math. Acad. Sci. Paris 334 (2002), no. 10, 893-897. | DOI | MR | Zbl

[152] J.-M. Bismut, Holomorphic and de Rham torsion, Compos. Math. 140 (2004), no. 5, 1302-1356. | DOI | MR | Zbl

[153] J.-M. Bismut, Le Laplacien hypoelliptique, Séminaire: Équations aux Dérivées Partielles. 2003-2004, Sémin. Équ. Dériv. Partielles, École Polytech., Palaiseau, 2004, Exp. No. XXII, 15 pp. | EuDML | Numdam | MR | Zbl

[154] J.-M. Bismut, Le Laplacien hypoelliptique sur le fibré cotangent, C. R. Math. Acad. Sci. Paris 338 (2004), no. 7, 555-559. | DOI | MR | Zbl

[155] J.-M. Bismut, Une déformation de la théorie de Hodge sur le fibré cotangent, C. R. Math. Acad. Sci. Paris 338 (2004), no. 6, 471-476. | DOI | MR | Zbl

[156] J.-M. Bismut, Une déformation en famille du complexe de de Rham-Hodge, C. R. Math. Acad. Sci. Paris 338 (2004), no. 8, 623-627. | DOI | MR | Zbl

[157] J.-M. Bismut and S. Goette, Equivariant de Rham torsions, Ann. of Math. (2) 159 (2004), no. 1, 53-216. | DOI | MR | Zbl

[158] J.-M. Bismut and X. Ma, Holomorphic immersions and equivariant torsion forms, J. Reine Angew. Math. 575 (2004), 189-235. | MR | Zbl

[159] J.-M. Bismut, Eta invariants, differential characters and flat vector bundles, Chinese Ann. Math. Ser. B 26 (2005), no. 1, 15-44. With an appendix by K. Corlette and H. Esnault. | DOI | MR | Zbl

[160] J.-M. Bismut, The hypoelliptic Laplacian on the cotangent bundle, J. Amer. Math. Soc. 18 (2005), no. 2, 379-476. | DOI | MR | Zbl

[161] J.-M. Bismut and G. Lebeau, Laplacien hypoelliptique et torsion analytique, C. R. Math. Acad. Sci. Paris 341 (2005), no. 2, 113-118. | DOI | MR | Zbl

[162] J.-M. Bismut, The hypoelliptic Laplacian and Chern-Gauss-Bonnet, Differential Geometry and Physics, Nankai Tracts in Math., vol. 10, World Sci. Publ., Hackensack, NJ, 2006, pp. 38-52. | MR | Zbl

[163] J.-M. Bismut, L'opérateur de Dirac hypoelliptique, C. R. Math. Acad. Sci. Paris 343 (2006), no. 10, 647-651. | DOI | MR | Zbl

[164] J.-M. Bismut, The hypoelliptic Dirac operator, Geometry and Dynamics of Groups and Spaces, Progress in Mathematics, vol. 265, Birkhäuser, Basel, 2008, pp. 113-246. | DOI | MR | Zbl

[165] J.-M. Bismut, The hypoelliptic Laplacian on a compact Lie group, J. Funct. Anal. 255 (2008), no. 9, 2190-2232. | DOI | MR | Zbl

[166] J.-M. Bismut, Loop spaces and the hypoelliptic Laplacian, Comm. Pure Appl. Math. 61 (2008), no. 4, 559-593. | DOI | MR | Zbl

[167] J.-M. Bismut, A survey of the hypoelliptic Laplacian, Astérisque 322 (2008), 39-69. Conference in honor of J.-P. Bourguignon. | Numdam | MR | Zbl

[168] J.-M. Bismut and G. Lebeau, The Hypoelliptic Laplacian and Ray-Singer Metrics, Annals of Mathematics Studies, vol. 167, Princeton University Press, Princeton, NJ, 2008, x+367 pp. | MR | Zbl

[169] J.-M. Bismut, Duistermaat-Heckman formulas and index theory, (2009). Conference in honor of Hans Duistermaat. | MR | Zbl

[170] J.-M. Bismut, Hypoelliptic Laplacian and orbital integrals, (2009). | MR | Zbl