Invited Lectures
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INVITED LECTURES (Bruce Driver)

1.     Convergence of the 4-dimensional U(1) lattice gauge theory to its continuum limits.  Given at the Conference on Mathematical Aspects of String Theory, held at UCSD, July 21 -August 1, 1986. 

2.     Convergence of the U(1)4 lattice gauge theory.  Given at MIT, December 12, 1986. 

3.     Convergence of lattice YM2 and loop expectations via heat kernels.  Given at Conference on Construction of Quantized Gauge Fields, May 31 - June 4, 1988

4.     Quantum Field Theory:  Fact or Fiction?  Colloquium talk given at the University of Rhode Island, May 25, 1989. 

5.     Lattice and continuum two dimensional Yang-Mills theory, given at Conference on Probability Models in Mathematical Physics, University of Colorado at Colorado Springs, May 24-26, 1990. 

6.     Can you ``really'' change the distribution of perfume diffusing on a manifold by blowing on it?  Colloquium talk given at the Mathematics Department of the University of New Mexico in Albuquerque, December 5, 1991. 

7.     A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold, given at Third European Symposium on Analysis and Probability, Institut Henri Poincare*, Paris France, January 3 - 10, 1992.

8.     Flows on Wiener space over Rd and compact manifolds, given at the Workshop on Stochastic Analysis and Geometry, Universitat Bonn, Germany, April 6-10, 1992.

9.     Loop Space, Curvature, Quasi-invariance, a series of four lectures given for the Semestre Di Analisi A Infinite Dimensioni, at Dipartimento di Matematic- Centro Vito Volterra (Rome II), Oct. 14, 15,16, 19, 1992.

10.  A Cameron-Martin Theorem for Manifolds, given in the probability seminar at University of Barcelona, Barcelona Spain, Oct. 22, 1992

11.  What happens when you blow on perfume diffusing on a manifold, given in the probability seminar at University of Rochester, Rochester, NY, Nov 18, 1992.

12.  What happens when you blow on perfume diffusing in a manifold, joint probability seminar and Colloquium, given at Cornell University, Nov. 23, 1992.

13.  Cameron-Martin Theorem for manifolds (Alias:  What happens when you blow on perfume diffusing on a manifold.), talk given in the probability seminar at York University, Toronto Canada, Dec. 4, 1992.

14.  A Cameron-Martin Theorem for manifolds, talk given and University of California at Irvine, in the probability seminar, June 6, 1993.

15.  Towards Calculus and Geometry on Path Spaces, talk given at 1993 American Mathematical Society Summer Research Institute, Cornell University, Ithaca, NY, July 25, 1993.

16.  What happens when you blow on Perfume diffusing on a Manifold, colloquium talk given at Rice University, Houston, TX, September 9, 1993.

17.  On Dirichlet Forms on Path Spaces, talk given at the International Conference on Dirichelt Forms and Stochastic Processes, Beijing, China, October 30, 1993.

18.  A Cameron Martin Theorem for Brownian motion on Path spaces, talk given at Beijing University, November 1, 1993.

19.  A Cameron Martin Theorem for Wiener space based on a Riemannian Manifold, talk given at Southern California Probability Symposium, UCLA, Los Angeles, CA, December 5, 1993.

20.  The non-equivalence of Dirichlet forms on path spaces, talk given at U.S.-Japan Bilateral Seminar, at Louisiana State University, Baton Rouge Louisiana, January 4., 1994.

21.  On the Kakutani-Ito-Segal-Gross and the Segal-Bargmann-Hall Isomorphisms, 2 hour talk given September 22, 1994 at Closed Workshop of the 1994 Taniguchi Symposium, (titled "New Trends in Stochastic Analysis"), Charingworth Manor, Charingworth, England.

22.  Three isomorphisms associated to compact type Lie groups, talk given during 1994 Taniguchi open Symposium, in the Mathematics Research Centre, University of Warwick, England, September 28, 1994.

23.  A chaos expansion for compact Lie groups, given at the Mittag-Leffler Institute, January 19, 1995.

24.  A chaos expansion for compact Lie groups, given at University of Bonn, February 10, 1995.

25.  A chaos expansion for compact Lie groups, given at ETH (Zürich), February 15, 1995.

26.  A primer on Riemannian geometry and Stochastic analysis on path spaces, a series of four (2 hour long) lectures, given in February 1995.The first talk was given at the University of Zürich while the remaining talks were given at ETH (Zürich).

