Mentors and Projects

Dr. Banuelos' groups

The genome of organisms is composed of the letters {A, G, C, T} and changes to its composition are known as genomic variants. Detecting and understanding these variations have implications in health and personalized medicine. Students and community college faculty working with Dr. Banuelos will incorporate machine learning approaches to detect how groups (or coalitions) of genomic mutations affect quantitative phenotypes in individuals. Dimension-reduction techniques provide a population-level map of these genomic differences. One project will focus on creating a supervised learning framework to predict statistically significant genomic variant groupings. The other project will aim to use an unsupervised learning approach to infer population structure and uncover other significant mutations.

Students wishing to work on these projects should have a solid foundation in linear algebra and elementary statistics. Computational experience is welcome - we will use Python in this research project.

Dr. Forgacs' groups

Students working with Dr. Forgács will study (generally speaking) hyperbolicity preserving linear operators on R[x] which are diagonal in certain bases. Their action in these bases can therefore be understood as multiplication by scalars, giving rise to the notion of a B-multiplier sequence, where B is a particular basis. Laguerre-Pólya theory tells us that certain functions interpolate B-multiplier sequences. One project will aim to characterize the collection of even polynomials which interpolate Legendre multiplier sequences, while another will seek to complete a characterization of Hermite diagonal operators H in terms of the coefficient polynomials in the representation H=\sum Q_k(x)D^k, following a 2014 paper considering this problem .

Students wishing to work on these projects should have a solid foundation in calculus (real and/or complex analysis is a plus) and linear algebra. Computational experience is welcome - we will use Mathematica extensively for our investigations.