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The National Conference on Undergraduate Research is an annual student conference dedicated to promoting undergraduate research, scholarship, and creative activity in all fields of study. Unlike meetings of academic professional organizations, this gathering of young scholars welcomes presenters from institutions of higher learning from all corners of the academic curriculum. This annual conference creates a unique environment for the celebration and promotion of undergraduate student achievement, provides models of exemplary research and scholarship, and helps to improve the state of undergraduate education.

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Title: Informatics and Modeling Platform for Stable Isotope-Resolve Metabolomics

Abstract: Recent advances in stable isotope-resolved metabolomics (SIRM) are enabling orders-of-magnitude increase in the number of observable metabolic traits (a metabolic phenotype) for a given organism or community of organisms.  Analytical experiments that take only a few minutes to perform can detect stable isotope-labeled variants of thousands of metabolites.  Thus, unique metabolic phenotypes may be observable for almost all significant biological states, biological processes, and perturbations.  Currently, the major bottleneck is the lack of data analysis that can properly organize and interpret this mountain of phenotypic data as highly insightful biochemical and biological information for a wide range of biological research applications.  To address this limitation, we are developing bioinformatic, biostatistical, and systems biochemical tools, implemented in an integrated data analysis platform, that will directly model metabolic networks as complex inverse problems that are optimized and verified by experimental metabolomics data.  This integrated data analysis platform will enable a broad application of SIRM from the discovery of specific metabolic phenotypes representing biological states of interest to a mechanism-based understanding of a wide range of biological processes with particular metabolic phenotypes.

Title:  Smoothness of isometries between subRiemannian manifolds

Abstract:  In a joint work with Enrico Le Donne (Jyvaskyla, Finland), we show that the group of isometries (i.e., distance-preserving homeomorphisms) of an equiregular subRiemannian manifold is a finite-dimensional Lie group of smooth transformations. The proof is based on a new PDE argument, in the spirit of harmonic coordinates, establishing that in an arbitrary subRiemannian manifold there exists an open dense subset where all isometries are smooth.

Title:  Higher-order analogues of the exterior derivative complex

Abstract:  I will discuss some earlier joint work with E. M. Stein concerning div-curl type inequalities for the exterior derivative operator and its adjoint in Euclidean space R^n. I will then present various higher-order generalizations of the notion of exterior derivative, and discuss some recent div-curl type estimates for such operators. Part of this work is joint with A. Raich.

Title:  Automating and Stabilizing the Discrete Empirical Interpolation Method for Nonlinear Model Reduction

Abstract:  The Discrete Empirical Interpolation Method (DEIM) is a technique for model reduction of nonlinear dynamical systems.  It is based upon a modification to proper orthogonal decomposition which is designed to reduce the computational complexity for evaluating reduced order nonlinear terms.  The DEIM approach is based upon an interpolatory projection and only requires evaluation of a few selected components of the original nonlinear term.  Thus, implementation of the reduced order nonlinear term requires a new code to be derived from the original code for evaluating the nonlinearity.  I will describe a methodology for automatically deriving a code for the reduced order nonlinearity directly from the original nonlinear code.  Although DEIM has been effective on some very difficult problems, it can under certain conditions introduce instabilities in the reduced model.  I will present a problem that has proved helpful in developing a method for stabilizing DEIM reduced models.

A talk by Kathleen Fitzpatrick, Professor of Media Studies, Ponoma College and Director of Scholarly Communication, Modern Language Association. What if the academic monograph is a dying form? If scholarly communication is to have a future, it's clear that it lies online, and yet the most significant obstacles to such a transformation are not technological, but instead social and institutional. How must the academy and the scholars that comprise it change their ways of thinking in order for digital scholarly publishing to become a viable alternative to the university press book? This talk will explore some of those changes and their implications for our lives as scholars and our work within universities.