Prof. Rudolf Schmid -- Home Page

Yale University. Assistant Professor, 1981-1986
Emory University.

Associate Professor, 1986-1995
Professor, 1995 - 2007
Professor Emeritus, 2007 - date

Georgia Tech. "CDSNS"

Adjunct Professor, 1991 - date

Visiting Professor:

Federal University, Porto Alegre, Summer 1982
MSRI, Berkeley, 1983-1984
Forschungsinstitut für Mathematik ETH Zürich, Summer 1985
Sonderforschungsinstitute, University of Heidelberg, June 1985
University of Naples, Summer 1987
MSRI, Berkeley, Spring & Summer 1989
CDSNS, Georgia Tech., Atlanta, Spring & Summer 1991
Erwin Schrödinger Inst. for Math. Physics, Vienna, Summer 1993
Ernst-Moritz-Arndt University, Greifswald, Summer 1995, 97, 99, 2001

Most Recent Papers

Infinite -Dimensional Hamiltonian Systems . Encyclopedia of Mathematical Physics, J-P. Francoise , G.L.Naber, T.S. Tsung (eds.), Elsevier, Academic Press (2006) 37-44.
On the Supersymmetry Group of the Classical Bose-Fermi oscillator (with T. Glimm), Journal of Geometry and Symmetry in Physics, 2 (2005) 1-13,
Infinite Dimensional Lie Groups with Applications to Mathematical Physics Journal of Geometry and Symmetry in Physics, 1 (2004) 1-67.
g-Symplectic Orbits and a Solution of the BRST Consistency Condition. Geometry, Integrability and Quantization, 4, I.M. Mladenov, G.L.Naber (eds.) (2003), 284 - 295.
Fourier Integral Operators with Applications to Fluid Dynamics and Quantization. Proc. XX. Intl. Conf. on Geometric Methods in Physics , Bialowieza, Poland, 2003, 1-25.
Relativity Without the First Postulate. ( with Q. Sun), Proc. Inst. Math. of Natl. Acad. Sci. of Ukraine, 43 (2002), 577-588.
The Lie Groups of Invertible Fourier Integral on Open Manifolds (SURVEY), Infinite Dimensional Lie Groups in Geometry and Representation Theory, A. Banyaga et al. (eds.) , World Scientific Publ. (2002), 44-64.
Lie Groups of Fourier Integral Operators on Open Manifolds (with J. Eichhorn), Comm. Anal. Geom. 9, no 5 (2001) 983-1040.
Bäcklund Transformations Induced by Symmetries , CRM Montreal Lecture Notes, 29 (2001) 405-410.
A Finite Dimensional Completely Integrable System Associated with the WKI- and Heisenberg Hierarchies, (with T. Xu, Z. Li), Journal of Nonlinear Mathematical Physics, 8 (2001), 261-265.
Symplectic Discretization for Maxwell's Equations , (with X. Lu), J. of Math. and Computing, 25 (2001), 1-21.
Symplectic Integration of Sine-Gordon Type Systems (with X. Lu), Mathematics and Computers in Simulation, 50, (1999) 143-160.
Symplectic Algorithm for Maxwell's Equations, (with X. Lu) , Proc. New Applications of Multisymplectric Field Theory, Salamanca (1999), 10-25.
A Numerical Study of the Riemann Solutions for Gasdynamic Combustion, (with X. Lu), Applied Math. and Computation, 91 (1998), 143-160,
Form Preserving Diffeomorphisms on Open Manifolds ( with J. Eichhorn), Annals of Global Analysis and Geometry, 14 (1996) 147-176.
Infinite Dimensional Hamiltonian Systems with Symmetries, Proc. of the Int. Conference on Differential Geometry, Hamiltonian Systems and Operator Theory, S. Goldberg (Ed.), UWI University Press, 1995, 213-239.
On Bäcklund Transformations for the Korteweg-de Vries Equation (with X. Yang, H. Wu) (preprint 1995), 1-31.
Symplectic Algorithms for Wave Equations (with X. Lu), Proc. 14th IMACS World Congress on Computational and Applied Mathematics, W.F. Ames (Ed.), 3( 1994) 1363-1366.
Local Cohomology in Gauge Theories, BRST Transformations and Anomalies, Differential Geometry and its Applications, 4 (1994) 107-116.
Bäcklund Transformations Induced by Symmetries, (with X. Yang), Physics Lett. A, 195 (1994) 63-74.
A Solution of the BRST Consistency Condition and g - Symplectic Orbits, "The Erwin Schrödinger Institute for Mathematics Physics", preprint ESI # 41, Vienna, 1993
A Few BRST Bicomplexes , 21th International Conference on Differential Geometric Methods in Mathematical Physics, Nankai Institute of Mathematics, Tianjing, P.R.China, C.N. Yang et al. (Eds.), World Scientific, Singapore, (1993), 375-379.
BRST Bicomplexes , preprint 1992

