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), p. xxv-xxxvii
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     title = {The mathematical work of Jean-Michel Bismut: a brief summary},
     booktitle = {From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut},
     editor = {Dai Xianzhe and L\'eandre R\'emi and Xiaonan Ma and Zhang Weiping},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {327},
     year = {2009},
     pages = {xxv-xxxvii},
     language = {en},
     url = {http://www.numdam.org/item/AST_2009__327__R25_0}
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 (ed.). The mathematical work of Jean-Michel Bismut: a brief summary, in 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/

[1] J.-M. Bismut, Intégrales convexes et probabilités, C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A915-A917. | MR 315442 | Zbl 0284.60009

[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 315443 | Zbl 0259.46036

[3] J.-M. Bismut, Conjugate convex functions in optimal stochastic control, J. Math. Anal. Appl. 44 (1973), 384-404. | Article | MR 329726 | Zbl 0276.93060

[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. | Article | MR 441372 | Zbl 0265.90068

[5] J.-M. Bismut, Intégrales convexes et probabilités, J. Math. Anal. Appl. 42 (1973), 639-673. | Article | MR 324734 | Zbl 0268.60003

[6] J.-M. Bismut, An example of optimal stochastic control with constraints, SIAM J. Control 12 (1974), 401-418. | Article | MR 368896 | Zbl 0253.93048

[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 396022 | Zbl 0317.93076

[8] J.-M. Bismut, Growth and optimal intertemporal allocation of risks, J. Econom. Theory 10 (1975), no. 2, 239-257. | Article | MR 439027 | Zbl 1011.91504

[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. | Article | MR 376223 | Zbl 0318.93055

[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 396023 | Zbl 0331.60031

[11] J.-M. Bismut, Jeux différentiels stochastiques, C. R. Acad. Sci. Paris Sér. A-B 282 (1976), no. 6, Aii, A333-A335. | MR 469441 | Zbl 0326.90086

[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 415759

[13] J.-M. Bismut, Linear quadratic optimal stochastic control with random coefficients, SIAM J. Control Optimization 14 (1976), no. 3, 419-444. | Article | MR 406663 | Zbl 0331.93086

[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 421690 | Zbl 0348.60109

[15] J.-M. Bismut, Théorie Probabiliste du Contrôle des Diffusions, Mem. Amer. Math. Soc. 4 (1976), no. 167, xiii+130 pp. | MR 453161 | Zbl 0323.93046

[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 426137 | Zbl 0337.60045

[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. | Article | MR 651551 | Zbl 0342.60037

[18] J.-M. Bismut, Dualité convexe, temps d'arrêt optimal et contrôle stochastique, Z. Wahrsch. Verw. Gebiete 38 (1977), no. 3, 169-198. | Article | MR 438465 | Zbl 0336.60070

[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. | Article | MR 444246 | Zbl 0353.93052

[20] J.-M. Bismut, Probability theory methods in zero-sum stochastic games, SIAM J. Control Optimization 15 (1977), no. 4, 539-545. | Article | MR 497225 | Zbl 0358.93031

[21] J.-M. Bismut, Sur un problème de Dynkin, Z. Wahrsch. Verw. Gebiete 39 (1977), no. 1, 31-53. | Article | MR 444218 | Zbl 0336.60069

[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 440689 | Zbl 0366.60063

[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 440690 | Zbl 0359.60044

[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. | Article | MR 651550 | Zbl 0342.60036

[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. | Article | MR 521775 | Zbl 0383.31005

[26] J.-M. Bismut, An approximation method in optimal stochastic control, SIAM J. Control Optimization 16 (1978), no. 1, 122-130. | Article | MR 490357 | Zbl 0411.93044

[27] J.-M. Bismut, Control of jump processes and applications, Bull. Soc. Math. Prance 106 (1978), no. 1, 25-60. | Numdam | MR 508948 | Zbl 0391.93036

[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. | Article | Numdam | MR 520007 | Zbl 0389.93052

[29] J.-M. Bismut, Duality methods in the control of densities, SIAM J. Control Optim. 16 (1978), no. 5, 771-777. | Article | MR 529436 | Zbl 0393.49013

