Zoom Meeting: https://ncsu.zoom.us/j/93046132033?pwd=dkZiTjlKazgzK2Q3aXJra1g2R1Q0dz09 Meeting ID: 930 4613 2033 Passcode: 075251
Reading’s shard intersection order is a lattice structure on a finite Coxeter group which is weaker than the weak order. This structure also appears in the representation theory of finite-dimensional algebras as the inclusion order on certain subcategories of modules. Algebraically, the cover relations of this lattice are traversed by applying a “reduction operation” associated…
The speakers will talk about how to use Gradescope to streamline the grading process for assignments and exams. No experience with Gradescope is assumed, but the speakers will share tips that will benefit experienced users as well as newbies. Participants will be able to join a demo course to experience Gradescope from both the student…
Zoom Meeting: https://ncsu.zoom.us/j/93046132033?pwd=dkZiTjlKazgzK2Q3aXJra1g2R1Q0dz09 Meeting ID: 930 4613 2033 Passcode: 075251
We describe an algorithm to compute Whitney stratifications of real algebraic varieties. The basic idea is to first stratify the complexified version of the given real variety using conormal techniques, and then to show that the resulting stratifications admit a description using only real polynomials. This method also extends to stratification problems involving certain basic…
A theorem of Liouville asserts that the simplest conformal transformations on Euclidean space---translations, dilations, reflections, and inversions---generate all conformal transformations when the dimension is at least 3. I will describe a new proof of this theorem which is shorter and more elementary than the argument, due to Nevanlinna, found in most modern textbooks.
Determining the sensitivity of model outputs to input parameters is an important precursor to developing informative parameter studies, building surrogate models, and performing rigorous uncertainty quantification. Determining parameter sensitivities over a range of parameter values, termed global sensitivity analysis, requires many model evaluations sampled over the parameter space, which is intractable for many large-scale computational…
Speaker’s webpage: https://math.sciences.ncsu.edu/people/jpmather/
Research shows inequitable participation patterns are pervasive in mathematics classrooms. Thus, an important consideration for mathematics instructors is promoting participation by students with historically marginalized backgrounds. Existing literature often focuses on identifying and countering mathematics instructors’ implicit biases against minoritized students. However, redressing inequitable participation patterns requires changing social practices, looking beyond individual minds. In…
We discuss a sharp area estimate for minimal submanifolds that pass through a prescribed point in a geodesic ball in a space form. The estimate in Euclidean space was first conjectured by Alexander, Hoffman, and Osserman in 1974 and proven in full generality by Brendle and Hung in 2017. We will show the sharp area estimate also holds…
We introduce a Swarm-Based Random Descent (SBRD) method for non-convex optimization. The swarm consists of agents, identified with positions, x, and masses, m. There are three key aspects to the SBRD dynamics: (i) persistent transition of mass from high to lower ground; (ii) marching along the gradient descent: an m-dependent random choice of marching direction…
This talk will introduce cluster algebras, with an emphasis on their combinatorics, and describe a recent joint result with Vincent Pilaud and Sibylle Schroll. At the heart of a cluster algebra is a complicated, branching recursion that defines cluster variables (certain rational functions organized into finite sets called clusters). The recursion looks bizarre at first…
In this talk we present some recent result about the long time behavior of the solutions for some diffusion processes on a metric graph. We study evolution problems on a metric connected finite graph in which some of the edges have infinity length. We show that the asymptotic behaviour of the solutions of the heat…
Chromatin structure tightly regulates gene expression and epigenetic processes. The nuclear environment is complex, featuring tension exerted by force-generating proteins and molecular crowding modulated by different ionic concentrations. Understanding the impact of these factors on chromatin structure is crucial for elucidating the molecular mechanisms of chromatin accessibility and organization. However, it is unclear how chromatin…
It is common to assume that the data was sampled from a low-dimensional manifold in a high-dimensional space. In real life, neither the dimension of this manifold nor its geometry is known, and the data is often contaminated with noise and outliers. In this talk, we first present a method for denoising and reconstructing a…
In traditional Euclidean geometry, points serve as the foundational elements for constructing and analyzing space. In contrast, Laguerre geometry, a non-Euclidean geometry, uses oriented circles (or hyperspheres, in the context of higher dimensions) and oriented lines (or hyperplanes), as fundamental objects. Here, a “point” is simply a circle with radius zero, i.e. having no special…