List of Publications and Invited Talks

Recent Lectures

GUT, Rincon University, 2009
General Theory of Relativity, Rincon University, 2009
How do you differentiate in infinite dimensions ? SIDIM XXIII , University of Puerto Rico, CArolina, Feb. 29 -Mar. 1, 2008.
SUSY, Supersymmetric Reduction University of Puerto Rico, Mayagüez, Mathematics Colloquium , Sept. 27 , 2007.
The Geometry of Euler's Equations SIDIM XIX, , University of Puerto Rico, Cayey, Feb. 27 -28, 2004.
Infinite Dimensional Hamiltonian Systems with Symmetries University of Puerto Rico, Rio Pierdas, San Juan, Mathematics-Physics Colloquium Feb. 26, 2004
The Geometry of Euler's Equations, 6th Caribbean Conference on Fluid Dynamics, University of the West Indies, St. Augustine, Trinidad, Jan. 22 - 24, 2004.
Infinite Dimensional Lie Groups and Physical Applications University of Puerto Rico, Mayagüez, Mathematics-Physics Colloquium, Aug. 22, 2002.
The Geometry of Non-Linear Sigma Models, 3rd Tropical Workshop on Particle Physics and Cosmology, San Juan, Puerto Rico, Aug. 19 - 23, 2002.
Infinite Dimensional Lie Groups and Applications in Mathematical Physics ,VARNA 2002, 4th International Conference on Geometry, Integrability and Quantization . Sts Constantine and Elena, Bulgaria, June 5-16, 2002 (plenary speaker, 6 lectures)
The Lie Group of Fourier Integral Operators on Open Manifolds International Workshop on Infinite dimensional Lie groups: CMR, University of Montreal, Canada, Nov.1-7, 2001.
The Lie Group of Fourier Integral Operators and Applications to Hydrodynamics; 4th International Conference on Symmetry in Nonlinear Mathematical Physics. National Academy of Science of Ukraine, Kyiv, Ukraine, July 9-15, 2001.
The Lie Group of Fourier Integral Operators on Open Manifolds with Applications; XXth Workshop on Geometric Methods in Physics. Bialowieza, Poland, July 1-7, 2001.
Super Symmetries; Rostock University, Rostock, Germany, Mathematics Colloquium, June 22, 2001.
BRST and Super Symmetries; Ernst-Moritz-Arnst University , Greifswald, Germany, Mathematics Colloquium, June 21 , 2001.
The Lie Group of Fourier Integral Operators and Applications to Hydrodynamics; Penn. State University, Mathematics Colloquium, April 5. 2001.
The Lie Group of Fourier Integral Operators on OPEN Manifolds ; Infinite Dimensional Lie Groups in Geometry and Representation Theory. Howard University, Washington DC. August 17-21, 2000.
Infinite Dimensional Lie Groups in Mathematical Physics; Clemson University, Clemson SC, Mathematics Colloquium, Oct. 14. 1999.
Symplectic Discretization for Maxwell's Equation; Internatl. Conference on New Applications of Multisymplectic Field Theory ,University of Salamanca, Spain Sept. 20-24, 1999.
Finite dimensional completely integrable systems associated with WKI and Heisenberg equations, Academy of Crete, Greece, NEEDS '99 Conference on Nonlinear Evolution Equations and Dynamical Systems, June 20-30,1999.
Bäcklund Transformations Induced by Symmetries, AARMS-CRM Workshop on Bäcklund and Darboux Transformations, Halifax, Canada, June 4 - 9, 1999.
Symplectic Algorithms for Wave Equations, Academy of Sciences of the Czech Republic, Prague : IMACS Conference on Mathematical Modelling and Computational Methods in Mechanics and Geodynamics, July 7-11, 1998.