[30] J.-M. Bismut, An introductory approach to duality in optimal stochastic control, SIAM Rev. 20 (1978), no. 1, 62-78. | Article | MR 469466 | Zbl 0378.93049

[31] J.-M. Bismut, Régularité et continuité des processus, Z. Wahrsch. Verw. Gebiete 44 (1978), no. 3, 261-268. | Article | MR 505956 | Zbl 0369.60041

[32] J.-M. Bismut, Contrôle de processus alternants et applications, Z. Wahrsch. Verw. Gebiete 47 (1979), no. 3, 241-288. | Article | MR 525309 | Zbl 0381.60033

[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. | Article | MR 547465 | Zbl 0414.49020

[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. | Article | MR 547478 | Zbl 0407.60044

[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. | Article | Numdam | MR 544820 | Zbl 0407.60045

[36] J.-M. Bismut, Temps d'arrêt optimal, quasi-temps d'arrêt et retournement du temps, Ann. Probab. 7 (1979), no. 6, 933-964. | Article | MR 548890 | Zbl 0432.60052

[37] J.-M. Bismut, Un problème de contrôle stochastique avec observation partielle, Z. Wahrsch. Verw. Gebiete 49 (1979), no. 1, 63-95. | Article | MR 539665 | Zbl 0393.60075

[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 576033 | Zbl 0432.70032

[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 592975 | Zbl 0476.49019

[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 571388 | Zbl 0428.60067

[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 568362 | Zbl 0419.60067

[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 572651 | Zbl 0424.60064

[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 647682 | Zbl 0484.60067

[44] J.-M. Bismut, Convex inequalities in stochastic control, J. Funct. Anal. 42 (1981), no. 2, 226-270. | Article | MR 624367 | Zbl 0474.93071

[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. | Article | MR 608026 | Zbl 0456.60063

[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. | Article | MR 620987 | Zbl 0457.60034

[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. | Article | MR 621660 | Zbl 0445.60049

[48] J.-M. Bismut, Mécanique Aléatoire, Lecture Notes in Math., vol. 866, Springer-Verlag, Berlin, 1981, xvi+563 pp. With an English summary. | MR 629977 | Zbl 0457.60002

[49] J.-M. Bismut and D. Michel, Diffusions conditionnelles. I. Hypoellipticité partielle, J. Funct. Anal. 44 (1981), no. 2, 174-211. | Article | MR 642916 | Zbl 0475.60061

[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 618898 | Zbl 0464.60061

[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. | Article | MR 814104 | Zbl 0517.58040

[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 665595 | Zbl 0528.60048

[53] J.-M. Bismut, Partially observed diffusions and their control, SIAM J. Control Optim. 20 (1982), no. 2, 302-309. | Article | MR 646955 | Zbl 0486.93076

[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 647076 | Zbl 0475.60062

[55] J.-M. Bismut, Calcul des variations stochastique et processus de sauts, Z. Wahrsch. Verw. Gebiete 63 (1983), no. 2, 147-235. | Article | MR 701527 | Zbl 0494.60082

[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 777597 | Zbl 0531.60071

[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 736249 | Zbl 0539.58034

[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. | Article | MR 701054 | Zbl 0524.60020

[59] J.-M. Bismut, Addendum: "Control of alternating processes and applications" [Z. Wahrsch. Verw. Gebiete 47 (1979), no. 3, 241-288;], | Article | MR 751583 | Zbl 0381.60033

J.-M. Bismut, Addendum: "Control of alternating processes and applications" Z. Wahrsch. Verw. Gebiete 66 (1984), no. 3, 485. | Article | MR 751583 | Zbl 0541.60038

[60] J.-M. Bismut, The Atiyah-Singer theorems: a probabilistic approach. I. The index theorem, J. Funct. Anal. 57 (1984), no. 1, 56-99. | Article | MR 744920 | Zbl 0538.58033

[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. | Article | MR 756173 | Zbl 0556.58027

[62] J.-M. Bismut, The calculus of boundary processes, Ann. Sci. Ecole Norm. Sup. (4) 17 (1984), no. 4, 507-622. | Article | Numdam | MR 776287 | Zbl 0561.60081

