Mat Titus who received Graduate School Travel award to defer travel costs to the Joint Mathematics Meeting in Seattle, January where he will give an oral presentation. Congratulations!
The Center for Computing Research (CCR) at Sandia National Laboratories seeks multiple students to participate in collaborative research across a wide range of areas in computer science, applied mathematics, discrete mathematics, mathematical modeling, computational science and engineering, computational neuroscience and cognitive science (including cognitive and experimental psychology, neuroscience, and linguistics). To access the posting, go to http://www.sandia.gov , click on “Careers” then click on “View All Jobs” and search for the job opening number - 651287 for graduate students and 651289 for undergraduates. Applications should include a CV and a cover letter describing the area that they would like to gain research experience. Students must have a cumulative GPA of 3.5/4.0 and be legally authorized to work in the United States of America. Desired Qualifications include (1) Software development and programming experience (C++, C, Fortran, Matlab, Java, Python), (2) Knowledge or the interest to learn parallel programming such as MPI,...
Translation surfaces are topological surfaces that when punctured are equipped with an atlas of local charts to the complex plane for which the transition functions are translations. This atlas gives us a well defined notion of whether or not a map from one translation surface to another has a constant Jocobian or is 'affine'. The Veech group of a translation surface is the group of Jacobians of orientation preserving affine self homeomorphisms of the surface. The size of this group can inform us on the dynamics (periodic/ergodic) of the geodesic flow in a given direction [Veech 1989].
Last spring I restricted to a certain class of translation surfaces, and introduced an infinite set of points on a toy translation surface whose stabilizer is the Veech group of our original surface. I will present the successful generalization of this construction to all translation surfaces, as well as demonstrate the need for only a finite subset of these points when testing all matrices up to a given Frobenius norm.
This talk will be a survey of problems and results about the volume of certain geometrically interesting subsets of Euclidean space. For example, we will describe Gromov’s waist inequality for spheres, and Gromov's conjectured waist inequality for cubes. The waist inequality for cubes would be a deep non-linear generalization of the cube slicing inequality proved by the speaker in 1978. Another interesting problem is the volume of the set of points in Euclidean space which are the coefficients of a polynomial with Mahler measure bounded by 1. This set is the unit ball for a non-convex distance function, and turns out to have a volume which is a rational number in each dimension. As time permits, several further problems and results about the volume of interesting sets will be described. The talk will be mostly expository, and suitable for a general mathematical audience.
Understanding rainfall patterns is and will be a challenge for those working in hydrological sciences. The complexity of rainfall resembles turbulence (not phenomenologically), and some models for describing rainfall have been inspired by turbulence. In this lecture, some ideas about the statistical description of rainfall will be presented, and how some of its geometrical features obtained from the fractal geometry can help us to identify symmetries in the physical process of rainfall. These symmetries are indexed by time and if one identifies the breaking of these symmetries, the space-time dynamics of rainfall could be explained. Some approaches related to the latter statement will also be discussed.
(Work with Richard Bumby, Rutgers)
The divided cell algorithm was designed in the 1950s to answer questions about non-homogeneous approximation. This talk will begin with a review the history of known results on the structure of both the homogeneous and non-homogeneous Markoff spectra as well as the geometric interpretation of continued fractions that inspired the divided cell algorithm. We will then restrict our attention to the divided cell algorithm and describe how a finer analysis of its structure is providing new information on the non-homogeneous spectrum.
The collection of metabolisms that process and regulates iron inside the cell is called cellular iron homeostasis. Scientists have been interested in understanding these processes better due to the links that have been found between the anomalous cellular iron homeostasis and several diseases, like diabetes, Alzheimer's, and breast cancer. Anomalous iron homeostasis can raise or decrease the iron levels in an organism, with high levels of cellular iron being toxic to the cell whilst low levels of iron hinder the cellular growth. Different models that simulate iron homeostasis have been provided in the past, mainly focused on the iron inside of the cytoplasm, but there is relevance also in the iron inside of the mitochondria, since it is linked with diseases like Friedreich's Ataxia or malfunction of the mitochondria. In this talk, we present a different model that seeks to simulate cytoplasmic iron and also the levels of mitochondrial iron. This model includes a robust system of differential equations within the biologically relevant framework (i.e., positive parameters and state variables). It is proven that the system has at least one equilibrium point and the nonoccurrence of bifurcation. We also provide some tools applied for the study of the stability of the system and numerical results that point out asymptotic stability.
This study presents a hybrid-mixed stress model for the dynamic analysis of structures. In this model, both the stress and the displacement fields are approximated in the domain of each Element, while the Dirichlet boundary conditions are also imposed in a weighted residual form. While different approximation functions can be used in this framework, in this presentation the orthonormal Legendre polynomials are selected as approximation functions, as the selection of these functions enables the use of analytical closed form solutions for the computation of all structural operators, which leads to the development of very effective \emph{p-}refinement procedures. The model being discussed is applied to the solution of frame structures, plane elasticity, and Reissner-Mindlin plate bending problems. To validate the model and to illustrate its potential, several numerical examples are discussed and comparisons are made with analytical solutions and solutions obtained using other numerical techniques, such as modal superposition and Newmark time integration.
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