Preprints & Notes
Home Log-Sob on Pinned Loop Groups Lie Brackets on Wiener Spaces Spaces of Holomorphic Functions IBP for Heat Kernels IBP and Quasi-Inv. on Loop Groups Path Integral Formulas Yang-Mills and Segal Bargmann Rome Lectures on Quasi--Invariance Stochastic Geometry Primer Heat Equation Derivative Formulas Absolute Continuity of Heat Kernel Measure with Pinned Wiener Measure on Loop groups Equivalence of heat kernel measure and pinned Wiener measure on loop groups No Fixed Vectors

Preprints 

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Li-Yau inequalities for positive harmonic functions by Marc Arnaudon, Bruce K. Driver, and Anton Thalmaier

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Hypoelliptic heat kernel inequalities on the Heisenberg group  by Bruce Driver and Tai Melcher

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Curved Wiener Space Analysis

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Heat Kernels Measures and Infinite Dimensional Analysis

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Analysis of Wiener measure on Path and Loop Groups,  appears in the volume in honor of Leonard Gross in the AMS Contemporary Mathematics Proceedings series.

 

Reprints

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Heat Equation Derivative Formulas for Vector Bundles
(Joint with Anton Thalmaier) J. Funct. Anal. {\bf 183} (2001), no.~1, 42--108
 

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Absolute Continuity of Heat Kernel Measure with Pinned Wiener Measure on Loop groups (Joint with Vikram Srimurthy) The Annals of probability, 2001, Vol 29, No. 2, 691-273.
 

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Equivalence of heat kernel measure and pinned Wiener measure on loop groups  (Joint with Shigeki Aida)  C. R. Acad. Sci. Paris S\'er. I Math. {\bf 331} (2000), no.~9, 709--712
 

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The energy representation has no non-zero fixed vectors 
(Joint with Brian Hall) , in {\it Stochastic processes, physics and geometry: new interplays, II (Leipzig, 1999)}, 143--155, Amer. Math. Soc., Providence, RI, 2000;
 

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Logarithmic Sobolev Inequalities for Pinned Loop Groups 
(Joint with T. Lohrenz. Appeared in Journal for Functional Analysis, Vol 140 (1996) p. 381-448.)
 

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The Lie Bracket of Adapted Vector Fields on Wiener Spaces
Appl. Math. Optim. {\bf 39} (1999), no.~2, 179--210
 

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HILBERT SPACES OF HOLOMORPHIC FUNCTIONS ON COMPLEX LIE GROUPS (Joint with L. Gross. in {\it New trends in stochastic analysis (Charingworth, 1994)}, 76--106, World Sci. Publishing, River Edge, NJ, 1997
 

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Integration by Parts for Heat Kernel Meausres Revisited

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Integration by Parts and Quasi-Invariance for Heat Kernel
Meausres on Loop Groups

 

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Finite dimensional approximations to Wiener measure and path integral formulas on manifolds 
(Joint with Lars Anderson)
 

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Yang-Mills Theory and the Segal-Bargmann Transform
(Joint with Brian Hall)

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Lecture Notes

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AMS - Meeting Talk at LSU, March 15, 2003: Slides from the talk and for a more detail expository paper see, IHP02.

 

bullet LOOP SPACE, CURVATURE, AND QUASI-INVARIANCE
(Centro Vito Volterra Lecture Notes, Universita Degli Studi Di Roma II, October 1992.)

bullet A Primer on Riemannian Geometry and Stochastic Analysis on Path Spaces
(Lecture notes of talks given at the ETH (Zurich, Switzerland) in February of 1995.)

bulletAnalysis on loop groups. Notes for the talk given for the Conference on " Stochastic Analysis and
Harmonic Analysis," June 26-30, 2000 at Northwestern University, Evanston, IL 60208. Get either the PDF version  or the DVI version.

Seminar Notes

bulletTopology and Geometry seminar,  given 11/15/1999: PDF version  and DVI version.
bulletTopology and Geometry seminars,  given 4/11/2000 : PDF version  and DVI version. These are notes on Woodhouse's book on geometric quantization.

Nelder Lecture slides/notes at Imperial College, London (Fall 2014)

  1.  "Path Integrals on Riemannian Manifolds," Wednesday 29th October 2014.
  2. "Quantized Yang-Mills (d=2) and the Segal-Bargmann-Hall Transform,"  Wednesday, 5th November 2014.
  3. "On the Classical Limit of Quantum Mechanics,"  Wednesday, 19th November 2014.

 

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The work found here has been in part supported by :

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DMS 9101720

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DMS 9223177

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DMS 9612651

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DMS 9971036.

 

06/09/2010 04:47 PM