[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 780753 | Zbl 0566.60057

[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 755001 | Zbl 0537.35003

[65] J.-M. Bismut, On the set of zeros of certain semimartingales, Proc. London Math. Soc. (3) 49 (1984), no. 1, 73-86. | Article | MR 743371 | Zbl 0543.60047

[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 819773 | Zbl 0589.58026

[67] J.-M. Bismut, Index theorem and equivariant cohomology on the loop space, Comm. Math. Phys. 98 (1985), no. 2, 213-237. | Article | MR 786574 | Zbl 0591.58027

[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 797809 | Zbl 0608.57023

[69] J.-M. Bismut, The infinitesimal Lefschetz formulas: a heat equation proof, J. Funct. Anal. 62 (1985), no. 3, 435-457. | Article | MR 794778 | Zbl 0572.58021

[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. | Article | MR 775853 | Zbl 0551.60077

[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 799464 | Zbl 0589.58025

[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 816739 | Zbl 0572.60074

[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 818550 | Zbl 0618.58034

[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. | Article | MR 813584 | Zbl 0592.58047

[75] J.-M. Bismut, Localization formulas, superconnections, and the index theorem for families, Comm. Math. Phys. 103 (1986), no. 1, 127-166. | Article | MR 826861 | Zbl 0602.58042

[76] J.-M. Bismut, Probability and geometry, Probability and Analysis (Varenna, 1985), Lecture Notes in Math., vol. 1206, Springer, Berlin, 1986, pp. 1-60. | Article | MR 864711 | Zbl 0626.58022

[77] J.-M. Bismut, The Witten complex and the degenerate Morse inequalities, J. Differential Geom. 23 (1986), no. 3, 207-240. | Article | MR 852155 | Zbl 0608.58038

[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 853982 | Zbl 0657.58037

[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. | Article | MR 861886 | Zbl 0657.58038

[80] J.-M. Bismut, Demailly's asymptotic Morse inequalities: a heat equation proof, J. Funct. Anal. 72 (1987), no. 2, 263-278. | Article | MR 886814 | Zbl 0649.58030

[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 915561

[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 934249 | Zbl 0693.58023

[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 901625 | Zbl 0645.58036

[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 901140 | Zbl 0617.32042

[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 955849 | Zbl 0648.58033

[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 976212 | Zbl 0677.58040

[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 966255 | Zbl 0652.32020

[88] J.-M. Bismut, Transgressed Chern forms for Dirac operators, J. Funct. Anal. 77 (1988), no. 1, 32-50. | Article | MR 930389 | Zbl 0646.46067

[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 958789 | Zbl 0652.32019

[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. | Article | MR 929146 | Zbl 0651.32017

[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. | Article | MR 929147 | Zbl 0651.32017

[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. | Article | MR 931666 | Zbl 0651.32017

[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 967362 | Zbl 0655.57012

[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 972080 | Zbl 0658.32025

[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 1004951 | Zbl 0673.58043

[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 983667 | Zbl 0661.53050

[97] J.-M. Bismut, A local index theorem for non-Kahler manifolds, Math. Ann. 284 (1989), no. 4, 681-699. | Article | MR 1006380 | Zbl 0666.58042

[98] J.-M. Bismut and J. Cheeger, η-invariants and their adiabatic limits, J. Amer. Math. Soc. 2 (1989), no. 1, 33-70. | MR 966608 | Zbl 0671.58037

[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 1055464 | Zbl 0681.53034

[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. | Article | MR 1016875 | Zbl 0687.32023

[101] J.-M. Bismut, Equivariant Bott-Chern currents and the Ray-Singer analytic torsion, Math. Ann. 287 (1990), no. 3, 495-507. | Article | MR 1060688 | Zbl 0682.58045

[102] J.-M. Bismut, Eta invariants and complex immersions, Bull. Soc. Math. France 118 (1990), no. 2, 211-227. | Article | Numdam | MR 1087379 | Zbl 0721.58057

[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. | Article | MR 1017783 | Zbl 0702.58071

[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. | Numdam | MR 1073195 | Zbl 0706.53037

