Doctoral Exam: Jai Aslam, NC State, TDA Applied to Cancer Genomics and Chromatic Hypergraph Catergorification
SAS 2235Advisor is Radmila Sazdanovic
Events
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Pure Math Graduate Student Seminar: Kylan Schatz, NC State, Fusion Rules for G-crossed Extensions of Modular Categories
SAS 2102Determining the fusion coefficients for an abstract fusion category is very difficult, and generalizes the problem of plethysm for group representations. As is the case in finite groups, restricting the class of objects we consider can help us to obtain better general results. When one has a group acting on a modular category, it is possible to…
Numerical Analysis Seminar: Deep Ray, The University of Maryland, VarMiON: A variationally mimetic operator network
SAS 4201Operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input functions that describe material properties, forcing functions and boundary data to the solution of a PDE, i.e., they learn the solution operator of the PDE. In this talk, we consider a new type…
Numerical Analysis Seminar: Deep Ray, University of Maryland, College Park, VarMiON: A variationally mimetic operator network
SAS 4201Operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input functions that describe material properties, forcing functions and boundary data to the solution of a PDE, i.e., they learn the solution operator of the PDE. In this talk, we consider a new type…
Triangle Topology Seminar: Nur Saglam, Georgia Tech , Fillability of Contact Structures on the 3-manifolds obtained by surgeries on the trefoil knot
SAS 4201Let M be the 3-manifold obtained by r-surgery on the right handed trefoil knot. Classification of contact structures on such manifolds have been mostly understood for r\geq 1 and r=0. Etnyre-Min-Tosun has an upcoming work on the classification of the tight contact structures for all r. The fillability of contact structures on M is mostly understood if r is not…
Differential Equations and Nonlinear Analysis Seminar: Ayman Rimah Said, Duke University, Logarithmic spirals in 2d perfect fluids
SAS 4201In this talk I will present recent results with In-Jeong from Seoul national university where we study logarithmic spiraling solutions to the 2d incompressible Euler equations which solve a nonlinear transport system on $\mathbb{S}$. We show that this system is locally well-posed in $L^p, p\geq 1$ as well as for atomic measures, that is logarithmic…
Pure Math Graduate Student Seminar: Alex Betz, NC State, Module Categories and Algebra Objects
SAS 2102When studying Tensor Categories we want to understand what algebra objects can be found in those categories. After finding such objects it's natural to consider their A -modules and more importantly the category of A (bi)-modules. This talk will attempt to explain this concept and enlighten listeners with motivating examples. Zoom Meeting link: https://ncsu.zoom.us/j/92762214990?pwd=MnA1TnNVQUpzUlo3cTM5RmlNWVF4Zz09 Password:…
Numerical Analysis Seminar: Li Wang, University of Minnesota, Neural network based solvers for kinetic equations
SAS 4201Deep learning method has emerged as a competitive mesh-free method for solving partial differential equations (PDEs). The idea is to represent solutions of PDEs by neural networks to take advantage of the rich expressiveness of neural networks representation. In this talk, we will explore the applicability of this powerful framework to the kinetic equation, which…
Biomathematics Seminar: Didong Li, UNC Chapel Hill, Inference for Gaussian processes on compact Riemannian manifolds
Cox 306Gaussian processes (GPs) are widely employed as versatile modeling and predictive tools in spatial statistics, functional data analysis, computer modeling and diverse applications of machine learning. They have been widely studied over Euclidean spaces, where they are specified using covariance functions or covariograms for modelling complex dependencies. There is a growing literature on GPs over…
Special Seminar: Page Thorn, University of Mississippi, The Vector Lattice Tensor Product of Ideals
SAS 4201In this brief talk, I introduce Archimedean Riesz spaces, also known as vector lattices, and their Archimedean Riesz space tensor product as defined by Fremlin. I define what it means to be an ideal in a Riesz space, then provide a counterexample to the statement ``the Fremlin tensor product of ideals is an ideal." Specifically,…
Graduate Training Seminar: Seyma Shabbir, NC State, Setting Up Your Webpage in WordPress
SAS 4201Effective webpages are an increasingly important medium for disseminating information related to classes and research. For TAs, they provide a critical way to share material with your class whereas for those entering the job market, they are often checked by potential employers interested in obtaining more information about candidates. Hence it is important to construct…
Pure Math Graduate Student Seminar: Rachel Morris, NC State, The Mathematics of Adversarial Learning
SAS 2102One common problem in machine learning is to train a computer to correctly classify some data set when the potential set of features is known. However, the problem of classification becomes even more tricky if an adversary gains access to the input data set and can modify the features. In this talk, I will first…
Doctoral Exam: Justin Geddes, NC State, Mathematical Modeling & Signal Processing of Postural Orthostatic Tachycardia Syndrome (POTS)
Cox 306Advisor is Mette Olufsen.