27.  A Logarithmic Sobolev inequality for pinned loop groups: I. and II.  Talks were  given at Warwick University, February 24 and 28, 1995.

28.  A chaos expansion for compact Lie groups, given at Imperial College (London), March 7, 1995.

29.  A Logarithmic Sobolev inequality for pinned loop groups, talk given July 13, 1995 at the Greygynog (Wales, Great Britain) Symposium on ``Stochastic Analysis and Applications.''

30.  A Logarithmic Sobolev inequality for pinned loop groups, talk given July 21, 1995 at the session on ``Infinite Dimensional Analysis'' held at the University of Warwick, Coventry England

31.  A loop group Logarithmic Sobolev inequality, talk given January 12, 1996, in the AMS special session on Stochastic Differential equations, during the 1996 Winter meeting of the AMS in Orlando, FL.

32.  A Logarithmic Sobolev inequality for loop groups, Colloquium talk given at the University of Arizona, Tucson,  Feb 8, 1996.

33.  On the geometry of Wiener spaces, talk given March 5, 1996 at the 15th Annual Western States Mathematical Physics Meeting at the California Institute of Technology.

34.  Ito chaos and complex wave transformations for Lie Groups, talk given April 20, 1996 at the Southern California Analysis and PDE Seminar at the California Institute of Technology.

35.  Logarithmic Sobolev inequalities for pinned loop groups, talk given July 1, 1996 at the 1996 Summer IAS/Park City Mathematics Institute, held at the Institute for Advanced Study, Princeton, NJ.

36.  Path and Loop Space Analysis, series of two talks given at the Eighteenth Midwest  Probability Colloquium at Northwestern University, October 17, 1996.

37.  Heat Kernel Measures on Loop Groups, talk given October 29, at the meeting: "Stochastische Analysis" held at Mathematisches Forshungsinstitut Oberwolfach, Germany, October 27- November 2, 1996.

38.  Geometry of Wiener measure, talk given June 2, 1997 at the Work Shop: "Geometry and analysis on loop spaces," held at Mathematisches Forshungsinstitut Oberwolfach, Germany, June 1 - 6, 1997.

39.  Analysis of heat kernel measures on loop spaces, talk given June 3, 1997 at the Work Shop: "Geometry and analysis on loop spaces," held at Mathematisches Forshungsinstitut Oberwolfach, Germany, June 1 - 6, 1997.

40.  Path Integrals (Sponsor's Day Talk), October 3, 1997 at the Mathematical Science Research Institute, Berkeley, CA.

41.  Geometry and Cartan's Development Map, October 7, 1997, the first of a series of three introductory lectures given at Mathematical Science Research Institute, Berkeley, CA.

42.  Smoothness Properties of Wiener Measures, October 8, 1997, the second of a series of three introductory lectures given at Mathematical Science Research Institute, Berkeley, CA.

43.  A Survey of Recent Results and Future Directions in Path and Loop Space Analysis,  October 10, 1997, the second of a series of three introductory lectures given at Mathematical Science Research Institute, Berkeley, CA.

44.  Quasi-Invariance of Heat Kernel Measure on Loop Groups, November 4, 1997 given at Mathematical Science Research Institute, Berkeley, CA during the Workshop #2 ("Infinite Dimensional Analysis and Dirichlet Forms") of the year in Stochastic Analsysis.  (See http://www.msri.org/  for the talk on video.)

45.  Volume Measures on Path and Loop Spaces, November 21, 1997 given in the Mathematics Department at the University of California at Davis.

46.  Bismut type integration by parts formulas for heat kernel measures, May 25, 1998 given at the meeting on Stochastic Analysis held at l'institut Henri Poincaré from May 25-30.

47.  Finite dimensional approximation to Brownian motion on a compact Riemannian manifold, June 3, 1998, given at the l'institut Henri Poincaré  (France) for the special Trimestre on  "INEGALITES DE SOBOLEV LOGARITHMIQUES, MECANIQUE STATISTIQUE, GRANDES DEVIATIONS."

