I strongly support undergraduate research opportunities in which students work closely with a faculty mentor to produce new knowledge within a field of mathematics.
Student Researchers:
Mea Simonsen
Ezra Fader
Objectives:
Create a Maple database within the DifferentialGeometry package for the 6-dimensional Lie algebras appearing in the Snobl-Winternitz classification. (x)
Classify (up to Lie algebra automorphism) all 2-dimensional subspaces of these 6-dimensional Lie algebras which are bracket-generating. (x)
Find explicit homogenous models of these distributions and calculate their symmetry algebras. (o)
-- funded by the Southern Oregon Unviersity STEMReX program.
Classification of 7-Dimensional Symmetry Subalgebras | Summer 2022 - Present
Student Researchers:
Andrew Eskenazi
Objectives:
Classify all 7-dimensional symmetry subalgebras (up to Lie algebra automorphism) of the maximally symmetric Monge equations on 6-manifolds:
) z' = (y''')^2
) z'' = (y'')^2
List those subalgebras which act intransitively on the equation manifold.
Student Researchers:
Jonny Burt
Patrick Latham
Objectives:
Calculate classical and nonclassical symmetries of Klein and Sine-Gordon equations. (x)
-- funded by the Southern Oregon Unviersity STEMReX program.
Student Researchers:
Lily Colas
Objectives:
Calculate classical and nonclassical symmetries equations appearing in mathematical neuroscience. (x)
Student Researchers:
William Helman
Daniel Sinderson
Objectives:
Calculate classical and nonclassical symmetries of the Gibbons-Tsarev and Born-Infeld equations. (x)
Classify 1-dimensional subalgebras and their normalizers. (x)
Find group-invariant solutions for each equation. (x)
-- funded by the Southern Oregon Unviersity STEMReX program.