Events
Department of Mathematics and Statistics
Texas Tech University
In this talk, we will go through what closure and interior
operations are and some ways they are used, what that has to do with
inner product spaces, and how that leads us to consider pair
operations. Expanding on the work of Kemp, Ratliff and Shah, for any
closure cl defined on a class of modules over a Noetherian ring, we
develop the theory of cl-prereductions of submodules and the dual
notion of i-postexpansions. Pair operations can be endowed with
specific properties: we will consider how they behave under Matlis
duality, how combining them can force the operation to become the
constant or the identity operation, and how pair operations can be
constructed in a multitude of ways to preserve properties.
There are similar characterizations in terms of complexes of flat
modules and complexes of injective modules.
Follow the talk via this Zoom link
Meeting ID: 913 0074 4693
Passcode: 586188
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of complexity one can assign to the repeated iterations of the map. One of the foundational discoveries of dynamical systems theory is that these have a common limit, known as the topological entropy of the system. This talk presents a category-theoretic view of entropy. Category theory is a structural approach to mathematics, in which mathematical properties are derived as consequences of structural arrangements rather than internal properties. The category theoretic approach reveals how the common limit is a consequence of the structural assumptions on these notions. The various notions of complexity are expressed as functors, and natural transformations between these functors lead to their joint convergence to the common limit.
Preprint link
Abstract. Moving boundary (or often called "free boundary") problems are ubiquitous in nature and technology. A computational perspective of moving boundary problems can provide insight into the "invisible" properties of complex dynamics systems, advance the design of novel technologies, and improve the understanding of biological and chemical phenomena. However, challenges lie in the numerical study of moving boundary problems. Examples include difficulties in solving PDEs in irregular domains, handling moving boundaries efficiently and accurately, as well as computing efficiency difficulties. In this talk, I will discuss three specific topics of moving boundary problems, with applications to ecology (population dynamics), plasma physics (ITER tokamak machine design), and cell biology (cell movement). In addition, some techniques of scientific computing will be discussed.
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room MATH 011 (basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 944 4492 2197
* Passcode: applied
 | Thursday
Feb. 29
6:30 PM
MA 108
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| Mathematics Education
Math Circle
Jeff Lee
Mathematics and Statistics, Texas Tech University
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Math Circle spring poster