# 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.

 Date Presenter, Affiliation Title, Abstract 20 Apr 2018 Noah Rhee, University of Missouri-Kansas City How to compute spectral projectors numericallyFor a given square matrix $$A$$, there are spectral projectors associated with the eigenvalues of $$A$$. The spectral projectors have some important applications. Among them one application is that they can be used to compute $$f(A)$$, if the function fulfills certain smoothness conditions at the eigenvalues of $$A$$. In this talk, we discuss how to compute the spectral projectors of $$A$$ numerically. 6 Apr 2018 (3pm) Vivian Moody On teaching the Chain Rule(no abstract) 6 Apr 2018 (2pm) Suzanne Shontz, University of Kansas Mesh Warping Algorithms for Use in Dynamic Finite Element SimulationsDynamic meshes are used to capture deforming geometry in computational simulations involving motion. Mesh warping algorithms employ interpolation and/or extrapolation to transfer the mesh from the source geometry to the target geometry. Using mesh warping for generating dynamic meshes is advantageous with respect to both accuracy and efficiency. In this talk, I will present our parallel log barrier-based tetrahedral mesh warping algorithm. I will also present our high-order curvilinear tetrahedral mesh generation algorithm which deforms the linear tetrahedral mesh into a high-order mesh. This talk represents joint work with Thap Panitanarak, Chulalongkorn University, and Mike Stees, University of Kansas 23 Mar 2018 Haiyan Tian, USM The method of time integration and approximate fundamental solutions for nonlinear Poisson-type problemsThrough a fictitious time approach, a nonlinear Poisson-type problem is converted into a time-dependent quasilinear problem. This is further approximated by a sequence of time-dependent linear nonhomogeneous modified Helmholtz boundary value problems, which are solved by the method of particular solutions of Delta-shaped basis functions and approximate fundamental solutions. Numerical results are provided to show the accuracy and validity of the computational method. 9 Mar 2018 Shanda Hood, University of Arkansas On teaching the Chain Rule(No abstract) 23 Feb 2018 Douglas Leonard, Auburn University Under-appreciated uses of the extended euclidean algorithmThe extended euclidean algorithm famously gives us $$\gcd(a, b) = am + bn$$. This suffices to produce inverses in finite fields, but the intermediate computations have many uses:They solve the key equation $$c/d = s$$ to find error positions and magnitudes for Reed-Solomon codes.I can reconstruct fractions $$c/d$$ by working modulo one large prime or several small primes. This allows me to lift algorithms I wrote for finite fields to ones that work in characteristic 0 as well.Generalizations to several inputs allow the production of unimodular matrices describing unimodular transformations, that I use for desingularization of surfaces.I’ll give at least one simple example for each topic.

## 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.