[105] J.-M. Bismut, Superconnection currents and complex immersions, Invent. Math. 99 (1990), no. 1, 59-113. | Article | MR 1029391 | Zbl 0696.58006

[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. | Article | MR 1064578 | Zbl 0709.32019

[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. | Article | MR 1042214 | Zbl 0696.53021

[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. | Article | MR 1052337 | Zbl 0711.53023

[109] J.-M. Bismut, H. Gillet, and C. Soulé, Bott-Chern currents and complex immersions, Duke Math. J. 60 (1990), no. 1, 255-284. | Article | MR 1047123 | Zbl 0697.58005

[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 1086887 | Zbl 0744.14015

[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. | Article | Numdam | MR 1096593 | Zbl 0711.32015

[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, | Article | Numdam | MR 1125836 | Zbl 0755.58009

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 1125836 | Zbl 0755.58009

[113] J.-M. Bismut and J. Cheeger, Transgression de la classe d'Euler de sl(2n,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 1096620 | Zbl 0719.58039

[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 1173033 | Zbl 0727.58045

[115] J.-M. Bismut and G. Lebeau, Complex immersions and Quillen metrics, Inst. Hautes Études Sci. Publ. Math. (1991), no. 74, ii+298 pp. | Numdam | MR 1188532 | Zbl 0784.32010

[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 1139837 | Zbl 0743.57014

[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 1191492 | Zbl 0774.32018

[118] J.-M. Bismut, Bott-Chern currents, excess normal bundles and the Chern character, Geom. Funct. Anal. 2 (1992), no. 3, 285-340. | Article | MR 1177315

[119] J.-M. Bismut, Complex equivariant intersection, excess normal bundles and Bott-Chern currents, Comm. Math. Phys. 148 (1992), no. 1, 1-55. | Article | MR 1178134 | Zbl 0759.53040

[120] J.-M. Bismut, On certain infinite-dimensional aspects of Arakelov intersection theory, Comm. Math. Phys. 148 (1992), no. 2, 217-248. | Article | MR 1178144 | Zbl 0763.53033

[121] J.-M. Bismut and J. Cheeger, Transgressed Euler classes of sl(2n,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. | Article | Numdam | MR 1186908 | Zbl 0768.58048

[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 1174905 | Zbl 0784.32023

[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 1185803 | Zbl 0781.58039

[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 1215969 | Zbl 0799.58076

[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 1218270 | Zbl 0773.53026

[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 1212208 | Zbl 0784.32022

[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 1209270 | Zbl 0780.57023

[128] J.-M. Bismut and W. Zhang, Real embeddings and eta invariants, Math. Ann. 295 (1993), no. 4, 661-684. | Article | MR 1214954 | Zbl 0795.57010

[129] A. Berthomieu and J.-M. Bismut, Quillen metrics and higher analytic torsion forms, J. Reine Angew. Math. 457 (1994), 85-184. | MR 1305280 | Zbl 0804.32017

[130] J.-M. Bismut, Equivariant short exact sequences of vector bundles and their analytic torsion forms, Compositio Math. 93 (1994), no. 3, 291-354. | Numdam | MR 1300765 | Zbl 0817.32014

[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 1310673 | Zbl 0830.32007

[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 1282906

[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. | Article | MR 1262703 | Zbl 0830.58030

[134] J.-M. Bismut, Equivariant immersions and Quillen metrics, J. Differential Geom. 41 (1995), no. 1, 53-157. | Article | MR 1316553 | Zbl 0826.32024

[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 1328720 | Zbl 0844.32010

[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. | Article | MR 1303026 | Zbl 0837.58028

[137] J.-M. Bismut, Holomorphic Families of Immersions and Higher analytic Torsion Forms, Astérisque (1997), no. 244, viii+275 pp. | Numdam | MR 1623496 | Zbl 0899.32013

[138] J.-M. Bismut, Quillen metrics and singular fibres in arbitrary relative dimension, J. Algebraic Geom. 6 (1997), no. 1, 19-149. | MR 1486991 | Zbl 0871.32003

[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. | Article | MR 1485620 | Zbl 0889.14013

