# Weekly Colloquium

The Department hosts a weekly colloquium on Fridays at 2pm, usually in Southern Hall, room 303. If you would like to present, please contact Dr. Huiqing Zhu with a title and abstract. Please see our tips on abstracts below. You can also find links to previous years' titles and abstracts below.

Date | Presenter, Affiliation | Title, Abstract | |

5 Feb 2016 | Dr. Bernd Schröder, USM |
This talk will give a brief introduction why fixed points are important, why \(L^p\) spaces are important and then proceed to prove that every order-preserving self map of the \(L^p\) unit ball has a fixed point. We will then talk about how this result is applied and how it could be extended. | |

13 Nov 2015 | Dr. Jun Liu, Jackson State University | Iterative One-shot Methods for PDE-Constrained OptimizationThis talk presents new iterative methods for solving the discretized optimality KKT system of PDE-Constrained optimization. The beginning briefly introduces finite difference discretization and multigrid method, as well as Krylov subspace method. Then, semismooth Newton (SSN) method is motivated to handle non-smooth and non-linear PDE constraints. Putting it all together, we obtain several new iterative methods for elliptic-type, parabolic-type and hyperbolic-type PDE constraints. Numerical tests verify our numerical algorithms in terms of the accuracy (of the scheme) and the efficiency (of the solver). | |

6 Nov 2015 | Dr. Satish C. Bhatnagar, UNLV |
From a cursory examination of the history of mathematics, it is clear that these conditions are functions of at least three major factors; namely, political systems, educational models, and organized religions. All three are structured institutions and are reflected in the growth of mathematics as a super organized discipline. The talk will focus on the examples in support and further exploration of these factors. | |

30 Oct 2015 | Dr. John Perry, USM |
Dickson's Lemma states that any subset of the \(n\)-dimensional lattice \(\mathbb N^n\) has a finite set of “minimal” points, where “minimal” is decided componentwise. Aside from its inherent interest, the relationship between the lattice and monomial ideals means that Dickson's Lemma is featured in most textbook proofs of Hilbert's Basis Theorem for polynomial ideals. We show that Dickson's Lemma is equivalent to the statement that a certain combinatorial game must end with a winner, and prove the latter statement, thereby providing a different proof of Dickson's Lemma than the one presented in textbooks. | |

9 Oct 2015 | Dr. Sharon Crook, Arizona State University |
Using Mathematics to Understand the BrainHow does the brain work? What does it do? Mathematical models of neural processes form the basis of computational studies that aim to explain how the brain represents and processes information. These computational models are created with the goal of replicating and explaining observed data in order to obtain a deeper understanding of the dynamics of brain activity. In this presentation, we will look at a few examples of how such models help us understand the nervous system. We also will consider a few of the grand challenges in neuroscience that will require interdisciplinary approaches that bring together experimental neuroscientists, mathematicians, physicists, and computer scientists. | |

2 Oct 2015 | Dr. Jiu Ding, USM |
We shall discuss how to write a good math article, including how to compose the Abstract, Title, Introduction, main body, and Conclusions. We'll also give some tips on References and citations. Finally | |

24 Apr 2015 | Dr. Gopinath Subramanian, USM |
Damage accumulation in rubbery elastomers is a long-timescale problem of interest to many engineering applications. This talk will present a method for computing reaction rates on a Generalized Force-Modified Potential Energy Surface, how these rates relate to damage accumulation, and some (very) preliminary results on the Accelerated Molecular Dynamics of rubbery elastomers. | |

17 Apr 2015 | Dr. Noah Rhee, University of Missouri at Kansas City |
Calculating minimum distance between two celestial bodies orbiting the same star is a difficult task even when computational methods are employed. In this talk we address this problem for the case involving Earth and a coplanar comet, and we offer a detailed discussion of a novel tandem application of two well-known rootfinding methods to solve it. | |

10 Apr 2015 | Jiu Ding, USM |
the world's largest matrix. Finally we give a spectral analysis for rank-\(1\) and more general rank-\(k\) perturbed matrices. | |

27 Mar 2015 | James Lambers, USM |
The aim of this talk is to give an overview of the beautiful mathematical relationships between matrices, moments, orthogonal polynomials, quadrature rules and Krylov subspace methods. The underlying goal is efficient numerical methods for estimating \(I[f]={\mathbf u}^T f(A){\mathbf v}\), where \({\mathbf u}\) and \({\mathbf v}\) are vectors, \(A\) is a symmetric nonsingular matrix, and \(f\) is a smooth function. An obvious application is the computation of | |

20 Mar 2015 | Wonryull Koh, USM |
Stochastic simulation of a reaction-diffusion system enables computational investigation of the system’s spatiotemporal activity and stochastic variations within. Although an exact stochastic simulation that simulates every individual reaction and diffusion event gives a most accurate trajectory of the system’s state over time, it can be too slow for many practical applications. We present algorithms for accelerated stochastic simulation of biochemical reaction-diffusion systems. We present numerical results that illustrate the improvement in simulation speed achieved by our algorithms. We discuss strategies to facilitate adjusting the balance between the degree of exactness in simulation and the simulation speed. | |

13 Feb 2015 | D. L. Young, Taiwan University |
This talk will focus on demonstrating that the Localized Method of Approximated Particular Solutions (LMAPS) is a stable, accurate tool for simulating multidimensional, incompressible viscous flow fields governed by the Navier-Stokes equations. The LMAPS is tested by non-uniform point distribution, extremely narrow rectangular domain, internal flow, velocity or pressure driven flow and high velocity or pressure gradient, etc. All results are similar with results of FEM or other existing literature, and it is concluded that the LMAPS has high potential to be applied to more complicated engineering applications. A further attempt to solve three-dimensional Navier-Stokes equations will be addressed and discussed. | |

30 Jan 2015 | Bernd Schroeder, USM |
This talk will present an inequality that arose in a colleague's analysis of the behavior of micro-air vehicles. We will discuss how a theorist who had stopped doing analysis a decade ago can become involved in such activities. We will specifically focus on some approaches that turned out to not work, because these indicate the challenges that lie ahead for attempts to generalize the inequality or to simplify that presenter's (rather tedious) proof. | |

23 Jan 2015 | Drew Lewis, University of Alabama in Tuscaloosa |
For a ring \(R\), a polynomial \(f \in R[x_1,\ldots,x_n]\) is called a |

## Tips on abstracts

*Dear speaker:* We like to maintain a list of titles, topics, and abstracts, so that we (and you) have a record of who has visited and talked about which topic.

- The topic should be short, similar to the headlines in the AMS subject classifications.
**Please aim for no more than 100 words in your abstract.**We're not fanatically rigorous about this, but an abstract should summarize the essence of a presentation, not give every detail. It’s a sales pitch, not a business plan. Keeping the abstract at 100 words also is a good preparatory step for a concise and informative talk that communicates the salient points of your work.- You may notice that we are MathJax-enabled, so feel free to use \(\mathrm{\LaTeX}\) markup in your abstract when appropriate.