In order to explain the bi-concave shape of red blood cells, Helfrich proposed to study the minimisation of a bending energy amongst closed surfaces with given fixed area and volume. In the homogeneous case, the Helfrich functional simplifies to the scaling invariant Willmore functional. Thus, for the minimisation, the two constraints on area and volume…
Zoom link sent via email.
The first SIAM event of the semester will be a MATLAB tutorial! This will be a two-part series, starting from the basics of MATLAB coding and building further into more complicated coding necessities. People with all levels of coding backgrounds are welcome to attend and there will be something new for everyone! We especially recommend…
Hello fellow graduate students! Are you completely new to LaTeX, and need to learn before your first homework? Are you already familiar and looking to practice some basic skills? Are you looking for some nice templates for use in your courses? Come to the Intro to LaTeX workshop on August 20th from 1:55-2:45, during the…
For this week, we have a special Algebra and Combinatorics meet & greet where we'll get to chat informally and discuss some ideas for the seminar and the upcoming talks. Join Zoom Meeting https://ncsu.zoom.us/j/98353887156?pwd=cUN6VnNwbHQ5Vyt2aFVCZmVPNm5nQT09 Meeting ID: 983 5388 7156 Passcode: Alg&Com21
Determining anomalies in data using classical machine learning techniques typically requires characterizing the notion of what is "normal" or "expected" in the instance space. Upon doing so, one would then utilize this profile to identify points that do not coincide with this description of normal. However, this process tends to be costly computationally, thus limiting…
I will give a brief introduction to Heegaard Floer homology and survey what's known about its "extended" structure via Lipshitz-Ozsvath-Thurston's bordered Floer homology and Douglas-Lipshitz-Manolescu's cornered Floer homology. Then I will sketch a connection between this extended structure and a more algebraic problem, the construction of tensor products for higher representations, arising from my recent work with…
The first SIAM event of the semester will be a MATLAB tutorial! This will be a two-part series, starting from the basics of MATLAB coding and building further into more complicated coding necessities. People with all levels of coding backgrounds are welcome to attend and there will be something new for everyone! We especially recommend…
In this talk, I will share with you what kind of problems I work on and what's my motivation. We will talk about the representation theory of finite groups and symmetric functions, and how algebraic combinatorics appears in the less expected places. This talk aims to be mostly informal and accessible for grad students. Speaker’s…
The issue of parameter identifiability is a pervasive one in determining model parameters from data, specifically in trying to answer whether unique parameter estimation is possible for a given problem. Many related definitions of identifiability with subtle distinctions can be found in existing literature, and in this talk, we highlight some of the most utilized…
Often in large numerical simulations decisions are made to reduce the fidelity of particular features in order to simulate the event duration. One common method is the application of shell formulations instead of 3D continuum, especially for objects with large aspect ratios of extent to thickness. While these reductions allow for longer duration events to…
In the 1980s Xavier proved that a complete non-planar minimal surface with bounded curvature of $\mathbb{R}^{3}$ can not lie in half-space. In 1990, Hoffman-Meeks proved that this half-space property holds for properly immersed non-planar minimal surfaces of $\mathbb{R}^{3}$ as well. And they went further, proving what is called "the strong half-space theorem" that states that…
In 2018, Khovanov and Robert introduced a version of Khovanov homology over a larger ground ring, termed U(1)xU(1)-equivariant Khovanov homology. This theory was also studied extensively by Taketo Sano. Ross Akhmechet was able to construct an equivariant annular Khovanov homology theory using the U(1)xU(1)-equivariant theory, while the existence of a U(2)-equivariant annular construction is still…
In this talk we present well posedness of Measure Differential Equations, i.e. evolution equations in the Wasserstein space of probability measures driven by dissipative probability vector fields. We take inspiration from the theory of \emph{dissipative operators} in Hilbert spaces and of Wasserstein gradient flows of geodesically convex functionals. Our approach is based on a measure-theoretic…
Are you a graduate student that has to do a "Preliminary Oral Exam" at some point in the future? Do you also have no idea what a "Preliminary Oral Exam" is? This event is designed for you! As part of the Graduate Training Modules series, MGSA is hosting a "What is a Prelim?" event consisting of…
Fusion categories are algebraic structures that generalize the representation categories of finite groups. I will explain how fusion categories have become involved in diverse areas of mathematics and physics, from topologically ordered phases of matter in 2-dimensions to quantum symmetries of noncommutative spaces. Jointly in person and virtually on Zoom. SAS 4201 for in-person…
Accurate simulations of neutron transport within nuclear reactors are an important component in developing safe and efficient reactors and operation protocols. However, high-fidelity simulations of an entire core are often too costly for use in multi-query applications, such as multi-physics coupling, uncertainty quantification, or optimal experimental design. To facilitate efficient simulations, we utilize a simulation…
The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems. However, efficient numerical solution methods for MHD are extremely challenging due to disparate time and length scales, strong hyperbolic phenomena, and nonlinearity. Therefore the development of scalable, implicit MHD algorithms and high-resolution adaptive mesh refinement strategies…
The ADM mass of an isolated gravitational system is a geometric invariant measuring the total mass due to matter and other fields. I'll describe how to compute this invariant (in 3 spatial dimensions) by studying harmonic functions as well as solutions to other elliptic equations. Recent results in this context will be presented, focusing on applications to…