Events
Department of Mathematics and Statistics
Texas Tech University
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. 25
|
| Algebra and Number Theory
No Seminar
|
Analytical surfaces have an important place in differential geometry. These surfaces are frequently used in geometric design. The ability to define such surfaces with parametric and implicit equations is very useful for modeling with "computer-aided geometric design". In this study, we consider some characterizations of magnetic surfaces, which are an important type of analytical surfaces. Carved surfaces and also Monge surfaces are interesting examples of magnetic surfaces. Among them, molding surfaces are quite impressive in terms of aesthetics in architectural design and exterior cladding of buildings.
US CDT is UTC-5. This Differential Geometry, PDE and Mathematical Physics seminar is available over zoom.
Abstract: Physics-informed neural networks (PINNs) provide a promising framework for solving inverse problems governed by partial differential equations (PDEs) by integrating observational data with physical constraints into a unified optimization objective. However, the inherently ill-posed nature of PDE inverse problems renders PINNs highly sensitive to noise. Even a small fraction of corrupted observations can distort the learned representations, significantly degrading accuracy and destabilizing training. Motivated by recent advances in machine unlearning and structured network pruning, we propose P-PINN, a selective pruning framework that removes the influence of corrupted data from a pretrained PINN. Numerical experiments on a diverse set of PDE inverse-problem benchmarks demonstrate that P-PINN significantly enhances robustness, accuracy, and training stability under noisy conditions, achieving up to a 96.6% reduction in relative error compared to baseline PINNs.
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
Intra-tumour heterogeneity, either the product of genetic mutations or phenotypic adaptation, is a leading cause of treatment failure and disease progression in cancer. Accordingly, there is increased interest in the development of mathematical approaches that capture this heterogeneity and its role in the development of treatment resistance. Here, I'll discuss some recent work focused on developing mathematical approaches to understand the emergence of treatment resistance in preclinical experiments of treatments for solid cancers from both agent-based and continuum perspectives.
The Biomath seminar may be attended virtually Friday at 11:00 AM CDT (UTC-5) via this Zoom link.
Meeting ID: 938 8653 3169
Passcode: 883472
abstract noon CDT (UTC-5)
Zoom link available from Dr. Brent Lindquist upon request.