[140] J.-M. Bismut and J. Lott, Torus bundles and the group cohomology of GL(N,𝐙), J. Differential Geom. 47 (1997), no. 2, 196-236. | Article | MR 1601604 | Zbl 0902.57028

[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. | MR 1648029 | Zbl 0982.58016

[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 1677887 | Zbl 0967.58014

[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. | Article | MR 1711061 | Zbl 0952.53034

[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. | Article | MR 1772272 | Zbl 0997.53066

[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. | Article | MR 1756962 | Zbl 0955.58026

[146] J.-M. Bismut and S. Goette, Holomorphic equivariant analytic torsions, Geom. Funct. Anal. 10 (2000), no. 6, 1289-1422. | Article | MR 1810746 | Zbl 0974.58033

[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. | Article | MR 1756961 | Zbl 0955.58027

[148] J.-M. Bismut and S. Goette, Families Torsion and Morse Functions, Astérisque (2001), no. 275, x+293 pp. | Numdam | MR 1867006 | Zbl 1071.58025

[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. | Article | MR 1805624 | Zbl 0982.58022

[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. | Article | MR 1933666 | Zbl 1019.32016

[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. | Article | MR 1909935 | Zbl 1010.32015

[152] J.-M. Bismut, Holomorphic and de Rham torsion, Compos. Math. 140 (2004), no. 5, 1302-1356. | Article | MR 2081158 | Zbl 1091.58020

[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. | Numdam | MR 2117053 | Zbl 1292.35097

[154] J.-M. Bismut, Le Laplacien hypoelliptique sur le fibré cotangent, C. R. Math. Acad. Sci. Paris 338 (2004), no. 7, 555-559. | Article | MR 2057029 | Zbl 1049.58005

[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. | Article | MR 2057728 | Zbl 1044.58005

[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. | Article | MR 2056471 | Zbl 1058.58009

[157] J.-M. Bismut and S. Goette, Equivariant de Rham torsions, Ann. of Math. (2) 159 (2004), no. 1, 53-216. | Article | MR 2051391 | Zbl 1094.58013

[158] J.-M. Bismut and X. Ma, Holomorphic immersions and equivariant torsion forms, J. Reine Angew. Math. 575 (2004), 189-235. | MR 2097553 | Zbl 1063.58019

[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. | Article | MR 2129894 | Zbl 1083.58020

[160] J.-M. Bismut, The hypoelliptic Laplacian on the cotangent bundle, J. Amer. Math. Soc. 18 (2005), no. 2, 379-476. | Article | MR 2137981 | Zbl 1065.35098

[161] J.-M. Bismut and G. Lebeau, Laplacien hypoelliptique et torsion analytique, C. R. Math. Acad. Sci. Paris 341 (2005), no. 2, 113-118. | Article | MR 2153967 | Zbl 1073.58024

[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 2322387 | Zbl 1128.53022

[163] J.-M. Bismut, L'opérateur de Dirac hypoelliptique, C. R. Math. Acad. Sci. Paris 343 (2006), no. 10, 647-651. | Article | MR 2271740 | Zbl 1110.58019

[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. | Article | MR 2402405 | Zbl 1157.58011

[165] J.-M. Bismut, The hypoelliptic Laplacian on a compact Lie group, J. Funct. Anal. 255 (2008), no. 9, 2190-2232. | Article | MR 2473254 | Zbl 1183.43005

[166] J.-M. Bismut, Loop spaces and the hypoelliptic Laplacian, Comm. Pure Appl. Math. 61 (2008), no. 4, 559-593. | Article | MR 2383933 | Zbl 1147.58038

[167] J.-M. Bismut, A survey of the hypoelliptic Laplacian, Astérisque 322 (2008), 39-69. Conference in honor of J.-P. Bourguignon. | MR 2521653 | Zbl 1180.58001

[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 2441523 | Zbl 1156.58001

[169] J.-M. Bismut, Duistermaat-Heckman formulas and index theory, (2009). Conference in honor of Hans Duistermaat. | MR 2809466 | Zbl 1267.58015

[170] J.-M. Bismut, Hypoelliptic Laplacian and orbital integrals, (2009). | MR 2567001 | Zbl 1183.58001