Events
Department of Mathematics and Statistics
Texas Tech University
This Statistics seminar is also the Qualifying Exam for Thilini Weerasekara. Since it starts early, attendance is not mandatory for grad students.
Committee Members:
Dr. Fangyuan Zhang (Chair)
Dr. Alex Trindade
Dr. Asim Dey
An under-appreciated notion from Mathematics is that of a mapping space. In many circumstances, a class of maps between two topological spaces might be a topological space of its own. This notion is generalized into the notion of an internal hom-object in several branches of Math. For example in Measure theory, this allows mapping spaces between measurable spaces to be treated as new measurable spaces, and in higher-order logic, it is a bedrock of the Curry-Howard-Lambek correspondence. I will present the structural interpretation of a mapping space, some examples and challenges in realizing them for ordinary topological or measurable spaces. As an application, I will show how this naturally leads to the notion of a path-space and shift-space for dynamical systems, and how they are defined uniquely by universal properties.
 | Wednesday
Mar. 11
|
| Algebra and Number Theory
No Seminar
|
Abstract: Second-order differential equations arise naturally in many physical and biological applications, including molecular dynamics, string vibration, and spatial discretization of wave equations. For their time integration of such systems, classical Runge-Kutta-Nyström integrators and their extended variants are widely used. While effective for small-scale or non-stiff problems, these methods often suffer from stability restrictions and inefficiency when applied to large, stiff, or highly oscillatory systems. To address these limitations, we develop and analyze a new class of time integration methods, termed exponential Nyström (expN) methods. These methods permit significantly larger time steps without sacrificing accuracy. Within the framework of strongly continuous semigroups on a Banach space, we prove convergence results up to fifth-order accuracy, with error bounds independent of the stiffness or high frequencies of the system. Our numerical experiments demonstrate that the proposed expN methods outperform existing Nyström-type integrators in both efficiency and accuracy.
This work is a collaboration with Professor V.T. Luan.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this
Direct Link that embeds meeting and ID and passcode.
- Choice #2: Log into zoom, then join by manually entering the meeting ID and passcode ...
* Meeting ID: 949 9288 2213
* Passcode: Applied
TTU Math Circle Spring Flyer 6:30-7:30 PM Thursdays in the basement of Math, room 010
abstract 2 PM CDT (UTC-5)
Zoom link available from Dr. Brent Lindquist upon request.
