2013: Professor Smith supervised two honors students,
and Molly Logue, together with PhD student Robert Walker, on an NSF-funed REU project investigating the connections between mononomial valuations of k(x,y) and continued fractions.
You can see the paper
Monomial Valuations, Cusp Singularities, and Continued Fractions
on the arxiv.
2005-current: As PI on Michigan RTG grant for algebraic geometry and its boundries, Karen Smith helped distribute NSF funds to four undergraduate students each summer.
2002: Professor Smith funded through her NSF grant a team of four students to research problems in
combinatorics under the direction of Assistant Professor
now at Dartmouth College.
Maggie Peters investigated applications of
linear algebra to building effective internet search engines,
and also to analyzing voting patterns in the United Nations. Maggie is now professor of political science at Yale, after doing a PhD in political science at Stanford.
Betseygail Rand, who eventually went on to get
a PhD from U Texas and is now a professor at Texas Lutheran, conducted research with Professor
Smith on sparse matrices. The project was assisted by (then) PhD student
Amanda Johnson. The goal is to find matrices with as many
zero entries as possible which still have many non-zero sub-determinants.
As the number of non-zero determinants increases, so must the number of
non-zero entries. How can one describe this function?
This has applications to finding sparse systems of parameters
for projective algebraic varieties.
For more information on undergraduate research opportunities,
see Christine Betz in the Math Office, East Hall 2084.