Events
Department of Mathematics and Statistics
Texas Tech University
The Helfrich functional is a type of elastic energy which extends the well-known Willmore energy. The Euler-Lagrange equation describing equilibria is a fourth order nonlinear elliptic partial differential equation the understanding of which is essential to analyze the morphology of cellular membranes.
In this talk, we present a second order reduction of this Euler-Lagrange equation, known as the reduced membrane equation, and exploit its properties to analyze the original fourth order equation.
The cobordism hypothesis classifies extended topological quantum field theories (TQFTs) in terms of algebraic information in the target category. One of the core principles in quantum field theory - unitarity - says that state spaces are not just vector spaces, but Hilbert spaces. Recently in joint work with many others, we have defined unitarity for extended TQFTs, inspired by Freed and Hopkins. Our main technical tool is a higher-categorical version of dagger categories; categories $C$ equipped with a strict anti-involution $\dagger: C \to C^{op}$ which is the identity on objects. I explain joint work in progress with Theo Johnson-Freyd, Cameron Krulewski and Lukas Müller in which we prove a version of the cobordism hypothesis for unitary TQFTs. The main observation is that the \emph{stably} framed bordism $n$-category is freely generated as a symmetric monoidal dagger $n$-category with unitary duals by a single object: the point.We will discuss several algebraic public key exchange proposals involving semigroups, highlighting similarities and differences and the best known attacks on each.
Join the Zoom Meeting at 3 PM (CST UT-6)
Meeting ID: 958 5298 7437
Passcode: 922447
"Nanofluids: Small Name, Big Impact!" With advancements in nanotechnology and the growing need for efficient thermal management, nanofluids have emerged as innovative replacements for conventional fluids. These engineered fluids leverage the superior thermal conductivity and enhanced surface area of nanoparticles to significantly boost heat and mass transfer properties. As a result, nanofluids are revolutionizing applications in energy systems, cooling technologies, and biomedical devices, delivering unparalleled efficiency and performance in systems demanding precise thermal regulation and improved fluid dynamics.
In this talk, we will delve into nanofluids' evolution, applications, and mathematical modeling, focusing on optimizing the thermal performance of hybrid nanofluids using advanced tools like response surface methodology and artificial neural networks.
This presentation may be viewed in the TTU Mediasite catalog via eraider login.