# 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 23 Feb 2018 Douglas Leonard, Auburn 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.