Topological Euler Equations and Diffeomorphism Groups, Temple University, Philadelphia, AMS Meeting, April 4-5, 1998.
Infinite Dimensional Lie Groups in Mathematical Physics Penn State University, March 5-8, 1998.
Diffeomorphism Groups of OPEN Manifolds; Workshop on Lie Groups and Lie Algebras in Infinite Dimensions. Stefan Banach International Mathematical Center, Warsaw, Poland, Sept. 8-13, 1997;
Fourier Integral Operators on Open Manifolds Rostock University, Rostock, Germany , July 25, 1997.
Pseudodifferential Operators on Open Manifolds, (4 lectures); Fourier Integral Operators on Open Manifolds, (4 lectures); Ernst-Moritz-Arndt University , Greifswald, Germany, Juny 15 -31, 1997.
Symmetries in Mathematical Physics Adam Mickiewicz University , Poznan, Poland, June 9, 1995.
Symmetries in Mathematical Physics, Rostock University, Rostock, Germany, June 6, 1995.
BRST Symmetries, (4 lectures); Anomalies in Gauge Theories, (4 lectures); Pseudodifferential- and Fourier Integral Operators, (4 lectures). Ernst-Moritz-Arnst University , Greifswald, Germany, June 1 -30 , 1995.
BRST Bicomplexes and Cohomologies; ICM94, International Congress of Mathematicians. Zürich, Switzerland, Aug. 3-11, 1994; (poster)
The Geometry of BRST Symmetries; XIth International Congress of Mathematical Physics, Paris, short communication, July 18-23, 1994.
Infinite Dimensional Hamiltonian Systems with Symmetries; Conference on Differential Geometry, Hamiltonian Systems and Operator Theory. University of the West Indies, Mona Campus, Jamaica, Feb. 7-11, 1994.
Local Cohomology and BRST Symmetry; University of California, Davis, Oct. 13, 1993.
BRST Symmetries; MSRI, Berkeley, Oct. 11, 1993.
BRST Symmetries; The Erwin Schrödinger International Institute for Mathematical Physics, Vienna, Austria, July 14, 1993.
BRST Symmetries and Anomaliess, The Fields Institute for Mathematical Sciences, Waterloo, Canada, June 7-9, 1993.
Infinite Dimensional Lie Groups in Mathematical Physics I \& II, Academica Sinica, Beijing and Beijing University, P.R. China, June 10-11, 1992. \item
BRST: Bicomplexes and Cohomologies, Nankai Institute of Mathematics, Tianjing, P.R. China, International Conference on Differential Geometry Methods in Theoretical Physics, June 3-9, 1992.
Infinite Dimensional Lie Group Cohomologies and Applications, Fudan University, Shanghai, P.R. China, June 1-3, 1992.
Graduate Students
Master Students:
A. McAffe: The Schwarzschild Metric. M.S. Thesis, Yale, 1983.
L. Osserman: The Korteweg-deVries Equation. M.S. Thesis, Yale 1983.
P. Chandra: Completely Integrable Systems. M.S. Thesis, Yale 1984.
T. Glimm: Symplectic Recostruction for the Free Symmetric Top and the Falling Cat Problem. M.S. Thesis, Emory 1999.
PhD Students:
Qicun Sun: Relativistic Theories in F-Atlas . Emory, 1994.
Xinfa Yang: On Bäcklund Transformations for Nonlinear Differential Equations . Emory, 1994.
Xiaowu Lu: Symplectic Integration for Hamiltonian Systems and Applications. Emory, 1999.
Jan Fricke : Riemannsch Geometrie von Konfigurationsräumen, Co-adviser,Greifswald, Germany, 1999.
Taixi Xu: Finite Dimensional Completely Integrable Systems Associated with Soliton Equations, Emory, 2000.
Tilmann Glimm: Supersymmetric Reduction , Emory, 2003.