48.  Loop Group Analysis, June 10, 1998, given at the l'institut Henri Poincaré  (France) for the special Trimestre on  "INEGALITES DE SOBOLEV LOGARITHMIQUES, MECANIQUE STATISTIQUE, GRANDES DEVIATIONS."

49.  Quantized Yang-Mills theory on a space-time cylinder,  June 17, 1998, given at the l'institut Henri Poincaré  (France) for the special Trimestre on  "INEGALITES DE SOBOLEV LOGARITHMIQUES, MECANIQUE STATISTIQUE, GRANDES DEVIATIONS."

50.  Towards the Hodge de Rham Theorem on Path and Loop Spaces, June 15, 1988 given at l'institut Henri Poincaré  (France) for the special Trimestre on  "INEGALITES DE SOBOLEV LOGARITHMIQUES, MECANIQUE STATISTIQUE, GRANDES DEVIATIONS."

51.  The Cameron-Martin Theorem for Brownian motion on a compact Riemannian manifold, June 23, 1998 given at "Seminare de Probabilites," University of Paris VI.

52.  Two dimensional Yang-Mills and the Segal-Bargmann Transform, September 18, 1998 given at Mathematics Department, Bielefeld University, Bielefeld, Germany.

53.  Finite dimensional approximations to Wiener measure and path integral formulas on manifolds, September 22, 1998 given at: "Infinite-dimensional stochastic dynamics" in Jena, Germany.

54.  On path integral formulas on manifolds, March 20, 1999, given at "Seminar on Stochastic Processes 1999 ," at the Fields Institute, Toronto, Canada.

55.  Heat Kernel Analysis on Loop Groups, May 14, 1999, given at the Belgium London Joint Mathematical Society meeting in Brussels, Belgium.

56.  On the relationship between pinned Wiener measures and heat kernel measures on loop groups,  given  July 8, 1999 at the London Mathematical Society Durham meeting on Stochastic Analysis, held in the Mathematics Department of Durham University, Durham, England.

57.  Smoothness Properties of Wiener Measure on Manifolds, colloquium talk given September 1, 1999 at the University of Notre Dame mathematics Department, IN.

58.  Heat kernel versus pinned Wiener measure on Loop groups, probability seminar talk given September 2, 1999 at the University of Notre Dame mathematics Department, IN.

59.  Quasi-invariance of  heat kernel measure on loop groups, probability seminar talk given September 13, 1999 at Cornell University, NY.

60.  Path integrals on manifolds, Colloquium (Oliver Club) talk given September 16, 1999 at Cornell University, NY.

61.  Some aspects of quantum field theory , Topology/Geometry Seminar at UCSD, November 8, 1999.   

62.  Examples of quantum field theories, Topology/Geometry Seminar at UCSD, November 15, 1999.   

63.  Brownian motion and heat kernel derivative formulas, Center for Applied Mathematics Colloquium talk given February 4, 2000 at Cornell University, NY.

64.  Comparing heat kernel and pinned Wiener measure on loop groups, probability seminar talk given February 7, 2000 at Cornell University, NY.

65.  An introduction to prequantization, Topology and Geometry seminar at UCSD, May 2000.

66.  Prequantization revisited, Topology and Geometry seminar at UCSD, May 2000.

67.  Path integrals on manifolds, Analysis seminar at UCSD,  May 10, 2000.

68.  Analysis on loop groups,  talk given at the Conference on Stochastic Analysis and Harmonic Analysis, June 26 -- 30, 2000, Northwestern University.

69.  Path integrals on Manifolds and Heat Kernel derivative formulas,  given at the conference, "Geometry and Analysis on Path spaces and Related Fields," July 24-29, 2000 at University of Warwick, England.

70.  Loop Group Analysis, given in the Mathematics Department, Osaka University,  Japan on November 21, 2000.

71.  Loop Group Analysis, given in the Mathematics Department, Kyoto University,  Japan on November 22, 2000.

72.  Yang-Mills Theory and Hall's Transform, given at the Kansai Probability Seminar, at Kyoto University, Japan, November 24, 2000.

73.  Quantized Yang-Mills Theory, Chaos Expansions and Hall's Transform, given at the Southern California Probability Symposium held at University of California at Los Angeles on  December 3, 2000.

