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Algebra and Combinatorics Seminar: Eric Hanson, NC State, Finite-dimensional algebras and the shard intersection order

SAS 4201

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…

Algebra and Combinatorics Seminar: Martin Helmer, NC State, Effective Whitney Stratification of Real Algebraic Varieties

SAS 4201

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…

Geometry and Topology Seminar: Mathew Kushelman, NC State, On Liouville’s Theorem for Conformal Maps

SAS 1216

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.

Applied Math Graduate Student Seminar: Walker Powell, NC State, Quasiglobal Sensitivity Analysis for Computational Fluid Dynamic

SAS 4201

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…

Teaching and Learning Seminar: Sunghwan Byun, NC State College of Education, : Knowledge in Interaction: A Key to Promote Participatory Equity During Whole-Group Discussions

SAS 4201

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…

Colloquium: Eitan Tadmor, University of Maryland, Swarm-Based Random Descent Method for Non-Convex Optimization

SAS 4201

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…

Algebra and Combinatorics Seminar: Nathan Reading, NC State, Posets for cluster variables in cluster algebras from surfaces

SAS 4201

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…

Differential Equations Seminar and Nonlinear Analysis Seminar: Liviu Ignat, Institute of Mathematics, Simion Stoilow of the Romanian Academy, Romania, Asymptotic behavior of solutions for some diffusion problems on metric graphs

Zoom

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…

Biomathematics Seminar: Xingcheng Lin, Genome Organization from the Ground Up – Deciphering Molecular Mechanisms for Chromatin Organization

Cox 306

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…

Computational and Applied Mathematics Seminar: Shira Faigenbaum-Golovin, Duke University, Reconstruction, denoising, and studying the geometry of the base manifold in high-dimension space

SAS 4201

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…

Geometry and Topology Seminar: Ruzica Mijic, Technical University of Vienna, An Introduction to Laguerre Geometry

SAS 1216

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…

Algebra and Combinatorics Seminar: Corey Jones, NC State, Quantum cellular automata on fusion spin chains

SAS 4201

Quantum cellular automata (QCA) are models of discrete-time unitary dynamics of quantum spin systems. They can be characterized algebraically as certain automorphisms of the associative algebra generated by local observables of a spin system. We will give a gentle introduction to this topic, and explain some of our recent contributions to the problem of classification…