## Colloquium Series

The 2019 Spring colloquia are held according to the posted schedule. The Colloquium Series are open to public and the graduate students are highly recommended to attend.

Organizer: Dr. Xianping Li.

## Spring 2019 Schedule

03/08Jin FengUniversity of Kansas

Date |
Speaker |
Organization |

02/01 | Rylan Sampson | UMKC Math & Stat |

02/08 | Paul Cazeaux | University of Kansas |

03/15 | Jessie Bleile | National Geospatial-Intelligence Agency (NGA) |

03/22 | Justin Munyakazi | University of Western Cape, South Africa |

04/05 | Xing Xia | UMKC Math & Stat |

04/12 | Jin Feng | University of Kansas |

04/26 | Kyle Maddox | University of Missouri-Columbia |

Friday, April 26 , 2019

3:00-4:00PM, Haag Hall 312

**Kyle Maddox**

Department of Mathematics

University of Missouri-Columbia

**Ideals in Prime Characteristic Rings**

**ABSTRACT**

Every ring (commutative with unit) comes equipped with a natural map from the integers. When the kernel of this map is generated by a prime number, the ring has many interesting and deep properties. In this talk, I will define the characteristic of a ring and explore basic properties of the so-called Frobenius map, including how it acts on the set of ideals of the ring. Some basic abstract algebra (the definition of rings, ring maps, and ideals) will be assumed, but otherwise no prerequisites are necessary.

Friday, April 12 , 2019

3:00-4:00PM, Haag Hall 312

**Jin Feng**

Department of Mathematics

University of Kansas

**A Hamilton-Jacobi Theory for Derivations of Hydrodynamic Fluctuations on Nonlinear Heat**

**ABSTRACT**

We outline a Hamilton-Jacobi theory for deriving fluctuation structure of a nonlinear heat equation in hydrodynamic limit. A two scale particle model known as the Carleman model is used to illustrate the ideas. One can view this as an infinite particle version of the known weak KAM (Kolmogorov-Arnold-Moser) theory.

Friday, April 5 , 2019

3:00-4:00PM, Haag Hall 312

**Xing Xia**

Department of Mathematics and Statistics

University of Missouri-Kansas City

**Second-Order Efficiency of Bayes Risk for Estimating Product of 2 Means in Exponential Family**

**ABSTRACT**

Increasing availability of powerful hardware and increasing usability of software have resulted in a world that relies on technology. Powerful and accurate software have led to successes in the medical, industrial, military, academic, and other fields. Inaccurate software, however, can be ruinous or dangerous when that software is used in a safety critical system. Our reliance on software for important outcomes makes it incredibly important to estimate its reliability. We want to estimate reliability of sequential designed procedures with minimum errors, which can help improving software reliability testing as an application. The second-order lower bound of Bayes risk is derived to achieve this goal. In particular, this talk will present the second-order efficiency of the product of two means of independent populations in the Bayesian framework. The trials of samplings are from the one-parameter exponential family, which generalize the result to wider practical applications. We propose and test the derived result in two popular sampling designs: fully sequential sampling design and three-stage sampling design, by using Monte Carlo simulations. The trials of samplings are from Bernoulli distribution which is a demonstration of software reliability testing in application. The second-order efficiency is shown in both sampling schemes.

Friday, March 22 , 2019

3:00-4:00PM, Haag Hall 312

**Justin Munyakazi**

Department of Mathematics and Applied Mathematics

University of Western Cape, South Africa

**A robust finite difference scheme for singularly perturbed systems**

**ABSTRACT**

We present some qualitative properties of the solution to some singularly perturbed systems of differential equations and its derivatives. Then we propose a finite difference method to solve such systems efficiently. Through an error analysis, we prove that the method is uniformly convergent with respect to the perturbation parameters. We implement the method on some test examples to confirm its robustness.

Friday, March 15 , 2019

3:00-4:00PM, Haag Hall 312

**Jessie Bleile**

National Geospatial-Intelligence Agency (NGA)

**The National Geospatial-Intelligence Agency and its role in GPS**

**ABSTRACT**

In this presentation, I will present a brief overview of the National Geospatial-Intelligence Agency (NGA) and its career and internship opportunities. I will then discuss my work as an Orbit Analyst and the role NGA plays in Global Navigation Satellite Systems (GNSS) and specifically the U.S. operated Global Positioning System (GPS). Finally, I will give a talk on how GPS works.

Friday, February 8 , 2019

3:00-4:00PM, Haag Hall 312

**Paul Cazeaux**

Department of Mathematics

University of Kansas

**Relaxation and moiré patterns of incommensurate 2D heterostructures**

**ABSTRACT**

We discuss novel mathematical models for the analysis and computational prediction of mechanical relaxation of two-dimensional layered atomic crystals in the presence of large-scale moiré patterns. The concept of configuration space or hull, previously introduced for the study of transport properties in aperiodic materials by Bellissard et al., is shown to allow for a unified description of continuum as well as atomistic models of elastic relaxation for a wide range of materials in the truly incommensurate (aperiodic) regime.

In the case of twisted bilayers with identical materials, we will present some preliminary analysis and numerical results in the asymptotic regime of small twist angle (inducing a large-scale moiré pattern) and small interlayer Van der Waals forces, in particular the well-known case of graphene/graphene but also MoS2/MoS2.

Friday, February 1 , 2019

3:00-4:00PM, Haag Hall 312

**Rylan Sampson**

Department of Mathematics and Statistics

University of Missouri-Kansas City

**Factorization of triangular matrices over information algebras**

**ABSTRACT**

Given an information algebra, i.e., an antinegative semiring without zero-divisors, we explore factorization in the semiring of upper-triangular matrices with entries in the information algebra. We provide a classification of the atoms of this semiring in terms of both the additive and multiplicative structure of the underlying information algebra. We conclude with results on the maximum and minimum factorization lengths of such matrices, as well as other factorization-theoretic invariants.