Smart Ass
Visiting Professor:

Federal University, Porto Alegre, Summer 1982
MSRI, Berkeley, 1983-1984
Forschungsinstitut für Mathematik ETH Zürich, Summer 1985
Sonderforschungsinstitute, University of Heidelberg, June 1985
University of Naples, Summer 1987
MSRI, Berkeley, Spring & Summer 1989
CDSNS, Georgia Tech., Atlanta, Spring & Summer 1991
Erwin Schrödinger Inst. for Math. Physics, Vienna, Summer 1993
Ernst-Moritz-Arndt University, Greifswald, Summer 1995, 97, 99, 2001

Most Recent Papers

Infinite -Dimensional Hamiltonian Systems . Encyclopedia of Mathematical Physics, J-P. Francoise , G.L.Naber, T.S. Tsung (eds.), Elsevier, Academic Press (2006) 37-44.
On the Supersymmetry Group of the Classical Bose-Fermi oscillator (with T. Glimm), Journal of Geometry and Symmetry in Physics, 2 (2005) 1-13,
Infinite Dimensional Lie Groups with Applications to Mathematical Physics Journal of Geometry and Symmetry in Physics, 1 (2004) 1-67.
g-Symplectic Orbits and a Solution of the BRST Consistency Condition. Geometry, Integrability and Quantization, 4, I.M. Mladenov, G.L.Naber (eds.) (2003), 284 - 295.
Fourier Integral Operators with Applications to Fluid Dynamics and Quantization. Proc. XX. Intl. Conf. on Geometric Methods in Physics , Bialowieza, Poland, 2003, 1-25.
Relativity Without the First Postulate. ( with Q. Sun), Proc. Inst. Math. of Natl. Acad. Sci. of Ukraine, 43 (2002), 577-588.
The Lie Groups of Invertible Fourier Integral on Open Manifolds (SURVEY), Infinite Dimensional Lie Groups in Geometry and Representation Theory, A. Banyaga et al. (eds.) , World Scientific Publ. (2002), 44-64.
Lie Groups of Fourier Integral Operators on Open Manifolds (with J. Eichhorn), Comm. Anal. Geom. 9, no 5 (2001) 983-1040.
Bäcklund Transformations Induced by Symmetries , CRM Montreal Lecture Notes, 29 (2001) 405-410.
A Finite Dimensional Completely Integrable System Associated with the WKI- and Heisenberg Hierarchies, (with T. Xu, Z. Li), Journal of Nonlinear Mathematical Physics, 8 (2001), 261-265.
Symplectic Discretization for Maxwell's Equations , (with X. Lu), J. of Math. and Computing, 25 (2001), 1-21.
Symplectic Integration of Sine-Gordon Type Systems (with X. Lu), Mathematics and Computers in Simulation, 50, (1999) 143-160.
Symplectic Algorithm for Maxwell's Equations, (with X. Lu) , Proc. New Applications of Multisymplectric Field Theory, Salamanca (1999), 10-25.
A Numerical Study of the Riemann Solutions for Gasdynamic Combustion, (with X. Lu), Applied Math. and Computation, 91 (1998), 143-160,
Form Preserving Diffeomorphisms on Open Manifolds ( with J. Eichhorn), Annals of Global Analysis and Geometry, 14 (1996) 147-176.
Infinite Dimensional Hamiltonian Systems with Symmetries, Proc. of the Int. Conference on Differential Geometry, Hamiltonian Systems and Operator Theory, S. Goldberg (Ed.), UWI University Press, 1995, 213-239.
On Bäcklund Transformations for the Korteweg-de Vries Equation (with X. Yang, H. Wu) (preprint 1995), 1-31.
Symplectic Algorithms for Wave Equations (with X. Lu), Proc. 14th IMACS World Congress on Computational and Applied Mathematics, W.F. Ames (Ed.), 3( 1994) 1363-1366.
Local Cohomology in Gauge Theories, BRST Transformations and Anomalies, Differential Geometry and its Applications, 4 (1994) 107-116.
Bäcklund Transformations Induced by Symmetries, (with X. Yang), Physics Lett. A, 195 (1994) 63-74.
A Solution of the BRST Consistency Condition and g - Symplectic Orbits, "The Erwin Schrödinger Institute for Mathematics Physics", preprint ESI # 41, Vienna, 1993
A Few BRST Bicomplexes , 21th International Conference on Differential Geometric Methods in Mathematical Physics, Nankai Institute of Mathematics, Tianjing, P.R.China, C.N. Yang et al. (Eds.), World Scientific, Singapore, (1993), 375-379.
BRST Bicomplexes , preprint 1992

