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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.
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.
(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.
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.
The OSU Department of Mathematics will host the Annual Meeting of the Pacific Northwest Section of the MAA to be held on April 1-2, 2016. The eighth annual Northwest Undergraduate Mathematics Symposium (NUMS) will be embedded within the larger annual meeting.
The purpose of the Pacific Northwest Section is to advance collegiate-level mathematics on a regional level as well as to provide professional development and networking activities for section members and mathematics students. Much of the section’s activities center around the annual meeting, including Project NExT (New...
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...
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!