Office Hours: Monday 10:00-10:50, Wednesday 11:00-11:50, or by appointment

Courses Taught

Fall 2009

MTH 252 &ndash 400 Integral Calculus on the Web

MTH 254 Vector Calculus I, sections 010, 040

MTH 252 &ndash 400 Integral Calculus on the Web

MTH 252 &ndash 400 Integral Calculus on the Web

MTH 674 Differential Geometry of Manifolds

MTH 679 Topics in Geometry

Winter 2009

MTH 251 &ndash 400 Differential Calculus on the Web

MTH 306H Honors Matrix and Power Series Methods

MTH 430 Metric Spaces and Topology

Previous Courses

• Research Interests
  • In general terms my research deals with the theory and applications of transformation groups and their invariants in problems arising in geometry and mathematical physics.

• Areas of Interest
  • Symmetries, conservation laws, transformation groups, variational bicomplex

• Recent Papers
  • Peter Olver, Juha Pohjanpelto, Persistence of Freeness for Lie Pseudogroup Actions [pdf] (2009).
  • Jeffrey Early, Juha Pohjanpelto, Roger Samelson, Group Foliation of Equations in Geophysical Fluid Dynamics [pdf] (2009).
  • Peter Olver, Juha Pohjanpelto, Differential Invariant Algebras of Lie Pseudogroups [pdf]. To appear in Advances in Mathematics (2009).
  • Peter Olver, Juha Pohjanpelto, Francis Valiquette, On the Structure of Lie Pseudo-Groups [pdf]. SIGMA 004 (2009), 077.
  • Juha Pohjanpelto, Reduction of exterior differential systems with infinite dimensional symmetry groups [pdf]. BIT Numerical Mathematics 48 (2008), 337 &ndash 355.
  • Juha Pohjanpelto, Stephen Anco, Generalized symmetries of massless free fields on Minkowski space [pdf]. SIGMA 4 (2008) 004.
  • Gianni Manno, Juha Pohjanpelto, Raffaele Vitolo, Gauge invariance, charge conservation, and variational principles [pdf]. Journal of Geometry and Physics 58 (2008), 996 &ndash 1006.
  • Peter Olver, Juha Pohjanpelto, Moving frames for pseudo-groups [pdf]. Canadian Journal of Mathematics 60 (2008), 1336 &ndash 1386.
  • Peter Olver, Juha Pohjanpelto, Pseudo-groups, Moving Frames, and Differential Invariants [pdf]. In Symmetries and Overdetermined Systems of Partial Differential Equations, M. Eastwood, W. Miller, Jr. (Eds.), IMA Volumes in Mathematics and its Applications, Vol. 144, Springer (2008), 127 &ndash 150.
  • Jeongoo Cheh, Peter Olver, Juha Pohjanpelto, Algorithms for differential invariants of symmetry groups of differential equations [pdf]. Foundations of Computational Mathematics 8 (2008), 501 &ndash 532.
  • Peter Olver, Juha Pohjanpelto, Moving Frames and Differential Invariants for Lie Pseudogroups [pdf]. In Symmetry and Pertubation Theory, Proceedings of the International Conference on SPT 2007, G. Gaeta, R. Vitolo, S. Walcher (Eds.), World Scientific (2007), 172 &ndash 180.
  • Peter Olver, Juha Pohjanpelto, Differential Invariants for Lie Pseudo-Groups [pdf]. In Groebner Bases in Symbolic Analysis, M. Rosenkrantz, D. Wong (Eds.), de Guyter (2007), 217 &ndash 244.
  • Jeongoo Cheh, Peter Olver, Juha Pohjanpelto, Maurer-Cartan equations for Lie symmetry pseudogroups of differential equations [dvi, ps].Journal of Mathematical Physics 46 (2005), 023504.
  • Peter Olver, Juha Pohjanpelto, Regularity of pseudogroup orbits [dvi, ps]. In Proceedings of Symmetry and Pertubation Theory 2004, G. Gaeta, B. Prinari, S. Rauch-Wojciechowski, S. Terracini (eds.), World Scientific, Singapore (2005), 244 &ndash 254.
  • Peter Olver, Juha Pohjanpelto, Maurer-Cartan forms and the structure of Lie pseudo-groups [pdf]. Selecta Mathematica 11 (2005), 99 &ndash 126.
  • Stephen Anco, Juha Pohjanpelto, Symmetries and currents of massless neutrino fields, electromagnetic and graviton fields [dvi, ps]. In Symmetry in Physics: In Memory of Robert T. Sharp, P. Winternitz, J. Harnad, C. S. Lam, J. Patera (eds.), CRM Proceedings and Lecture Notes, Vol. 34 (2004), 1 &ndash 12.
  • Juha Pohjanpelto, Classification of generalized symmetries of Yang-Mills fields with a semi-simple structure group [dvi, ps]. Differential Geometry and its Applications 21 (2004), 147 &ndash 171.
  • Stephen Anco, Juha Pohjanpelto, Conserved currents of massless fields of spin s ≥ 1/2 [dvi, ps]. Proceedings of the Royal Society A 549 (2003), 1215 &ndash 1239.
  • Stephen Anco, Juha Pohjanpelto, Classification of local conservation laws of Maxwell's equations [dvi, ps]. Acta Applicandae Mathematicae 69 (2001), 285 &ndash 327.

• In Preparation
  • Cohomology of the variational bicomplex invariant under the symmetry group of the PKP equation.
  • Variational principles for third order natural differential operators in metric field theories (with Ian M. Anderson).

• Doctoral Students
  • Jonner Barrett, Thesis: Conserved densities for the nonlinear Schrodinger equation, in progress.

• Master's Students
  • Kyle Hickman, Paper: Structure Equations for the Generalized Fisher Equation (June 2005).