List of Publications and Invited Talks

Recent Lectures

GUT, Rincon University, 2009
General Theory of Relativity, Rincon University, 2009
How do you differentiate in infinite dimensions ? SIDIM XXIII , University of Puerto Rico, CArolina, Feb. 29 -Mar. 1, 2008.
SUSY, Supersymmetric Reduction University of Puerto Rico, Mayagüez, Mathematics Colloquium , Sept. 27 , 2007.
The Geometry of Euler's Equations SIDIM XIX, , University of Puerto Rico, Cayey, Feb. 27 -28, 2004.
Infinite Dimensional Hamiltonian Systems with Symmetries University of Puerto Rico, Rio Pierdas, San Juan, Mathematics-Physics Colloquium Feb. 26, 2004
The Geometry of Euler's Equations, 6th Caribbean Conference on Fluid Dynamics, University of the West Indies, St. Augustine, Trinidad, Jan. 22 - 24, 2004.
Infinite Dimensional Lie Groups and Physical Applications University of Puerto Rico, Mayagüez, Mathematics-Physics Colloquium, Aug. 22, 2002.
The Geometry of Non-Linear Sigma Models, 3rd Tropical Workshop on Particle Physics and Cosmology, San Juan, Puerto Rico, Aug. 19 - 23, 2002.
Infinite Dimensional Lie Groups and Applications in Mathematical Physics ,VARNA 2002, 4th International Conference on Geometry, Integrability and Quantization . Sts Constantine and Elena, Bulgaria, June 5-16, 2002 (plenary speaker, 6 lectures)
The Lie Group of Fourier Integral Operators on Open Manifolds International Workshop on Infinite dimensional Lie groups: CMR, University of Montreal, Canada, Nov.1-7, 2001.
The Lie Group of Fourier Integral Operators and Applications to Hydrodynamics; 4th International Conference on Symmetry in Nonlinear Mathematical Physics. National Academy of Science of Ukraine, Kyiv, Ukraine, July 9-15, 2001.
The Lie Group of Fourier Integral Operators on Open Manifolds with Applications; XXth Workshop on Geometric Methods in Physics. Bialowieza, Poland, July 1-7, 2001.
Super Symmetries; Rostock University, Rostock, Germany, Mathematics Colloquium, June 22, 2001.
BRST and Super Symmetries; Ernst-Moritz-Arnst University , Greifswald, Germany, Mathematics Colloquium, June 21 , 2001.
The Lie Group of Fourier Integral Operators and Applications to Hydrodynamics; Penn. State University, Mathematics Colloquium, April 5. 2001.
The Lie Group of Fourier Integral Operators on OPEN Manifolds ; Infinite Dimensional Lie Groups in Geometry and Representation Theory. Howard University, Washington DC. August 17-21, 2000.
Infinite Dimensional Lie Groups in Mathematical Physics; Clemson University, Clemson SC, Mathematics Colloquium, Oct. 14. 1999.
Symplectic Discretization for Maxwell's Equation; Internatl. Conference on New Applications of Multisymplectic Field Theory ,University of Salamanca, Spain Sept. 20-24, 1999.
Finite dimensional completely integrable systems associated with WKI and Heisenberg equations, Academy of Crete, Greece, NEEDS '99 Conference on Nonlinear Evolution Equations and Dynamical Systems, June 20-30,1999.
Bäcklund Transformations Induced by Symmetries, AARMS-CRM Workshop on Bäcklund and Darboux Transformations, Halifax, Canada, June 4 - 9, 1999.
Symplectic Algorithms for Wave Equations, Academy of Sciences of the Czech Republic, Prague : IMACS Conference on Mathematical Modelling and Computational Methods in Mechanics and Geodynamics, July 7-11, 1998.
Topological Euler Equations and Diffeomorphism Groups, Temple University, Philadelphia, AMS Meeting, April 4-5, 1998.