74.  On Smooth Measures in ``Infinite Dimensional Analysis,'' given in the analysis seminar at UCLA on February 8, 2001.

75.  "Loop Space Analysis" Colloquium talk given April 19, 2001 at Department of Mathematics and Statistics,  University of North Florida , Jacksonville, Florida.

76.  “Energy Representation has no Fixed Points,”  given at the Probability and Geometry Meeting in Dijon, France on September 14, 2001.

77.  “Finite Dimensional Approximations to Wiener Measure and Path Integral Formulas,” given in the joint McGill and Quebec University geometry seminar, Montreal, Canada on April 5, 2002.

78.  “Analysis on Loop Groups,”  given at Probability Day at McGill University, Montreal Canada on April 6, 2002.

79.  Heat Kernel Derivative Formula,”  given at the special Trimestre on  Heat Kernels, Random Walks And Analysis To Manifolds And Graphs,  at the l'institut Henri Poincaré, Paris France, June 24, 2002.

80.  “Quasi-Invariance of Heat Kernel Measures on Loop Groups,”  given at the special Trimestre on  Heat Kernels, Random Walks And Analysis To Manifolds And Graphs,  at the Centre Émile Borel, Paris France, June 24, 2002.

81.  “Analysis on Loop Groups,”  given at the "Analysis on graphs and on metric spaces workshop  at the Centre Émile Borel, Paris France, June 27, 2002.

82.  “Pinned Wiener Measure versus Heat Kernel Measure on Loop Groups,”  given at the special Trimestre on  Heat Kernels, Random Walks And Analysis To Manifolds And Graphs,  at Centre Émile Borel, Paris France, July 1, 2002.

83.   “Analysis on Loop Groups,” given in the PROBABILITY & STATISTICS SEMINAR given at USC , 3:00-4:00 PM, DRB 337 Friday November 8, 2002

84.  “Heat equations on loop groups,” given as a 50 minute invited address at the 2003 Spring Southeastern Sectional Meeting: Baton Rouge, LA, March 14-16, 2003
Meeting #984.

85.  “Heat equation on loop groups and two-dimensional quantized Yang-Mills equations,” 50 minute invited address at The Twenty-Fifth Midwest Probability Colloquium held at Northwestern University (Evanston, Il.) on October 17-18, 2003.

86.  “Hypoelliptic heat kernel inequalities on the Heisenberg group,” a 60 minute invited address given for the program on “Geometric and Analytic Aspects of Stochastic Processes,” held at the Banff International Research Station (Banff Canada) on April 10 - 15, 2004.

87.  “Path Integral Quantization,” a 60 minute invited talk given in the Research Seminar of the Math Departments at the university of Bonn (Germanay), on June 14, 2005.

88.  “Rough Path Integration and ODE’s,” a 50 minute invited talk given in the special session on Stochastic Analysis on Metric Spaces at the Joint Meeting of the AMS, DMV, and OMG, held at Johannes Gutenberg University, Mainz Germany, on June 16, 2005.

89.  “On Path Integral Quantization,” a 50 minute invited talk given in the special given for the Conference on Martingales, Stochastic Analysis, and Potential Theory, held at the University of Florida Campus at Gainsville, November 10 through November 13, 2005.

90.  “Holomorphic Functions and Subelliptic Heat Kernels over Lie groups,” an invited talk given in the special session on Holomorphic Methods and Heat Kernels in Harmonic Analysis and Quantization Theory at the AMS sectional meeting held at the University of Notre Dame, April 7-9, 2006.

91.  “Geometric Path Integrals,” a plenary talk given at the conference on “The Feynman Integral and Related Topics in Mathematics and Physics” (in honor of the 65th birthdays of Gerald (Jerry) Johnson and David Skoug) at the University of Nebraska Lincoln, May 12 - 14, 2006.

92.  “Path Integrals over Manifolds,” the first in a series of three invited “Andrejewski Lectures,” given at University of Leipzig, Germany, June 28, 2006.

93.  “Quantized Yang-Mills (d=2) and the Segal-Bargmann-Hall Transform,” the second in a series of three invited “Andrejewski Lectures,” given at Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, June 29, 2006.

94.  “Heat Equations on Loop Groups,” the third in a series of three invited “Andrejewski Lectures,” given at Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, June 29, 2006. 

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