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Seminars and Colloquia
3:30-4:30 PM every other Monday (starting 9/18/17), 103 Centennial Hall
Hyperspace and Topology Seminar
3-5 PM on selected Wednesdays, Rolla G5
10:50 AM-12:20 PM on selected Thursdays, Rolla G4
Real Analysis Seminar
3:30-4:30PM every other Monday (starting 9/25/17), 103 Centennial Hall
Time Scales Seminar
3:00-3:50 PM every Wednesday, Rolla G4
After he retired following the Fall 2002 semester, Professor W.T. Ingram, who was department chair from 1989-1998, generously set up an endowed fund to be used to bring well-known mathematical scientists to Rolla to give lectures on their work. All Ingram Lectures are open to the entire S&T community, and are widely advertised on campus. Visitors brought here under this program usually give two lectures, one of a general nature and accessible to students, and another more advanced aimed at faculty (though students are certainly welcome).
Fall 2017 Colloquia
Asymptotic behavior for the nonlinear Schrödinger equation with critical homogeneous nonlinearity
Department of Systems Innovation
Graduate School of Engineering Science
Friday, September 22, 2017
Rolla Bldg G-5
We will consider asymptotic behavior of solutions to nonlinear Schrödinger equations with a homogeneous nonlinearity of critical degree. It was previously known that for the critical case, the possible asymptotic behavior heavily depends on the shape of nonlinearity. In this talk, we consider general homogeneous nonlinearities including the non-polynomial case and discuss how to determine the behavior. We also discuss an application to Klein-Gordon equation.
Dr. Masaki earned his PhD in Mathematics from Kyoto University in the Spring of 2009 under the supervision of Yoshio Tsutsumi. He began his career at Gakushuin University in Spring 2010 as an Assistant Professor. In Fall 2012, he moved to Hiroshima University as an Associate Professor. Since Spring 2016, he has been an Associate Professor at Osaka University. Dr. Masaki's main research interests lie in the areas of harmonic analysis and nonlinear dispersive equations, with a primary focus on the asymptotic behavior of solutions to nonlinear Schrödinger equations.
On a modification of the Schur algorithm that leads to linear pencils of difference operators
Visiting Assistant Professor
Department of Mathematics
University of Mississippi
Friday, September 15, 2017
Rolla Bldg G-5
The Schur algorithm is one of the key ingredients of the theory of orthogonal polynomials on the unit circle. It is worth noting that the theory of orthogonal polynomials on the unit circle has witnessed a great development since the beginning of the century due to an enormous contribution by Barry Simon. However, the modification we are going to discuss was implicitly introduced by H.S. Wall in 1944 and it can be thought of as a transform between Schur functions, Carathéodory functions, and Herglotz-Nevanlinna functions. At the same time, this transformation provides us with a bijection between orthogonal polynomials on the unit circle and some new objects on the real line. More precisely, it will be shown that, when applying the Wall transformation, instead of orthogonal polynomials on the real line, we get a sequence of orthogonal rational functions that satisfy three-term recurrence relation of the form (H−λJ)u=0, where u is a semi-infinite vector, whose entries are rational functions. Besides, J and H are Hermitian Jacobi matrices for which a version of the Denisov-Rakhmanov theorem holds true.
For past colloquium information, click here.