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:  Sub-Exponential Decay Estimates on Trace Norms of Localized Functions of Schrodinger Operators

Abstract:  In 1973, Combes and Thomas discovered a general technique for showing exponential decay of eigenfunctions. The technique involved proving the exponential decay of the resolvent of the Schrodinger operator localized between two distant regions. Since then, the technique has been applied to several types of Schrodinger operators. Recent work has also shown the Combes–Thomas method works well with trace class and Hilbert–Schmidt type operators. In this talk, we build on those results by applying the Combes–Thomas method in the trace, Hilbert–Schmidt, and other trace-type norms to prove sub-exponential decay estimates on functions of Schrodinger operators localized between two distant regions.

In the wake of the triple disasters of March 11, 2011 which devastated the Tohoku region of Japan with a massive earthquake, an enormous set of tsunami, and the catastrophic failure of the Fukushima Dai-ichi nuclear reactor, both Japanese and foreign observers struggled to make sense of these events.  Bestor examines some ways in which Japanese culture frames disasters, and based on fieldwork in Tohoku in 2011 and 2012, how local meaning-making unfolds.

This event is free, open to the public, and sponsored in part by:  The Department of Anthropology, Student Government Association, and the Japan/America Society of Kentucky.

In the wake of the triple disasters of March 11, 2011 which devastated the Tohoku region of Japan with a massive earthquake, an enormous set of tsunami, and the catastrophic failure of the Fukushima Dai-ichi nuclear reactor, both Japanese and foreign observers struggled to make sense of these events.  Bestor examines some ways in which Japanese culture frames disasters, and based on fieldwork in Tohoku in 2011 and 2012, how local meaning-making unfolds.

This event is free, open to the public, and sponsored in part by:  The Department of Anthropology, Student Government Association, and the Japan/America Society of Kentucky

Title:  On the ground state of the magnetic Laplacian in corner domains

Abstract:  I will present recent results about the first eigenvalue of the magnetic Laplacian in general 3D-corner domains with Neumann boundary condition in the semi-classical limit.  The use of singular chains show that the asymptotics of the first eigenvalue is governed by a hierarchy of model problems on the tangent cones of the domain. We provide estimations of the remainder depending on the geometry and the variations of the magnetic field. This is a joint work with V. Bonnaillie-Nol and M. Dauge.

Title:  Compressible Navier-Stokes equations with temperature dependent dissipation

Abstract:  From its physical origin, the viscosity and heat conductivity coe!cients in compressible fluids depend on absolute temperature through power laws. The mathematical theory on the well-posedness and regularity on this setting is widely open. I will report some recent progress on this direction, with emphasis on the lower bound of temperature, and global existence of solutions in one or multiple dimensions. The relation between thermodynamics laws and Naiver-Stokes equations will also be discussed. This talk is based on joint works with Weizhe Zhang.