If you would like to give a talk, email pp010 at uark dot edu.
Zoom link: https://uark.zoom.us/j/87060910342?pwd=VGFMU25nbDZhQ3JYTFJwajRXd01LZz09
Meeting ID: 870 6091 0342
Passcode: 0j?Uf^ZU
| Date | Speaker | Time | Title |
| 1/27/21 | Minh Nguyen | 2:00 | A discussion about some classic questions in Low dimensional topology |
| 2/3/21 | Patrick Phelps | 4:00 | What function spaces go with the flow of Navier-Stokes? |
| 2/10/21 | Alexander Duncan | 4:00 | Hilbert Polynomials |
| 2/17/21 | Minh Nguyen | 4:00 | A brief introduction to Elliptic operators on manifolds |
| 2/24/21 | Patrick Phelps | 4:00 | Data Assimilation and Determining elements for the Navier-Stokes Equations |
| 3/10/21 | Thuy Scanlon | 2:00 | Monte Carlo Markov Chain Algorithms |
| TBA | Joshua Gregory | 2:00 | TBA (Accessibility, and racial biases in math education) |
| TBA | Will Blair | 4:00 | TBA (Generalized analytic functions) |
| TBA | Thuy Scanlon | 2:00 | Monte Carlo Markov Chain Algorithms (Continuation of previous talk) |
1/27/21
Speaker: Minh Nguyen
Title: A discussion about some classic questions in Low dimensional topology
Abstract: In this expository talk, we shall discuss the two fundamental questions about the topology of 4-manifolds: Is there any compact topological 4-manifold that does not admit any smooth structure? And is there an instance where two compact smooth 4-manifolds are homeomorphic but not diffeomorphic? The goal of this talk is to lay down motivation and background for Seiberg-Witten invariant–a smooth 4-manifold invariant that is derived from the analysis of a system of two non-linear PDEs. This area of research is a meeting point for analysis, topology, and geometry.
Access Passcode: uY.k1^pq
2/3/21
Speaker: Patrick Phelps
Title: What function spaces go with the flow of Navier-Stokes?
Abstract:
In this talk we will explore function spaces that serve as good sources of initial data for the Navier-Stokes, we well as spaces where it can be desirable for a solution to live. Certain data spaces can guarantee well-posedness, uniqueness, and regularity, as well as permit energy methods or other techniques to analyze our solution. Spaces where short time strong existence is known include the Homogenous Sobolev Space, Lebesgue Spaces, Weighted L^p spaces, weak L^3, and Morrey Spaces. Let’s see what makes them flow!
Access Passcode: Rzxd3v4^
2/10/2021
Speaker: Alexander Duncan
Title: Hilbert Polynomials
Abstract: Studying the Hilbert polynomial for a finitely generated graded module over the ring S = k[x_0, …, x_n] is a classical problem in both commutative algebra and algebraic geometry. In this talk, we will discuss how free resolutions give rise to Hilbert polynomials and then discuss applications and techniques for calculating these polynomials including an algorithm for generating graded free resolutions of S-modules using simplicial complexes. Betti tables will also be discussed.
Access Passcode: 7m=C2+.u
2/17/2021
Speaker: Minh Nguyen
Title: A brief introduction to Elliptic operators on manifolds
Abstract: This is a sequel to our previous talk. The ultimate goal is to understand the applications of Seiberg-Witten equations in low dimensional topology. For us to achieve such goal, it is necessary to familiarize ourselves with the language of analysis on smooth manifolds. In this talk, we shall introduce some of the prerequisite background pertaining to the notion of covariant derivatives (connections) associated to a vector bundle, (pseudo-)differential operators, Sobolev spaces of sections, and finally (if we have time) elliptic theory of operators. The area of global analysis is vast; but we mainly provide an overview of the subject with a motivation to understand Seiberg-Witten theory.
Access Passcode: $jVze1RF
Date: 2/24/2021
Speaker: Patrick Phelps
Title: Data Assimilation and Determining elements for the Navier-Stokes Equations
Abstract: A determining element for dissipative dynamical system is one which, if known to converge to zero for two solutions, implies they are identical. In 2-dimensions the Navier-Stokes have been shown to have a finite number of determining modes, nodes, and volume elements. Because global well-posedness is known for 2D, we may use continuous data assimilation to create approximating solutions from any type of measurement data for which an interpolation operator exists (including modes, nodes, and volume elements). This talk aims to define these determining data parameters, and give an introduction to interpolation operators through the lens of Navier-Stokes.
Date: TBA
Speaker: William Blair
Title: TBA (Generalized Analytic Functions)
Abstract:
Date: 3/10/2021
Speaker: Thuy Scanlon
Title: Monte Carlo Markov Chain Algorithms
Abstract: The goal of data modeling is to make predictions and inferences about parameters based on available sample data. This concept matches naturally with Bayesian statistics, which allows prior knowledge incorporated into the hierarchical models. Much of the statistical summaries about a distribution can be estimated if one can sample from that distribution. However, the result posterior distributions of Bayesian hierarchical models are often difficult or even impossible to sample directly from. Monte Carlo Markov Chain is the most efficient and reliable sampling method in these settings.
Access Passcode: %XdW^j3Q
Graduate Student Mathematics Colloquium 