Infinite Dimensional Lie Groups in Mathematical Physics Penn State University, March 5-8, 1998.
Diffeomorphism Groups of OPEN Manifolds; Workshop on Lie Groups and Lie Algebras in Infinite Dimensions. Stefan Banach International Mathematical Center, Warsaw, Poland, Sept. 8-13, 1997;
Fourier Integral Operators on Open Manifolds Rostock University, Rostock, Germany , July 25, 1997.
Pseudodifferential Operators on Open Manifolds, (4 lectures); Fourier Integral Operators on Open Manifolds, (4 lectures); Ernst-Moritz-Arndt University , Greifswald, Germany, Juny 15 -31, 1997.
Symmetries in Mathematical Physics Adam Mickiewicz University , Poznan, Poland, June 9, 1995.
Symmetries in Mathematical Physics, Rostock University, Rostock, Germany, June 6, 1995.
BRST Symmetries, (4 lectures); Anomalies in Gauge Theories, (4 lectures); Pseudodifferential- and Fourier Integral Operators, (4 lectures). Ernst-Moritz-Arnst University , Greifswald, Germany, June 1 -30 , 1995.
BRST Bicomplexes and Cohomologies; ICM94, International Congress of Mathematicians. Zürich, Switzerland, Aug. 3-11, 1994; (poster)
The Geometry of BRST Symmetries; XIth International Congress of Mathematical Physics, Paris, short communication, July 18-23, 1994.
Infinite Dimensional Hamiltonian Systems with Symmetries; Conference on Differential Geometry, Hamiltonian Systems and Operator Theory. University of the West Indies, Mona Campus, Jamaica, Feb. 7-11, 1994.
Local Cohomology and BRST Symmetry; University of California, Davis, Oct. 13, 1993.
BRST Symmetries; MSRI, Berkeley, Oct. 11, 1993.
BRST Symmetries; The Erwin Schrödinger International Institute for Mathematical Physics, Vienna, Austria, July 14, 1993.
BRST Symmetries and Anomaliess, The Fields Institute for Mathematical Sciences, Waterloo, Canada, June 7-9, 1993.
Infinite Dimensional Lie Groups in Mathematical Physics I \& II, Academica Sinica, Beijing and Beijing University, P.R. China, June 10-11, 1992. \item
BRST: Bicomplexes and Cohomologies, Nankai Institute of Mathematics, Tianjing, P.R. China, International Conference on Differential Geometry Methods in Theoretical Physics, June 3-9, 1992.
Infinite Dimensional Lie Group Cohomologies and Applications, Fudan University, Shanghai, P.R. China, June 1-3, 1992.
Graduate Students
Master Students:
A. McAffe: The Schwarzschild Metric. M.S. Thesis, Yale, 1983.
L. Osserman: The Korteweg-deVries Equation. M.S. Thesis, Yale 1983.
P. Chandra: Completely Integrable Systems. M.S. Thesis, Yale 1984.
T. Glimm: Symplectic Recostruction for the Free Symmetric Top and the Falling Cat Problem. M.S. Thesis, Emory 1999.
PhD Students:
Qicun Sun: Relativistic Theories in F-Atlas . Emory, 1994.
Xinfa Yang: On Bäcklund Transformations for Nonlinear Differential Equations . Emory, 1994.
Xiaowu Lu: Symplectic Integration for Hamiltonian Systems and Applications. Emory, 1999.
Jan Fricke : Riemannsch Geometrie von Konfigurationsräumen, Co-adviser,Greifswald, Germany, 1999.
Taixi Xu: Finite Dimensional Completely Integrable Systems Associated with Soliton Equations, Emory, 2000.
Tilmann Glimm: Supersymmetric Reduction , Emory, 2003.

Smart Ass

RUDOLF SCHMID

Professor Emeritus
Department of Mathematics

Education

Professional Experience

Most Recent Papers

Recent Lectures

Graduate Students

RUDOLF SCHMID

Professor Emeritus Department of Mathematics

Education

Professional Experience

Most Recent Papers

Recent Lectures

Graduate Students

Professor Emeritus
Department of Mathematics