Numerical Analysis Seminar: Pejman Sanaei, Georgia State University, On mathematical modeling and simulation of flight stability of objects, tissue engineering and droplets
SAS 4201In this talk, I will present 3 problems on fluid structure interaction: 1) Flight stability of wedges: Recent experiments have shown that cones of intermediate apex angles display orientational stability with apex leading in flight. Here we show in experiments and simulations that analogous results hold in the two-dimensional context of solid wedges or triangular prisms in planar…
Geometry and Topology Seminar: Dilara Siraeva, Fulbright Scholar, NC State, Symmetry reduction of a gas dynamic system of PDEs with a special state function
SAS 4201In this talk, I will present new results on the symmetry reduction of gas dynamic systems of PDEs following the general framework presented by Lev Ovsyannikov in his article "The “podmodeli” program. Gas dynamics" https://www.sciencedirect.com/science/article/pii/0021892894901376 The gas dynamics systems of equations, with an arbitrary state equation, has an 11-dimensional Lie algebra of symmetries which generates a group…
Algebra and Combinatorics Seminar: Andrew Harder, Lehigh University, The geometry of 2-loop Feynman integrals
SAS 2235Speaker’s webpage: https://math.cas.lehigh.edu/andrew-harder In particle physics, many quantities of interest are expressed in terms of Feynman integrals. These integrals are attached to combinatorial objects called Feynman graphs, and can be expressed as integrals over (infinite) domains inside the real plane. In examples, one often finds that Feynman integrals are equal to special values of functions that…
Differential Equations and Nonlinear Analysis Seminar: Mihaela Ifrim, University of Wisconsin Madison, Global solutions for 1D cubic defocusing dispersive equations: Part I
SAS 4201This article is devoted to a general class of one dimensional NLS problems with a cubic nonlinearity. The question of obtaining scattering, global in time solutions for such problems has attracted a lot of attention in recent years, and many global well-posedness results have been proved for a number of models under the assumption that…
Pure Math Graduate Student Seminar: Kevin Joy, NC State, A Brief Introduction to Affine Schemes
SAS 2102Classically, the primary objects one was concerned with in algebraic geometry were the zero sets of systems of polynomial functions, which we call varieties. Since the work of Grothendieck, the main objects of study in modern algebraic geometry are schemes. In this talk, I will introduce the concept of an affine scheme, a key part…
Applied Math Graduate Student Seminar: Walker Powell, NC State, Model Reduction and Validation Tools for Large-Scale Models
SAS 1220Of primary importance in computational science and applications is quantification and improvement of predictive capabilities of large-scale parameterized models, which often require the use of multi-query techniques that are intractable for computationally expensive models. This research focuses on three primary thrusts: sensitivity analysis, reduced-order modeling, and uncertainty quantification and algorithm and implementation choices that scale favorably…
Numerical Analysis Seminar: Koffi Enakoutsa and Xinghao Dong , UCLA, The Morrey Conjecture: Insights from Numerical Simulations on Quasi-Convexity and Rank-One Convexity.
ZoomThe Morrey Conjecture concerns quasi-convexity and rank-one convexity of functions. While the former implies the latter, it's unclear if the converse is true. Sverak proved the conjecture in 3D, but it remains unresolved in the planar case. Analyzing these properties analytically is difficult, especially for vector-valued functions, hence we perform numerical simulations using example functions…